Value Driven Product Planning and Systems Engineering

Value Driven Product Planning and Systems Engineering H.E. Cook and L.A. Wissmann Value Driven Product Planning and ...

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Value Driven Product Planning and Systems Engineering

H.E. Cook and L.A. Wissmann


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H.E. Cook, PhD Professor Emeritus Department of Industrial and Enterprise Systems Engineering (IESE) College of Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 USA

L.A. Wissmann Product and Process Quality Specialist Hamilton Sundstrand Windsor Locks, CT 06096-1010 USA

ISBN: 978-1-84628-964-4

e-ISBN: 978-1-84628-965-1

British Library Cataloguing in Publication Data Cook, H. E. (Harry E.) Value driven product planning and systems engineering 1. New products - Planning 2. Value analysis (Cost control) I. Title II. Wissmann, L. A. 658.5'038 ISBN-13: 9781846289644 Library of Congress Control Number: 2007931879 © 2007 Springer-Verlag London Limited Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com

To Valle and Juliana

Preface

Engineers and scientists often need to sell an innovative idea for a new product or a new product improvement to top management. Sometimes their tendency is to focus on the “WOW!” of the new technology at the expense of making a convincing business case. When the new technology represents a large cost reduction, there will be much less of a problem in convincing management to approve the project if the investment level is acceptable. The major rub comes when the new feature or technology is an improvement in customer value that also generates an increase in cost. This makes the sell difficult in spite of the fact that many of the inventive products available today are widely used because they provide very high value in relation to their added cost. For example, the laptop computer is infinitely more versatile than the inexpensive slide rule or abacus. Disc brakes are far superior to less costly drum brakes and radial tires are superior to bias-belted. The modern automobile itself is far superior to the horse and buggy for general transportation. Commercial aircraft provide value well beyond that for ocean liners for people who have limited time for travel. The list, of course, is almost endless but unfortunately, that does not make selling improved value any easier when costs are also increased. Because any change involves risk, getting the approval to develop and implement a new technology is far from certain because decision makers may not have confidence in the analysis methodology supporting the proposal if it appears ad hoc. Nevertheless, engineers and scientists are expected by management to come up with innovative ideas that make it to the marketplace so they need to have a wellgrounded, convincing methodology for selling the value improvement and profitability of their proposals. Many engineers and scientists also occupy product planning and systems engineering positions as decision makers who review and select ideas for improving value and profits that come from others inside and outside the company. Thus, as buyers, they also need a methodology for accurately evaluating the financial impact of new features and technologies while anticipating what their major competitors are likely to do to improve their next generation of product. These problems are exacerbated in today’s global economy because the number of competitors has increased markedly in many product segments and there are

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Preface

many technological alternatives available for consideration. The problem of anticipating the moves of your major competitor is particularly challenging because most firms keep their plans very secure. As a result, the engineer or scientist as product planner must learn to think like its major competitor using customer value as a guide. The objective of this book is to support engineers and scientists in assessing the likely business case for new, innovative product concepts and product improvements. We have tried to strike the right balance between rigor and simplicity. Rigor is compromised if product planning is based solely on the gut feel of a top executive. For example, when the Ford Taurus hit the marketplace in the mid 1980s, the CEO of a major competitor privately observed that the “potato shape” would never catch on; which means that it would not have seen the light of day in his company. Of course, the Taurus was the most successful car released by Ford in the last twenty years. However, a deep, protracted analysis that crosses all of the t’s and dots all of the i’s leads to products that are late to market. The view here is that the use of simple but quantitative tools, which allow a wider range of options to be considered relatively quickly, can be catalytic in bringing fresh, exciting products to market. The tools do not have to be perfect. Only better than what is being used and capable of improvements based upon feedback and learning from prior applications. There is also an important role for intuition in the early stages of product planning and this book describes a methodology for quantifying it for initiating the planning process. Top executives are encouraged to use it to quantify their intuition or gut feel. The book may also appeal to marketing research specialists as it includes methods and viewpoints, which may be unfamiliar to them. For example, in spite of its simplicity, the linear demand model is shown to provide both qualitative and quantitative insight into pricing and forecasting demand. Moreover, the connection between the linear and logit models is used to show that the price coefficient in the utility expression is different if demand floats as in a real market or is fixed as in certain surveys. The Direct Value survey method, which has been developed in the engineering literature, is covered here in some detail because its simplicity minimizes cognitive stress on respondents and provides a straightforward means for assessing customer value. The book is divided into four descriptive chapters, twelve case studies, and six appendices. Chapter 1 focuses on understanding customer value and its influence on price, demand, and profit. Chapter 2 describes the methods used to assess value and to construct surveys for accurately measuring value. Chapter 3 shows how to compute value and its statistical properties from survey results using spreadsheet programs without the need for special software. The spreadsheet expressions used in the computations are included as part of most tables. This facilitates the use of the material as a textbook supporting a course on customer value, which could be offered to students who have had an introductory course in statistics. Chapter 4 is a simulated product planning exercise for the redesign of an automobile, which demonstrates the use of the tools and methods developed. The case studies analyze

Preface

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and solve a variety of product planning problems using the methods developed and the spreadsheet templates downloaded from the publisher’s webpage.1 The expressions that show how value influences demand and price are presented in Appendix A. The methods for developing and classifying value curves for continuous attributes are developed in Appendix B. Value curves are mirror images of Taguchi’s curves for the cost of inferior quality and they have been incorporated into design of experiments at the system level.2 A key outcome is that the concept of robustness can now be imbedded formally into system design and linked in a seamless manner to Taguchi’s robust methods for component design. Product planners are encouraged to combine intuition and information from human factor studies to make rough, initial assessments of value curves. The results are then used to develop the formal survey needed to make a more accurate assessment of value. Appendix C describes how to use the spreadsheet templates to analyze the value of individual product attributes from the responses to a survey and how to determine the total value of each of the products competing in a market segment from their demand and price trends. Templates are also provided for estimating the variable costs of competing products and for computing the change in value when automotive attributes are changed. Appendix D shows how to use the results from a classical conjoint analysis survey to arrive at a measure of customer value in a more accurate and meaningful manner than given by classical part worth analysis. Appendix E demonstrates the special considerations that need to be made when analyzing the results from a presence/absence survey because of the number of choices not being constant from one choice set to the next. This problem, to our knowledge, has not been addressed before. Appendix F describes the use of orthogonal arrays (OAs) in designing surveys H. E. Cook L. A. Wissmann

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http://www.springer.com/978-1-84628-964-4 Cook HE (2005) Design for six sigma as strategic experimentation. ASQ Quality Press, Milwaukee, WI

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Acknowledgements

Important ideas and methods included in the book were generated by graduate students at the University of Illinois at Urbana-Champaign including Shandon Alderson, Hussein Ali, Curtis Busch, Elizabeth Cowen, Edwin Dair, Joe Donndelinger, Andy Elsbury, Joshua Freeman, Mike Gill, David Herington, Prakash Kolli, Mike Lee, Greg McConville, Eric Monroe, Terrence Mosely, Matthew Neidlinger, Mike Pozar, Mark Rimkus, John Runnion, Johann Schaser, Torsten Schildt, Orlando Sellers, Becky Silver, Mark Simek, Carlos Suarez, Kimberly Williams, Luke Wissmann (co-author), Anthony Woods, Andrew Wu, and Roberto Zavala. We are indebted to the research sponsorship provided by five US industrial firms. A special “Thank you!” goes to Andrew Porter, the artist for Figure 1.5. We also deeply appreciate the strong support from Anthony Doyle and Simon Rees at Springer-Verlag and Angela Böhl and Sorina Moosdorf at LE-TeX. Finally, we acknowledge the very helpful critique from three anonymous reviewers.

Contents

1 Customer Value: A Key Financial Metric ...................................................... 1 1.1 Financial Metrics: Bottom-line and Fundamental................................ 1 1.2 Quantifying Value................................................................................ 3 1.3 The Impact of Customer Value............................................................ 4 1.3.1 Fly Me to the Moon ............................................................... 4 1.3.2 Shifting the Demand Curve by Improving Value .................. 6 1.3.3 Does Profit Maximization Gouge the Customer.................... 7 1.3.4 The Innovative Power of a New Technology ........................ 9 1.4 Market dilution .................................................................................... 9 1.4.1 Loss of Pricing Power ........................................................... 9 1.4.2 US Automotive Market ....................................................... 10 1.5 Check of Demand Model ................................................................... 11 1.6 Research and Development Planning ................................................ 14 1.7 Summary ....................................................................................... 14 1.8 Supporting Case Studies .................................................................... 15 1.9 Exercises ....................................................................................... 15 1.10 References ....................................................................................... 16 2 Assessing Value using Surveys....................................................................... 17 2.1 Background ....................................................................................... 17 2.2 Value and Value Functions................................................................ 18 2.3 Causal Research of Value .................................................................. 20 2.4 Survey Project Design and Execution................................................ 21 2.4.1 Stage 1: Determine Objectives ............................................ 22 2.4.2 Stage 2: Respondent Selection............................................. 22 2.4.3 Stage 3: Methodology for Administering Survey................ 25 2.4.4 Stage 4: Questionnaire Design............................................. 26 2.4.5 Stage 5: Pretest Survey ........................................................ 27 2.4.6 Stage 6: Collect Data ........................................................... 27 2.4.7 Stage 7: Data Preparation and Analysis............................... 28 2.5 Summary ....................................................................................... 28

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2.6 Supporting Case Studies .................................................................... 29 2.7 Exercises ....................................................................................... 29 2.8 References ....................................................................................... 30 3 Analyzing Stated Choice Surveys .................................................................. 33 3.1 Background: Prospect Theory............................................................ 33 3.2 The Direct Value Stated Choice Survey ............................................ 34 3.2.1 Graphical Analysis of a DV Survey .................................... 35 3.2.2 Level 2 OLS Regression Analysis of a DV Survey ............. 36 3.2.3 Computing Standard Deviation and df of Value in a DV Survey ....................................................................................... 42 3.2.4 LOF Estimate of the Standard Deviation of Value .............. 45 3.3 The Multinomial Stated Choice Survey............................................. 45 3.4 Maximum Log Likelihood Estimate .................................................. 49 3.5 Summary ....................................................................................... 52 3.6 Supporting Case Studies ................................................................... 52 3.7 Exercises ....................................................................................... 53 3.8 References ....................................................................................... 58 4 Product Planning and Systems Engineering ................................................ 59 4.1 Nature of a System............................................................................. 59 4.2 Transitioning to Total Virtual Design and Development................... 61 4.3 Analyzing the As-Is/To-Be Transition using an Automotive Example ....................................................................................... 65 4.3.1 As-Is .................................................................................... 65 4.3.2 To-Be................................................................................... 66 4.3.3 Learning............................................................................... 75 4.3.4 Robustness to All Types of Variation.................................. 77 4.3.5 Sourcing New Technology .................................................. 78 4.4 Summary ....................................................................................... 81 4.5 Supporting Case Studies .................................................................... 81 4.6 Exercises ....................................................................................... 81 4.7 References ....................................................................................... 83 Case Study 1 Value Speculation in a Stock’s Price......................................... 85 CS1.1 Buyers and Sellers......................................................................... 85 CS1.2 Demand for a Speculative Stock ................................................... 86 CS1.3 Gold Mining Stock Example......................................................... 87 CS1.4 Summary....................................................................................... 87 CS1.5 References..................................................................................... 90 Case Study 2 Simulated Survey of Boston to Los Angeles Flights ................ 91 CS2.1 Experimental Design..................................................................... 91 CS2.2 OLS Solution with Satterthwaite’s df and Approximate t-Test .... 93 CS2.3 Solution using Maximum Log Likelihood Estimate ..................... 94 CS2.4 Summary....................................................................................... 95 CS2.5 References..................................................................................... 96

Contents

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Case Study 3 Analysis of a Multinomial Stated Choice Survey..................... 97 CS3.1 A Simulated Multinomial Survey ................................................. 97 CS3.2 Simulation Process........................................................................ 98 CS3.3 The Level 2 OLS Coefficients .................................................... 100 CS3.4 Summary..................................................................................... 100 Case Study 4 The Market for Hybrid and Diesel Mid-sized Sedans ........... 103 CS4.1 Prior Studies................................................................................ 103 CS4.2 This Study ................................................................................... 105 CS4.2.1 Comparing Individual NPV Forecasts with Survey Results ............................................................................ 105 CS4.2.2 Reference Price for Options.......................................... 105 CS4.2.3 Forecasts of Long Term Share of Three Competing Powerplants ................................................................................ 107 CS4.3 Summary..................................................................................... 109 CS4.4 References................................................................................... 109 Case Study 5 Revealed Values: Minivan Trends .......................................... 111 CS5.1 Consumers Reveal Preferences when They Buy......................... 111 CS5.2 Minivan Revealed Value Trends 1998 through 2002 Model Years ..................................................................................... 111 CS5.2.1 Ford Windstar ............................................................... 111 CS5.2.2 Honda Odyssey............................................................. 112 CS5.3 Learning by Comparing Forecast Value Improvements with Actual Improvements..................................................................... 113 CS5.4 Summary..................................................................................... 113 CS5.5 References................................................................................... 114 Case Study 6 Effect of Market Dilution when Value Differs between Competitors.......................................................................................... 115 CS6.1 Competing Products Differ in Value........................................... 115 CS6.2 Price Trends ................................................................................ 116 CS6.3 Attackers’ Advantage.................................................................. 116 CS6.4 Summary..................................................................................... 118 Case Study 7 Value of Interior Noise in a Luxury Automobile ................... 119 CS7.1 DV Survey .................................................................................. 119 CS7.2 Level 2 OLS Coefficients ........................................................... 120 CS7.3 Exponentially Weighted Parabolic Model .................................. 122 CS7.4 Prospect Theory Model............................................................... 124 CS7.5 Comparing the Two Models ....................................................... 124 CS7.6 Summary..................................................................................... 125 CS7.7 References................................................................................... 125 Case Study 8 Quantifying the Trade-off between Acceleration Performance and Fuel Economy ....................................................................... 127 CS8.1 A Key Auto Trade-off................................................................. 127

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CS8.2 Experimental Design................................................................... 128 CS8.3 Values of Attributes Relative to Vehicle at 22 mpg.................... 129 CS8.4 Exponential Weighting Coefficient for Acceleration Performance ..................................................................................... 130 CS8.5 Time Horizon and Discount Rate for Fuel Economy.................. 131 CS8.6 References................................................................................... 132 Case Study 9 Value of Mustang Options ....................................................... 133 CS9.1 Survey of Mustang Owners......................................................... 133 CS9.2 Automatic Transmission Option ................................................. 134 CS9.3 Anti-lock Brake Option............................................................... 135 CS9.4 Option Price Elasticities.............................................................. 135 CS9.5 Summary..................................................................................... 136 CS9.6 References................................................................................... 139 Case Study 10 Simulated Survey of Choice between Auto and Transit Bus Modes ...................................................................................... 141 CS10.1 Maximum Log Likelihood Solution.......................................... 141 CS10.2 LOF Workaround Solution ....................................................... 144 CS10.3 Summary ................................................................................... 147 CS10.4 References................................................................................. 147 Case Study 11 Assessing Relative Brand Value .............................................. 149 CS11.1 Survey Method.......................................................................... 149 CS11.2 Outcomes .................................................................................. 149 CS11.3 Summary ................................................................................... 150 CS11.4 References................................................................................. 152 Case Study 12 Value and Cost Benchmarking a Yogurt Market.................. 153 CS12.1 Value and Cost Benchmarking.................................................. 153 CS12.2 Cost Estimation......................................................................... 154 CS12.3 Yogurt Case Study .................................................................... 155 CS12.4 Summary ................................................................................... 157 CS12.5 References................................................................................. 157 Appendix A Models of Demand Price, and Choice Probability................. 159 A.1 The Linear Demand Model ............................................................. 159 A.2 The Logit Model ............................................................................. 163 A.3 Connection to the Probit (Normal) Model ...................................... 165 A.4 References ..................................................................................... 166 Appendix B Modeling Value using Automotive Examples ........................ 167 B.1 Nature of Attributes......................................................................... 167 B.2 Empirical Model for Value Curves ................................................. 168 B.3 Estimating Value Curves................................................................. 169 B.4 Multiattribute Value ........................................................................ 169 B.5 Values of Selective Automotive Attributes..................................... 170

Contents xvii

B.5.1 Fuel Economy ................................................................... 171 B5.2 Front Leg Room................................................................. 171 B.5.3 Interior Noise .................................................................... 173 B.5.4 Reliability.......................................................................... 173 B5.5 Range ................................................................................. 173 B5.6 Acceleration Performance.................................................. 174 B.5.7 Shoulder Room ................................................................. 174 B5.8 Head Room ........................................................................ 175 B.5.9 Seating Capacity ............................................................... 177 B5.10 Luggage Space ................................................................. 177 B5.11 Turning Radius................................................................. 177 B.6 References ..................................................................................... 178 Appendix C Templates ................................................................................. 179 C.1 Overview ..................................................................................... 179 C.2 Templates for the Direct Value Stated Choice Survey.................... 179 C.3 Templates for Multinomial Stated Choice Surveys......................... 180 C.4 DV 3 Binary Template Example ..................................................... 181 C.4.1 Level 2 OLS Outcomes..................................................... 182 C.4.2 LOF Outcomes.................................................................. 183 C.4.3 MLLE Outcomes .............................................................. 185 C.4.4 Outcomes Summary and Logit Plot .................................. 185 C.5 Additional Templates ...................................................................... 186 C.5.1 Value Trend and Cournot Cost Templates........................ 186 C.5.2 Value of Automotive CTV Template................................ 188 Appendix D Stated Choice Analysis of a Classical Conjoint Survey ......... 189 D.1 Classical Conjoint Survey............................................................... 189 D.2 Theory versus Experiment .............................................................. 192 D.3 References ..................................................................................... 195 Appendix E Analysis of a Presence/Absence Stated Choice Survey.......... 197 E.1 Simulated Survey ............................................................................ 197 E.2 Analysis of Outcomes ..................................................................... 199 E.3 References ..................................................................................... 203 Appendix F Using Orthogonal Arrays to Construct Stated Choice Survey and other Experimental Designs.................................. 205 F.1 Taguchi and Konishi Notation......................................................... 205 F.2 Analysis of Simulated Multinomial Design..................................... 207 F.3 References ..................................................................................... 208 Index

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1 Customer Value: A Key Financial Metric

Synopsis Two types of financial metrics are examined, fundamental and bottom-line. The classic bottom-line metrics of demand, price, and profit are determined by the fundamental metrics of value to the customer, cost, and the pace of innovation. Special attention is given to value because in our experience it is the least understood fundamental metric. Although value is highly subjective, it can be assessed in dollars in a straightforward manner and used in setting price and forecasting demand. For example, the optimal price for a good sold by a monopoly is simply the sum of its value and cost, divided by two. If value or cost increases by $10, the monopolist should increase price by only $5. Pricing power is greatly reduced when competitors enter the market. Graphs based upon the classic Cournot model show that price falls dramatically as the number of competitors increase, this being painfully obvious to anyone who has experienced market dilution as a result of the addition of new, viable competitors. A new metric that measures the innovative power of an advanced technology is introduced to aid the setting of research and development priorities.

1.1 Financial Metrics: Bottom-line and Fundamental The “bottom-line” metrics of cash flow, demand, price, and return on investment are driven by a second set of financial metrics represented by value to the customer, cost, and the pace of innovation. Get them right relative to competition and impressive bottom-line results should follow. Because of their importance, we call value to the customer, variable cost, and the pace of innovation the “fundamental metrics.” Most of us have heard them expressed as “better, cheaper, and faster,” today’s mantra for surviving in the highly competitive global

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marketplace. Customer value is the measure of better; variable cost is the measure of cheaper; and the pace of innovation is the measure of faster.1 Cost estimating is a well-developed skill in most firms. Relocating manufacturing operations to low wage locations is a major means of reducing costs today. The traditional ways of using existing components wherever possible, and reducing overall design complexity, of course, still apply. The methods for improving the pace of innovation or speed are also wellknown: increase the use of simulation software versus prototype hardware for developing new designs, reduce the layers of management to speed decision making, and increase the use of teams that cut across design, engineering, manufacturing, marketing, service, and finance. Finally, it is necessary to have strong-willed, knowledgeable, and persistent champions leading new product development teams within a disciplined innovation process (Carlson and Wilmot, 2006). Our experience is that value is poorly understood relative to cost and speed. Some of the ignorance comes from the belief that the highly subjective nature of value prevents it from being quantified. But this is simply not correct and there are several excellent books on value that look at it from different perspectives thereby providing both quantitative and qualitative insight and understanding. The classic book by Ben-Akiva and Lerman (1985) takes the reader through a rigorous development of the mathematical foundations for assessing value using discrete choice analysis. The more recent book by Louviere, Hensher, and Swait (2000) includes the major developments since 1985 and explores the elements of stated choice surveys in detail and depth. More descriptive books stress the strategic side of customer value while minimizing the mathematical development. These include the books by DeBonis, et. al. (2002), Gale (1994), Kordupleski and Simpson (2003), and Pardee (1996). The recent book by Carlson and Wilmot (2006) emphasizes the importance of customer value in driving the innovative process. The authors stress the need to generate a quantifiable “value proposition” as a key element in successfully selling a new product concept to a firm’s management or to a venture capitalist. Kim and Mauborgne (2005) have emphasized the need for discovering value opportunities in new market spaces where competition is non-existent, at least initially. This book strikes a balance between simplicity and rigor using a four step process: Step one: Use of the simple but insightful linear demand model to introduce the concept of value and to show clearly how price is related to value, cost, and the number of competitors. Step two: Use of surveys for assessing value that are easy for respondents to complete with minimal cognitive stress. Such surveys are also easy to design. The analysis of the outcomes for value is straightforward using the logit model in its simplest form.

1

For simplicity in what follows, we will use the word “value” to mean customer value and “cost” to mean variable cost.

Customer Value: A Key Financial Metric

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Step three: Use of aggregate value assessments based upon all survey responses. But value, if necessary, can also be disaggregated along demographic lines such as gender, age, income, education, geographical location, ethnicity, and lifestyle to provide additional insight. Step four: Use of analysis and statistical tools for assessing value that can be automated using a spreadsheet program without the need of special software.

1.2 Quantifying Value So how do you go about quantifying something as subjective as value? Fortunately, for many product planning problems, you only need to discover how value changes when one or more attributes of the product are modified.2 The process for measuring a value change starts by documenting how demand for an existing product changes with value and price. The relationships can be understood best by considering the demand D for a product sold by a monopoly: D = K (V − P )

(1.1)

In this expression, K is an empirical constant, V is value, and P is the price of the product. It follows from Equation (1.1) that the change in demand is a function of the changes in value and price:

δ D = K (δ V − δ P)

(1.2)

Thus, if price is changed by δ P and value is not changed, then demand D changes by δ D ' = − K δ P . If the firm holds price fixed but changes a Critical-To-Value (CTV) product attribute g by δ g ,3 this causes product demand to change by δ D '' . Since δ P is zero, we see from Equation (1.2) that the value change δ V due to the change in the attribute is exactly δ D ''/ K dollars. Now assume that the CTV attribute is changed by an amount δ g * and that price is carefully tweaked by an amount δ P * such that demand does not change. It follows from Equation (1.2) that the value change, δ V * , is exactly equal to the price change, δ V * = δ P * , and independent of the empirical coefficient K . This property is very important because it shows that the value change for a product

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Occasionally, however, we do want to know the total value of a product which can be estimated using linear demand theory from the prices and demands within a given market segment. 3 For example, CTV attributes of a laptop computer include its weight, time to boot up, speed of computation, and keyboard feel. The CTV attributes of an automobile include its exterior and interior style, acceleration performance, interior noise level, fuel economy, and range.

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improvement can be estimated by setting it equal to the price increment that leaves demand unchanged. This price increment can be determined using a survey designed specifically for this purpose (Donndelinger and Cook, 1997).

1.3 The Impact of Customer Value 1.3.1 Fly Me to the Moon

To explore the relationship of value to demand, price, and profits in more depth, let’s consider a fictitious company that is planning to offer flights to the moon. The company, which will initially enjoy a monopoly for this route, has made many prove-out flights to the moon without incident so the trip is deemed safe. The company has invested $70,000,000 in the venture and is now wrestling with how to price the ticket, which will guarantee a buyer a seat on one of the flights within the next two years. After this period, the company’s monopoly ends and several competitors are expected to enter the market. If the ticket price was $100, you might jump at the opportunity but if priced at $10,000 you might not. Somewhere within this range there is a price, let’s say $4,000, which you would grudgingly pay for the trip. Although the value of the ticket to you would be your limit price of $4,000, this will not necessarily be the asking price for the ticket. The reason is that the seller must set a single price for a group of buyers who value the trip differently. This is the classic pricing problem for a mass produced good sold by a monopoly. The targeted demographic group for the trip consisted of 100,000 individuals having ages, incomes, education levels, and spirited lifestyles similar to yours. A sample of 2000 from this group were randomly selected and asked about their willingness to pay for a round trip moon flight over a range of prices. Their simulated responses are shown as the fractional demand function versus price in Figure 1.1. At a price of $0 all respondents said that they would purchase a ticket. However, no one in the sample said they would purchase a ticket if it was priced over $5000. Thus, the demand function is seen adequately described by Equation (1.1) with a single, aggregate value V equal to $5,000, which is also called the market reservation price or choke price.4 The company can use the demand information in Figure 1.1 to develop the optimal ticket price as follows. First, the company must determine if the total available flight capacity over the next two years is a limiting constraint. If capacity were only 20,000 passengers, which is 20% of the segment, the optimal price would be $4,000, which can be read directly from Figure 1.1 because it is the

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The question is begged as to how serious the survey results for value should be accepted. The empirical record according to Louviere, et. al. (2000, p. 21) is very supportive of the findings from stated choice surveys. As surveys reveal both the mean and standard deviation of value, the conservative approach is to take value as equal to the mean less two standard deviations.


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largest price that will yield 20,000 customers. However, since the total flight capacity is actually 100,000 (100 flights can be made over two years with each flight having 1000 seats), the total flight capacity is not a limiting constraint.

1 0.9 0.8

Demand fraction

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 $0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

Price

Figure 1.1. Simulated demand versus ticket price for a flight to the moon

Next, the company needs to consider how price affects gross revenue which is equal to the number of passengers times the price they are willing to pay resulting in the parabolic form shown in Figure 1.2. The optimal price for maximizing gross revenue is seen to be $2,500, which is equal to (V + C ) / 2 . The variable cost C per passenger is zero here as the overall cost of a trip is fixed and independent of the number of passengers. Note that the price of $2,500 is well below the tickets’ value of $5,000! At the optimal price, we see from Figure 1.1 that the company can expect to have 50,000 passengers (0.5 × 100,000) over the next two years. Thus, it will need to schedule only 50 flights and each should be full with 1000 passengers, thereby generating gross revenues of $2,500,000 per flight. This amount is twice the maximum shown in Figure 1.2 because if 100 flights were scheduled they would only be half-full at the optimal price. The company has estimated that the operational cost per trip is $500,000 and independent of the number of passengers. Thus, over the two year period, net revenue should be $100,000,000, which exceeds the amount invested by $30,000,000.

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$1,400,000

Gross revenue

$1,200,000 $1,000,000 $800,000 $600,000 $400,000 $200,000 $0 $0

$1,000 $2,000 $3,000 $4,000 $5,000 Price

Figure 1.2. Gross revenue per flight as a function of ticket price

In this example, value was viewed in two different ways, one being the limiting price at the individual’s level and the other being the limiting price at the aggregate level for a well-defined, demographic segment. Both viewpoints are useful. If a company could fully customize and price its product for any given customer, then the individual view is appropriate. Custom built homes are a good example. But most mass-produced products and services are aimed at a demographic segment and carry a single, base price and feature set. However, optional features are often available, which can be purchased to provide a degree of individual customization. 1.3.2 Shifting the Demand Curve by Improving Value

Two linear demand curves are shown in Figure 1.3 for a monopoly. The dashed line is the new demand function, which has been shifted because of an improvement in product value. The parameter K is equal to 2 units per year per $ for both and it can be assumed to be unchanged if the shift in value is not too large. Value is $10 for the solid line and $14 for the dashed line. The $4 in added value shifted the demand curve positively by $4. Demand goes to zero as price approaches value because buyers gain nothing in paying $10 or $14 to get $10 or $14, respectively, in value. The added variable cost is assumed to be $1.


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30

Demand

25 20 15 10 5 0 0

5

10

15

Price

Figure 1.3. A change in value shifts the demand curve

The annual cash flow, A , shown in Figure 1.4 for each of the two demand curves in Figure 1.3 was computed using: A = D[P - C] − F − M

(1.3)

In Equation (1.3), the terms F and M are the annual fixed costs and investment, respectively. The cash flows in Figure 1.4 are again parabolic having a maximum at a price half-way between cost and value. Fixed cost and investment were assumed zero for simplicity. A large cash flow increase occurs because the $4 in added value versus the $1 in added cost generated an increase in both price and demand. 1.3.3 Does Profit Maximization Gouge the Customer?

Profit maximization may suggest that the customer is being unfairly treated. To explore this point of view, consider the transaction in Figure 1.5. The largest price the buyer will pay is the value of the product, V , and the smallest price that a seller will likely consider is the variable cost, C . When a buyer and seller have equal bargaining power, they should receive the same net value for a transaction in that the net value to the seller given by P − C should equal the net value to the buyer given by V − P . When the two net values are equated, the price they jointly arrive at is one-half value plus cost. This is the same expression for price that optimized revenue for the monopoly in Figure 1.2. If we extend this analogy to a monopoly selling products to a consumer group, the monopoly is simply sharing

8


Cash flow

equally with its customers the net value created much like the outcome in Figure 1.5. Thus, profit maximizing monopolists are not the devils sometimes depicted. The rest of society in Figure 1.5 is also a concerned participant in the transaction as a result of the cost of externalities, G, which is almost always negative due to the environmental impact of the manufacture, use, and disposal of the product. 45 40 35 30 25 20 15 10 5 0 0

2

4

6

8

10

12

14

16

Price

Figure 1.4. Cash flows for the linear demand curves in Figure 1.1 are parabolic

Rest of Society: G

Buyer: V - P

Seller: P - C

Figure 1.5. Schematic of net value changes for a simple transaction. (Redrawn from Source: Cook HE (1997) Product Management, Kluwer Academic, Figure 2.16, p. 44, © 1997, with kind permission Springer Science and Business Media.)

It has been suggested that a monopolist should price below the level that generates maximum revenue as this will limit competitors from entering the market. (See, for example, Kim and Mauborgne, 2005, p. 213). But this does not assure that competitors will not enter the market at a later time. Moreover, when the


9

monopolist lowers price, it reduces revenues available for new product development and encourages an increase in capacity to meet the added demand. Thus, when competitors do enter the market, the original monopolist is saddled with additional excess capacity for a product that has likely not grown much in value. An alternate strategy is for the monopolist to maintain the optimal price, plough substantial resources into innovative research and development, and incorporate the fruits of those activities in its product in a timely manner. This causes its product to grow continuously higher in value and lower in costs, making all would-be competitors think long and hard about entering its market. 1.3.4 The Innovative Power of a New Technology

The Innovative Power (IP) of a new technology measures the rate at which net value is being generated during development. It is equal to the added value δ V less the added cost δ C divided by the development time tD needed to go from concept to production: IP ≡

δV − δ C tD

(1.4)

The pace of innovation is defined as 1/ t D . If development time increases, the pace slows. Consider the addition of the second rear sliding door to the Dodge minivan in the 1997 model year, which added $1,250 in value based upon a national survey conducted jointly by Wu (1998) and Lee (1998). Assume that its added variable cost was $100 and its development time took 36 months. With these quantities, the innovative power per vehicle of this new feature was $32 per vehicle per month of development.5 In isolation, the $32 per vehicle per month does not convey much information. However, it becomes very meaningful when ranked against other possible advanced research and development projects. A key competitive aspect of the second sliding door was that it represented a feature that a competitor could not duplicate without either making a costly tear-up of its current design or waiting until its next major redesign to make the change.

1.4 Market Dilution 1.4.1 Loss of Pricing Power

When competitors enter the market, the loss of pricing power of the original monopolist gives a solid edge in the net value for a transaction to the customer.

5

A full accounting of added value must include the impact of the technology on the environment, representing the externalities.

10


Moreover, total demand becomes shared between the N competitors. If, for simplicity, all of the competing products are assumed to have the same price, value, and cost, the market share for each firm would be 1/ N and price (in theory) for each will approach cost as the number of competitors becomes very large. Of course N never becomes too large because, as the market dynamics evolve, some competitors fail along the way due to the inability to cover their fixed costs and/or debt burden. Some laggards are swallowed up by their competitors through mergers and acquisitions. These consequences are displayed by the model computations shown in Figures 1.6 through 1.9.6 Price drops approximately 17% in going from the monopoly to the duopoly. In regard to this nominal result, a major electronics company has stated in a personal communication that their products enjoy a 20% pricing advantage when they are first to market. Although demand per competitor decreases in Figure 1.7, overall demand increases with N because of the reduction in price that occurs with increasing N as shown in Figure 1.6. Gross revenue per firm falls in Figure 1.9 with N .7 Cash flow becomes negative at the point where fixed costs exceed gross revenue. Thus, Figure 1.9 suggests that this segment cannot support more than approximately seven competitors if fixed costs for this product for each firm exceed $500 million. At $1 billion fixed costs, the market can only support four firms profitably. 1.4.2 US Automotive Market

Trends of this nature are being experienced by the US automotive industry. In the early to mid 20th century, there were a relatively large number of US based automotive competitors. The number, however, had decreased to three majors by 1970. Since 1970, Japanese, Korean, and European manufacturers have entered the US market thereby increasing the number of major competitors in many segments from three to seven or more. China is next. The resulting market dilution has generated a marked decline in US market share for Chrysler, Ford, and General Motors. It is sobering to note that the equilibrium demand model for seven equally viable competitors is fewer than 15% share for each. It is doubtful that any US based automotive company currently recognizes 15% as being its market share end point because all likely believe that they can do better than 1/ N share by making consistently superior products. But in an industry as mature as automotive, any value, cost, or speed advantage currently enjoyed by any company will likely not last. Losses in share and profit by US manufacturers will need to be offset by gains in emerging markets outside the US. Case Study 6 reconsiders dilution in greater depth and assumes that the values between competitors are not constant.

6

Value and cost were taken to be $45,000 and $15,000, respectively. These numbers are somewhat representative of the US mid-sized automotive market. Price was computed from a Cournot/Nash model, which is described in Appendix A. 7 In many respects, N acts as a fourth fundamental metric.


11

Even though the gross revenue curve in Figure 1.9 is falling, new competitors enter the market because they gain revenue at the expense of the existing players. But this can lead to speculative behavior with many more entrants coming into the market than can be supported profitably. With oversupply, the falling shape of the revenue curve with increasing N should in time lead to a reduction in the number of competitors through failures, acquisitions, and cooperative behavior through alliances. The initial dynamics for this problem has some similarity to the speculative run up and collapse in the price of a stock discussed in Case Study 1. $30,000 $28,000

Value = $45,000 Cost = $15,000

Price

$26,000 $24,000 $22,000 $20,000 $18,000 $16,000 0

2

4

6

8

10

Number of competitors

Figure 1.6. Price falls as the number of competitors increase

1.5 Check of Demand Model The relationship given by Equation (1.1) in which demand goes to zero as price approaches value has been tested using a survey of 78 respondents that participated in the simulated purchase of lottery tickets with known payoffs (Cook and Wu, 2001). The fractional demands f versus price divided by the Expected Economic Values (EEVs) of the ticket in Figure 1.10 are for two different lottery tickets. One ticket had a 50% chance of winning $100 and the other had an 80% chance of winning $100. Thus, the EEVs of the tickets were $50 and $80, respectively. The two sets of data are reasonably superimposed, which is expected from the linear model. The extrapolation to zero demand is near P / EEV = 1 , which means that the values are approximately equal to their theoretical EEVs of $50 and $80. One of the respondents would pay more than $50 for the 50% ticket and two respondents would pay more than $80 for the 80% ticket. These represent outliers for the linear model and were not included in Figure 1.10. The logit model, which is discussed in Chapter 3 and Appendix A, allows for such behavior and also removes much of the sigmoidal curvature seen in Figure 1.10.

12


1200000 1100000 1000000 900000

Total demand

Demand

800000 700000 600000 500000 400000

Demand per competitor

300000 200000 100000 0 0

2

4

6

8

10


Market share

Figure 1.7. Demand per competitor falls as the number of competitors increase but total demand increases

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Value = $45,000 Cost = $15,000

0

2

4

6

8

10


Figure 1.8. Market share of each competitor falls as the number of competitors increase

Gross revenue (10 ^ 9 $)


10 9 8 7 6 5 4 3 2 1 0

13

Value = $45,000 Cost = $15,000

0

2

4

6

8

10


Figure 1.9. Gross revenue per competitor falls as the number of competitors increase

1.2 50% chance 1

80% chance Linear (50% chance)

0.8

Linear (80% chance) f

0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

1.2

P/EEV

Figure 1.10. The fraction of respondents indicating that they would buy a lottery ticket as function of the price P of the ticket divided by its Expected Economic Value (EEV). (Source: Wu A and Cook HE (2001) On the valuation of goods and selection of the best design alternative. Research in Engineering Design, 13:42-54, Figure 5 (re-drawn), ©Springer-Verlag 2001, with kind permission of Springer Science and Business Media.)

14


1.6 Research and Development Planning In planning research and development, there will often be more good new ideas than resources to support their development. Thus, a decision has to be made regarding which technologies should be included in the research program and which have to be left out—a process that has been likened to a lifeboat exercise where the items least likely to support survival are thrown overboard. Innovative power and cash flow estimates given by Equations (1.4) and (1.3), respectively, can be used as aids in selecting which new technologies should be targeted for development. It is relatively straightforward to make an early estimate of the innovative power of a new technology and to update it as development progresses; whereas, estimating the profitability of a new technology in its early stages of development is more complex and error prone. The reason is that a profit estimate requires projecting the price and demand for the new product, which in turn requires that estimates be made of the prices and values of the competing products. Nevertheless, we show in Chapter 4 how profitability projections can be made for a new technology in its later stages of development. Such projections should play a significant role in deciding whether or not to make the transition to production. Thus, innovative power can be used to set priorities on new technologies in the early stages. Nearer production, this metric should be replaced by a projected bottom-line metric, such as profitability, cash flow, or breakeven time in assessing whether or not to take the technology to production.

1.7 Summary o o

o

o o o o

There are two types of financial metrics, bottom-line and fundamental. The fundamental metrics of value, cost, and pace of innovation determine what the bottom-line metrics will be. The number of competitors acts like a fourth fundamental metric. The innovative power of a new technology is a metric computed from its added value less its added cost, the quantity divided by the time from the start of development to production. Innovative power can be used to rank new technology proposals and set priorities for their development. Although value is a highly subjective financial metric, it can be determined about as accurately as cost. The price of a good is influenced by its value and cost and the values and costs of the products competing against it. As the number of competitors increase in a market segment, the prices of the goods are expected to fall along with the demand for each. Total demand summed over all of the competitors in the segment is expected to rise, however, because of the reductions in price.


15

1.8 Supporting Case Studies Case Study 1: Value Speculation in a Stock’s Price Case Study 6: Effect of Market Dilution when Value Differs between Competitors

1.9 Exercises 1.1

Discuss why net value to the seller is P-C.

1.2 Show analytically for a monopoly with a linear demand curve that an increase in value of dV shifts the demand curve by dP. 1.3 Show that revenue is a parabolic function versus price for a linear demand curve. Is the price for optimum revenue a function of fixed cost F? 1.4 Discuss why environmental quality is almost always negatively impacted by any product. 1.5 Assume that demand versus price is represented by a 1 minus cumulative distribution function having a mean price of 20 and a standard deviation of 5. Plot the fractional demand function and the net revenue function versus price. In constructing the plot, Use the expression f =1- NORMDIST(P,Mean,SD,1) for fractional demand. Use the LINEST function to construct a linear approximation to the cumulative distribution over the range mean minus 2 SD to mean plus 2 SD. 1.6 In Exercise 1.5, what does the linear model give for value in terms of the number of SD from the mean price of 20? 1.7 $30?

In Exercise 1.5, what is R^2 for the linear fit over the price range of $10 to

1.8 In Exercise 1.5, compute value for the probit model given by (See Equations (A.25) and (A.26) in Appendix A):

σ [ N + 1] 3 + PC π Now compute the parameters for the logit model from the normal model and then compute value for the logit model given by: VC =

VC =

[ N + 1] + P β'

C

Compare the linear, logit , and probit results for value. Why are the values higher than the mean of $20.

16


1.10 References Carlson CR and Wilmot WW (2006) Innovation: the five disciplines for creating what customers want. Crown Business, New York Cook HE (1997) Product management: value, quality, cost, price, profits, and organization. Kluwer Academic, Amsterdam Cook H.E. and Wu A (2001) On the valuation of goods and selection of the best design alternative. Research in Engineering Design 13:42-54 DeBonis JN, Balinski EW, and Allen P (2002) Value-based marketing for bottomline success: 5 steps to creating customer value. McGraw-Hill, New York Ben-Akiva M and Lerman SR (1985) Discrete choice analysis. MIT Press, Cambridge, MA Donndelinger JA and Cook HE (1997) Methods for analyzing the value of automobiles. SAE 1997 Transactions, Journal of Passenger Cars 106:12631281 Gale B (1994) Managing customer value: creating quality and service that customers can see. The Free Press, New York Kim WC and Mauborgne R (2005) Blue ocean strategy. Harvard Business School Press, Boston Kordupleski R and Simpson J (2003) Mastering customer value management. Pennaflex Educational Resources, Cincinnati, OH Lee MD (1998) Brands, brand management, and vehicle engineering. M.S. Thesis, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign Louviere JJ, Hensher DA, and Swait JD (2000) Stated choice methods. Cambridge University Press, Cambridge, UK Pardee WJ (1996) To satisfy and delight your customer: how to manage for customer value. Dorset House Publishing, New York Wu AE (1998) Value benchmarking the minivan segment. M.S. Thesis, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign

2 Assessing Value Using Surveys

Synopsis Value is measured and defined in different ways depending upon the domain. In product planning, the value of a product, is an aggregate measure of worth that can be used with price to forecast the product’s demand as it competes within a specified market segment. Social scientists have developed experimental techniques to estimate the relative importance of the attributes in the value functions and techniques to assess the validity of the results. Marketing research strives to understand the behaviors and preferences of consumers in a market-based economy. Surveys are one of the primary tools employed by market researchers to gain insight and provide important information for product planning decisions. The steps in a survey project are introduced and discussed to help the practitioner avoid common pit-falls.

2.1 Background In highly competitive markets, managers continually make decisions about what ideas to incorporate into their products and services as they strive to innovate to increase their competitiveness. If a new idea reduces cost without affecting performance, it is clear the idea should be incorporated. Likewise, if a new idea improves the performance without affecting cost, the idea will easily gain support from management. The challenge to the product planner comes when a new idea improves performance and increases cost. Often, costs are estimated and those responsible for product planning must rely on their instincts as to whether the innovative idea can garner additional profits. When making these decisions, managers often place too much attention on cost at the detriment of improved performance because it is frequently the only quantified financial metric upon which the decision can be made. This is the driving force for a value metric that rigorously converts performance changes into willingness to pay for a comparison against cost.

18


Value can take on several meanings depending on context. Value engineers define value as functional worth divided by cost (Fowler 1990). Alternatively, Taguchi’s “Cost of Inferior Quality” (CIQ) is a measure of value lost due to a specification being off from its ideal point (Taguchi and Wu, 1980). Utility, which incorporates a decision maker’s risk attitude, is often used as a measure of value when comparing two or more uncertain prospects (von Neumann and Morgenstern, 1947). In economics, utility takes on a different meaning as it is a proxy for satisfaction derived from quantities or combinations of commodities (Henderson and Quandt, 1980). Although each of these measures of value has demonstrated to be useful within each of their respective domains, these measures of value are not useful in product planning because they can not be used to provide insight into how changes in product performance will affect consumer behavior or the firm’s financial performance.

2.2 Value and Value Functions During product planning, the value Vi of a product i, is an aggregate measure of worth to the customer. This can be used with the price of the product Pi to forecast the product’s demand as it competes within a specified market segment. For a value metric to be useful in making product planning decisions, it must therefore possess the following properties: (1) it must have the same units as price; (2) the willingness to pay for the good must decrease as price approaches value; and (3) if a product change creates an increase in demand while holding price constant, value has been increased. All models that strive to forecast consumer behavior are founded upon the concept of a value function. A value function yields a real number that possesses the three properties listed above and is based upon a vector of Critical-To-Value (CTV) attributes, z, that are used to define abstractly each alternative—more of a good attribute increases Vi. This postulate is consistent with the view that consumers derive their satisfaction from a product’s bundle of attributes rather than satisfaction from mere ownership (Lancaster 1966, 1971). Value functions can be classified as either linear or non-linear, where the choice of functional form is dictated by the research design.1 Economic choice theory has been used by econometricians, decision scientists, and marketing researchers to parameterize value functions used to create descriptive models of consumer behavior for decades (McFadden, 1986; BenAkiva and Lerman, 1985; Train, 1985). These models, whose parameters can be estimated from historical purchase data (revealed choice) or psychometric market research surveys (stated choice), have well-defined statistical properties, several software packages to ease the computation burden, and a legacy of successful applications in industry.

1

Louviere, et al. (2000) devote a chapter to choosing amongst choice models.

Assessing Value using Surveys

19

If the tickets of Chapter 1 were for a real lottery and were offered for sale to different groups at different prices (each group being randomly selected from the same large population) their actual purchases would constitute a revealed choice survey. Asking buyers to reveal the brand and price for a recent vehicle purchase is another example of a revealed choice survey. The choice models parameterized using revealed methods have high external validity because the input data comes from real transaction data. There are a few downsides of revealed methods however. Because prices in the real-world vary within small ranges, the results of a revealed study are not useful for predicting behavior for prices outside those ranges (Ben-Akiva, et al. 1994). Moreover, it is impossible for revealed models to estimate value parameters for product attributes that are not yet available in the market place. Therefore, revealed models are limited to forecasting consumer behavior for new products that are priced within the same small range as existing products with the same CTV attributes. The revealed choice study of the automobile market performed by Boyd and Mellman (1980) illustrates a few other important principles to consider when using choice models. First, the paper illustrated how important it is to compare parameter estimates with a priori beliefs. Indeed, their value estimates appeared to be higher than was expected, which later led to the conclusion that the impact of price was too small. Secondly, if multiple segments are to be investigated, a price coefficient should be calculated for each segment. Because the authors used a single price coefficient for all segments, the simulation yielded valuations that were generally too low for the luxury segments and valuations that were too high for the compact and sub-compact segments. Lastly, the study points out how the researcher must search for possible unobserved, yet correlated attributes that may ultimately be responsible for value differences between product alternatives. In the auto market, for example, very often the larger cars are more luxurious, have desirable styling, acceleration performance, passenger space and cargo volume. When conducting a revealed discrete choice study, the research must make sure that chosen attributes are not confounded by unintended correlated attributes. Demand-Price (DP) Analysis (described in Appendix A) is an alternative methodology for gleaning value information from phenomenological purchase data. Rather than try to link purchase behavior directly to product attributes, as with choice models, DP analysis uses a game theoretic model to estimate the total values of products based on each good’s historical price and demand. Stated techniques, on the other hand, can be used to build models of consumer behavior that span larger price ranges and new innovative product attributes. Stated research methods are usually classified as being based upon either conjoint analysis (Green and Srinivasan, 1990) or contingent valuation (Cameron and James, 1987; Mitchell and Carson, 1989). Conjoint analysis models are used to measure trade-off elasticities between attributes. Alternatively, the contingent valuation techniques have a respondent write-in threshold prices or state if they would purchase at certain prices. The values of the two lottery tickets determined in Chapter 1 were based upon the respondents’ stated willingness to pay for the prospect of winning the prizes and is therefore a good example of a contingent valuation stated choice survey. The results of contingent valuation and conjoint analysis surveys often differ (Backhaus, et al. 2005), but they also might be used to

20


cross-validate each other. Each method is subject to bias and has supporters and critics.2 As explained by Little (1970), models for decision making should be simple, robust, easy to control, adaptive, as complete as possible, and easy to communicate with. To date, even though choice models have gained widespread acceptance among market researchers and econometricians, product planners have found it difficult to utilize the models in their decision making for several reasons. First, the mathematical functions of the choice models are often very complex and require special software to translate survey data into function parameters. Second, the theory behind the choice models is very difficult to explain to laymen, which makes it hard to garner the trust and acceptance of decision makers. Third, it is very cumbersome to adapt the model as new information becomes available and therefore requires researchers to execute large studies rather than multiple focused studies. Fourth, it is very difficult to understand how uncertainty in parameters might influence the attractiveness of prospects to decision makers. The guiding rationale for the methods and tools advocated by this book is to balance simplicity and rigor through the use of analytical models that are phenomenological in nature. Simplicity is needed so that the models can parameterized with limited resources and the underlying techniques can be communicated and understood by management. Rigor, on the other hand, is needed so that the outputs of the model are trusted and used. While the steps in analyzing the data and obtaining results are indeed important, it is important that data being fed into the methodology is free of confounding and biases. The remainder of this chapter describes the steps for designing stated choice surveys for maximum effectiveness.

2.3 Causal Research of Value As mentioned earlier, multiple attributes are used to describe a product’s value because purchase decisions are rarely based upon a single criterion. Although the respective attribute preference weights are probabilistic and a researcher can never prove causality definitively, social scientists have developed experimental techniques to estimate the relative importance of the attributes in the value functions. The resulting value functions are said to be internally valid if the attributes demonstrate causality within a testing context. The results of an experiment have external validity if the results can be generalized to the real market environment. While the results of a revealed analysis are by definition externally valid, it is very difficult for stated techniques to demonstrate external validity. Indeed, a survey experiment must be carefully designed and executed just to earn the distinction of internal validity, which is only possible if the parameter estimates are free of experimental and cognitive biases. Biased estimators are those that for

2

The interested reader is referred to Louviere, et al. (2000) for an overall view of traditional stated choice methods and discrete choice literature.


21

some reason over- or underestimate, on average, the measure being estimated. An experimental bias occurs when extraneous variables confound the parameter estimates. Alternatively, the question format within a survey can introduce cognitive biases into the parameter estimates. Because obtaining an unbiased estimate of value functions is so important, much research has been carried out to develop rigorous techniques that mitigate cognitive biases stemming from survey design. There are three ways to limit confounding in an experiment: replication, randomization, and blocking. Replication allows the experimenter to estimate experimental error and to obtain a more precise estimate of a factor’s effect on value. Randomization mixes up the order in which trials of an experiment are performed, which helps to “average out” the effects of extraneous factors that may be present. Lastly, blocking is used to reduce variability stemming from nuisance factors, which are factors that could influence the value measurement but are not of particular interest. One of the predominant tools used in the cognitive sciences to increase the fidelity and efficiency of experiments is the statistical design of experiments (DOE).3 A DOE enables an experimenter to analyze and control causal variables in a way that allows several basic experiments to be conducted simultaneously and employ the three methods to limit confounding, concurrently. The specific advantages of using DOE’s are: (1) the experimenter can efficiently determine the effect of more than one independent variable; (2) confounding variables can be statistically controlled; and (3) some designs allow interactions between independent variables to be measured. For these reasons, using a carefully thought out and executed DOE is the most effective way to guard against experimental biases. When a DOE investigates more than one attribute, a design matrix is often used to designate the level setting for each attribute of a trial. When there are only two levels for a factor, they are often termed “low” and “high” and denoted as “-” and “+”, respectively. The low/high distinction can be used to describe both continuous factors (temperature, speed, etc.) and discrete factors (material, color, etc.). Alternatively, a code is often assigned to the low/high settings such as 0/1 or -1/1. When the factor under investigation is continuous, the researcher is often able to use results of an experiment to forecast the response of the system for levels between the high and low code using interpolation.

2.4 Survey Project Design and Execution Marketing research is a common form of applied sociology that strives to understand the behaviors and preferences of consumers in a market based economy. Surveys are one of the primary tools employed by market researchers to gain insight and provide important information for product planning decisions.

3

Experimental designs based upon orthogonal arrays (OAs) are described in Appendix F.

22


The goal of a survey project is to obtain information to aid decision making, which gives a clear indication (bias-free) of how the group under study will make choices based upon changes in product design. Researchers using these techniques have long known that the way questions are asked within a survey can bias the results and that the results of a survey are strongly influenced by who completes the survey. To ensure that the survey project meets the research goals, the project must pass through seven stages, regardless if it is quantitative or qualitative: 1. 2. 3. 4. 5. 6. 7.

Objective—Determine what you want to learn Respondent Selection—Determine the source of your respondents Methodology—Determine the method of administering the survey Questionnaire Design—Determine what and how to ask Pre-test—Determine if the questionnaire can be improved Collect Data—Distribute and conduct the survey Data Preparation and Analysis—Enter the data and draw conclusions

The remainder of this section further describes each stage with a focus on quantitative surveys and lists some important considerations during each step to reduce systemic biases that may develop, which might reduce the fidelity of the results and the ability to make effective policy decisions. 2.4.1 Stage 1: Determine Objectives In all cases, a survey project should only be executed after a management problem has been clearly expounded and management buys-in to the survey process and presumed results (Jones, 1985; Curren, et al. 1992). Some typical objectives of management that drive marketing research activities include concept testing, market segmentation, market positioning, brand name valuation, demand and sales forecasting, price elasticity determination, and understanding customer satisfaction. The methodology laid out in future chapters enables the researcher to address each one of these objectives in turn and, as will become clear later, not all objectives require the completion of a survey project. 2.4.2 Stage 2: Respondent Selection The respondent target population consists of all individuals about whom conclusions are to be made and is derived directly from the objective of the study. An imprecisely defined target population can lead to misleading results. For example, if the objective of the study is to determine how a change in the design of a semi-truck will affect the value of a brand name, the target population would likely include those who purchase semi-trucks and not include those who only purchase vehicles for personal transportation. Once the target population’s characteristics are defined by the researcher, a sampling strategy must be developed.


23

A sampling strategy describes how a subgroup of the population will be chosen to participate in the study. A poor sampling strategy can lead to selection bias, which results when the sample of respondents does not represent the target population in a statistical sense. There are at least four types of selection biases: confirmation bias, exclusion bias, self-selection bias, and non-response bias. Confirmation bias describes the tendency of the researcher to seek out respondents that are likely to confirm the researcher’s preconceived notions of what is true. Exclusion bias may result if the sample of respondents systematically excludes individuals from the target population. Alternatively, if respondents are informed of the purpose of the study and given the option to participate, the results may suffer from self-selection bias because the respondent choices to take part in the study may be correlated to traits that affect the study result. Lastly, when individuals of the target population are unable or unwilling to participate, the study may suffer from non-response bias. There are several ways to reduce non-response bias, including giving the respondent sufficient notification of event (Yu and Cooper, 1983), motivating the respondent (Fern, et al. 1986), providing honorariums, good questionnaire design, and survey personalization (Greer and Lohtia, 1994). Although one can not determine that the sample is unrepresentative from low response rates alone, a low response rate does increase the probability of non-response bias (Leslie, 1971). There are several prevailing sampling strategies (listed in Tables 2.1 and 2.2), which are classified as either non-probabilistic (Table 2.1) or probabilistic (Table 2.2) (Malhotra, 1996). Non-probabilistic sampling allows the researcher to use his/her personal judgment about whether to include or exclude a potential respondent. With probabilistic sampling, each potential respondent in the target population has a fixed chance of being selected for the sample. Because respondents are selected by chance, the researcher is able to calculate confidence intervals about the true population value for a given level of certainty. Ultimately, the best sampling strategy is the one that effectively balances the cost of obtaining respondents from the target population against the risk associated with selection biases that may be introduced from an unrepresentative sample. There are both qualitative and quantitative considerations for determining sample size. Important qualitative considerations include (Malhotra, 1996): (1) the importance of the decision, (2) the nature of the research, (3) the number of variables, (4) the nature of the analysis, (5) sample sizes used in similar studies, (6) incidence rates, (7) completion rates, and (8) resource constraints. In commercial marketing studies, it is often the resource constraints (financial analyst availability and timeline) that drive the research design and ultimately the sample size. Nevertheless, sample size influences the strength of a finding through statistical inference—the precision goes up as sample size increases. Kramer and Thiemann (1988) and Frankel (1983) both describe quantitative methods for determining sample size requirements based upon the necessary statistical precision when using random sampling. One shortcoming of the purely statistical calculations of sample sizes is that they do not consider the sampling cost. Kish (1965) and Sudman (1976) describe techniques to include cost considerations into sample size determination.

24


Table 2.1. Non-probability Based Strategic Sampling Techniques Type Convenience

Definition Respondents are often selected because they are readily available.

Positives It is the least expensive and time-consuming of all techniques.

Judgmental

Respondents are chosen based upon judgment of researchers. Quotas are established based on respondent characteristics and then convenience and/or judgmental sampling is used to fulfill the quota.

Inexpensive and not timeconsuming.

Quota

Snowball

An initial group is selected randomly and subsequent respondents are selected based upon referrals.

Once the quotas are defined there is considerable freedom in selecting respondents. It is possible to obtain results close to those for probability sampling. The process is carried out in waves and often leads to a snowballing effect.

Negatives Not representative of any population and therefore can not be used to make reliable inferences. Subject to many types of sampling biases.

If a characteristic is overlooked, the quota sample will not be representative of the target population.

Even though probability sampling may be used to identify the initial group, the final sample is nonprobabilistic.


25

Table 2.2. Probability Based Strategic Sampling Techniques Type Simple Random

Definition Each element in the population has a known and equal probability of selection as in a lottery.

Positives Easily understood and results can be projected upon population.

Systematic

From a list of the population, every ith element is chosen.

Stratified

Two step process: (1) population is partitioned into subpopulations (strata) based upon a stratification variable; (2) elements are selected from each strata using simple random selection. Two step process: (1) population is divided into mutually exclusive and collectively exhaustive subpopulations; (2) sample selected using random selection of clusters.

If the list is ordered with respect to a characteristic under investigation, a representative sample should result with lower sampling error. Increased precision without increased cost.

Cluster

Can reduce administrative costs such as travel.

Negatives Samples may be spread out geographically, which increases cost. Possibility that sample may not represent population. Lower precision and larger standard error than other random sampling techniques. Sometimes it may be hard to find the “right” characteristic to order the list.

Stratification variable may be hard to measure and/or apply.

Cluster sampling can increase the variability of sample estimates above that of simple random sampling based on how the clusters differ between themselves when compared to the withincluster variation.

2.4.3 Stage 3: Methodology for Administering Survey The objectives, respondent selection strategy, and resource constraints often dictate the survey methodology. Nevertheless, there are four broad categories for administering surveys in order of popularity: through the internet, over the telephone, person-to-person ,or through the mail. Administering surveys through the internet can be quite convenient, as the respondent can guide themselves to the

26


survey web-site and enter the data themselves. Moreover, the internet allows the survey to include multi-media, such as video and sound; input screens can be used to ensure responses meet the data field requirements; and personal information can be retained in the system to expedite future correspondences. Although surveys administered by phone require additional resources, sometimes they are necessary to help respondents resolve and clarify ambiguities. A downside is that the respondent loses the visual cues that can aid working memory such as videos, pictures, and lists. Surveys administered person-to-person share the benefits of both internet and telephone based methodologies, but are much more expensive because they require respondents and the administrators to be in physical proximity. In spite of this disadvantage, person-to-person administration allows researchers to include smell, taste, and feel attributes, which would be impossible using any of the other methods. With the advent of the internet, mail surveys have become even less popular than in the past. Mail surveys are still useful, however, in cases when resources are not available to create a web-based application and when there is a high confidence that the targeted respondent will indeed respond. 2.4.4 Stage 4: Questionnaire Design Questionnaire design must match the administration methodology chosen, such that the information transfer from survey to respondent and back is feasible. For example, choosing from a list may cause excessive cognitive stress if the survey is administered over the telephone. Likewise, it is impossible to ask the respondent about sound, taste, or feel attributes via a mail survey. Conjoint analysis techniques allow the researcher to vary several attributes at a time to create different design alternatives for the respondent to evaluate. The attributes in a conjoint analysis survey are often varied according to an experimental design (the benefits of DOEs were discussed earlier in this chapter), which allows the researcher to control extraneous variables and deliver importance weightings that can be used to rank attribute importance. When too many attributes are varied within a single experiment, the cognitive demands of the respondents can compromise choice consistency (DeShazo and Fermo, 2002). Indeed, long and complex surveys have been shown to increase cognitive stress, which in turn increases the variability of the results. There are five principle dimensions for measuring questionnaire complexity: number of design instantiations to be considered throughout the survey, number of attributes used to define those designs, number of levels for each of the attributes, range of attribute levels and the number of times a respondent must make a choice. Research into the influence of these five dimensions on experimental results demonstrated that the two most critical dimensions are number of attributes and number of alternatives (Caussade, et al. 2005). Increasing the number of attributes and having more or less than four alternatives decreased choice consistency. The results also suggested that having 9-10 choice situations and keeping the number and range of levels relatively small maximizes consistency. All of the aforementioned results confirm the adage that surveys should be kept short and simple. One of the simplest designs is the Direct Value (DV) survey discussed in Chapter 3.


27

Biases can also be introduced by the way questions are asked. There are five principle biases that stem from questionnaire design: Type I hypothetical bias, Type II hypothetical bias, framing bias, response bias, and the endowment effect. Type I hypothetical bias can manifest when respondents are asked to imagine a situation or product that they have never experienced before. Type II hypothetical bias refers to when the consequences of a respondent’s choice are hypothetical. Examples of Type II hypothetical bias include the studies conducted by Horowitz (1991) and Neill, et al. (1994), which indicated that subjects behaved as if cash payment requirements were hypothetical even when they were instructed to consider the situations as real. Framing bias manifests if the question is asked in a way that it might direct respondents to choose alternatives in an inconsistent way. Similarly, when the respondents answer the questions the way they think the researcher want them to rather than according to their true beliefs, it is called response bias. Lastly, since people typically place a higher value on the objects they own relative to objects they do not, the researcher must be aware of the endowment effect because willingness-to-pay will likely be different to willingness-to-accept. 2.4.5 Stage 5: Pretest the Survey Pretesting a survey is a necessary safeguard to identify and eliminate potential problems that may lead to unreliable or misrepresentative data (Hunt, et al. 1982). The pretest should include the entire questionnaire and the respondents should be members of the target population (Diamantopoulos, et al. 1994). The pretesting can be performed by conducting a one-on-one interview with the respondents to gain more direct feedback into clarity and perceptions. In protocol analysis, respondents are asked to “think aloud” as they move through the survey. Alternatively, debriefing involves interviewing the respondent after the survey has been completed. The data obtained from the pretest should be analyzed to ensure it will be useful in fulfilling the objectives (Reynolds, 1993). 2.4.6 Stage 6: Collect Data One of the greatest concerns while administering surveys is the possibility of experimenter effects (Rosenthal, 1976; Coulter, 1982; Singer, et al. 1983), which may occur if a researcher expects a given result and unconsciously manipulates an experiment or misinterprets the data in a way that affects the experimental conclusion. Some examples of experimenter effects include field worker personal or social attributes that may alter the way the question is answered by the respondent. Another example is the experimenter expectancy effect, where the respondent perceives cues from the field worker about how to answer. Lastly, Cottrell (1972) described evaluation apprehension as a phenomenon that an individual will behave differently in situations when there is an audience present. Experimenter effects can be controlled by using a double-blind methodology. Using direct computer data collection has been shown to provide results that are at least as accurate as personal interviews and self-administered surveys (Klein and Sobol, 1996). The study indicated that one trade-off of using computer-only

28


administration is that the response rates on list-type questions were lower than person-to-person interviews. Moreover, the study reported that three out of ten questions had “significantly more omissions” when the survey was administered by a computer. It is clear that each method of administering surveys has its own idiosyncrasies that might introduce bias into the results and therefore the risks of each method should be considered and methods to mitigate those risks should be identified. 2.4.7 Stage 7: Data Preparation and Analysis After all the surveys have been administered and the sample size criterion has been satisfied, the next step is to prepare the data and proceed with analysis. Checking the data is a necessary step because some questions may have been left unanswered, responses my be illegible, the pattern of responses may indicate that one or more of the questions were misunderstood by the respondent, or the responses are “too consistent,” which might indicate the respondent may not have given a good-faith effort. If responses are deemed unsatisfactory, there are three basic remedies: return the survey to the respondent, assign missing values, or discard the respondent’s entire data set. Since returning the survey is not always possible and discarding an entire data set is unsatisfactory, assigning missing values may sometimes be a desirable solution. Assigning missing values is permissible when: (1) the number of respondents with unsatisfactory responses is small compared to overall sample size, (2) the ratio of unsatisfactory responses for each of the respondents is small, and (3) the variables with unsatisfactory responses are not the key variables (Malhotra, 1987; 1996). Often, respondent data must be coded so that it can be efficiently tabulated and stored in a computer file. For example, responses to a Yes/No question may be coded as a 1 and 2, respectively. This technique works well for closed-end questions with predefined responses. Open-ended question coding is much more complex and requires a code to be developed after the survey has been administered, where the code list is mutually exclusive and collectively exhaustive.

2.5 Summary o o o o o

Consumers value a product because of its attributes. Historical purchase information can be used to reveal how consumer’s value features and technologies currently in the marketplace. Surveys can be used to understand how consumer’s value new features and technologies not currently in the marketplace. Surveys should use DOE methods and tools to minimize bias and correlation between factors. Seven stages of development were identified for developing a survey: (1) Objective Identification, (2) Selection of Respondents, (3) Methodology, (4) Design, (5) Pre-test, (6) Collection of Data, (7) Data Preparation and Analysis.


o

29

The designer of the survey should strive to minimize cognitive stress on the respondents by not making the survey complex and lengthy.

2.6 Supporting Case Studies Case Study 2: Simulated Survey of Boston to Los Angeles Flights Case Study 3: Analysis of a Multinomial Stated Choice Survey Case Study 5: Revealed Values: Minivan Trends Case Study 7: Value of Interior Noise in a Luxury Automobile Case Study 9: Value of Mustang Options Case Study 11: Assessing Relative Brand Value

2.7 Exercises 2.1 Write the definition of value or utility for each domain as indicated.

a) b) c) d) e) f)

Domain Economics Economics Decision Analysis Value Engineering Taguchi Product Planning

Metric Value Utility Utility Value Value Value

2.2 What are the three properties of a value metric that make it useful for product planning? 2.3 Explain the concept of purchasing a bundle of attributes versus purchasing a physical product. Why should product planners focus on Critical-To-Value (CTV) attributes and not all the attributes of a product? 2.4 What’s the difference between internal validity and external validity? Give an example. 2.5 List the three ways to limit confounding. 2.6 List and define four types of sampling biases. 2.7 List five dimensions that can be used to define questionnaire complexity. 2.8 List and define the five biases that stem from questionnaire design.

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2.8 References Backhaus K, Wilken R, Voeth M, and Sichtmann C (2005) An empirical comparison of methods to measure willingness to pay by examining the hypothetical bias. International Journal of Marketing Research 47:543-62 Ben-Akiva M and Lerman S (1985) Discrete choice analysis. MIT Press, Cambridge Ben-Akiva M, Bradley M, Morikawa T, Benjamin J, Novak TP, Thomas P, Oppewal H, and Rao V (1994) Combining revealed and stated preference data. Marketing Letters 5:335-50 Cameron TA and James MD (1987) Estimating willingness to pay from survey data: an alternative pre-test market evaluation procedure. Journal of Marketing Research 24:389-95 Caussade S, Ortuzar JD, Rizzi LI, and Hensher DA (2005) Assessing the influence of design dimensions on stated choice experiment estimates. Transportation Research Part B 39:621-40 Cottrell, NB (1972) Social facilitation. In McClintock C (ed.) Experimental social psychology. Holt, Rinehart & Winston: New York, NY, pp. 185-236 Coulter PB (1982) Race of interviewer effects on telephone interviews. Public Opinion Quarterly 46:278-84 Curren MT, Folkes VS, and Steckel JH (1992). Explanations for successful and unsuccessful marketing decisions: the decision maker’s perspective. Journal of Marketing 56:18-31 DeShazo JR and Fermo G (2002) Designing choice sets for stated preference methods: the effects of complexity on choice consistency. Journal of Environmental Economics and Management 44:123-143 Diamantopoulos A, Schlegelmilch BB, and Reynolds N (1994) Pretesting in questionnaire design: the impact of respondent characteristics on error detection. Journal of Market Research Society 36:295-314 Fern EF, Monroe KB, and Avila RA (1986) Effectiveness of multiple request strategies: a synthesis of research results. Journal of Marketing Research 23:144-53 Fowler TC (1990) Value analysis in design. Van Nostrand Reinhold, New York Frankel M (1983) Sampling theory, in Rossi PH, Wright JD and Anderson AB (eds.) Handbook of Survey Research. Academic Press, New York, pp 21-67 Green PE and Srinivasan V (1990) Conjoint analysis in marketing: new developments with implications for research and practice. Journal of Marketing 54:3-19 Greer TV and Lohtia R (1994) Effects of source and paper color on response rates in mail surveys. Industrial Marketing Management 23:47-54 Henderson JM and Quandt RE (1980) Microeconomic theory—a mathematical approach. McGraw-Hill, New York Horowitz JK (1991) Discounting money payoffs: an experimental analysis. Handbook of behavioral economics. JAI Press, Inc., Greenwich Hunt SD, Sparkman RD Jr, and Wilcox J (1982) The pretest in survey research: issues and preliminary findings. Journal of Marketing Research May: 269-73


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Jones S (1985) Problem-definition in marketing research: facilitating between clients and researchers. Psychology and Marketing 2:83-93 Kish L (1965) Survey sampling. Wiley, New York Klein G and MG Sobol (1996) Bias in computer-assisted surveys. IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans 26:566-571 Kraemer HC and S Thiemann (1988) How many subjects? Sage Publications, Newbury Park Lancaster K (1966) A new approach to consumer theory. Journal of Political Economy 74:132-57 Lancaster K (1971) Consumer demand: a new approach. Columbia University Press, New York Leslie L (1971) Are high response rates essential to valid surveys? Social Science Research Sept:332-34 Louviere JJ, Hensher DA, and Swait JD (2000) Stated choice methods: analysis and application. Cambridge University Press, Cambridge, UK Malhotra NK (1987) Analyzing marketing research data with incomplete information on the dependent variable. Journal of Marketing Research 4:74-84 Malhotra NK (1996) Marketing research: an applied orientation, 2nd edn. Prentice Hall, Upper Saddle River McFadden D (1986) The choice theory approach to market research. Marketing Science 5:275-97 Mitchell RC and Carson RT (1989) Using surveys to value public goods: the contingent valuation method. John Hopkins University Press, Baltimore Neill HR Cummings RG, Ganderton PT, Harrison GW, and McGuckin T (1994) Hypothetical surveys, provision rules and real economic commitments. Land Economics 70:145-54 Reynolds N, Diamantopoulos A, and Schlegelmilch BB (1993) Pretesting in questionnaire design: a review of the literature and suggestions for further research. Journal of the Market Research Society 35:171-82 Rosenthal R (1976) Experimenter effects in behavioral research, expanded edn. Irvington Publishers, New York Singer E, Frankel MR and Glassman MB (1983) The effect of interviewer characteristics and expectations on response. Public Opinion Quarterly 47:6883 Sudman S (1976) Applied sampling. Academic Press, New York Taguchi G and Wu Y (1980) Introduction to off-line quality control. Central Japan Quality Control Association, Nagoya Train K (1985) Qualitative choice analysis. MIT Press, Cambridge von Neumann J and Morgenstern O (1947) Theory of games and economic behavior, 2nd edn. Cambridge University Press, Cambridge, UK Yu J and Cooper H (1983) A quantitative review of research design effects on response rates to questionnaires. Journal of Marketing Research 20:36-44

3 Analyzing Stated Choice Surveys

Synopsis The Direct Value (DV) survey is a stated choice survey used to determine the value of an alternative relative to a baseline with minimal cognitive stress on the respondent. Two complementary tools, graphical and analytical, are used here to arrive at value from DV and other stated choice surveys. Each tool has a role to play in arriving at a fully informed analysis. The analytical treatments given here are complete. However, the details do not have to be recalled as all of the steps have been automated using spreadsheet templates.

3.1 Background: Prospect Theory Prospect theory shows that we sense the pain of a loss more intensely than the joy of an equivalent gain (Kahneman and Tversky, 1979). This behavioral trait is widely used in politics (Norvell, 2004) because a candidate will win more votes by speaking to the harm that an opponent will unloose, if elected, than by speaking to the gains that the candidate will bring to the electorate. Kahneman and Tversky (1979) also described a behavioral trait called the “endowment effect,” which describes the observation that a good once purchased is generally valued higher by the buyer than when it was purchased. For example, respondents to the lottery described in Chapter 1 were also surveyed for their willingness to accept payment for the lottery tickets assuming that the tickets had been given to them (Cook and Wu, 2001). Their average selling price for the 50 and 80% tickets were $49 and $72, respectively, which was a factor of 1.6 times the average price they were willing to pay! The endowment effect shows that we bargain in hopes of gaining a positive net value whether buying or selling and this includes the same good.

34


Another finding from prospect theory is that paired comparisons should be made against a fixed baseline. Thus, when designing surveys, choices are best posed when they are between the several alternatives of interest and a fixed baseline.

3.2 The Direct Value Stated Choice Survey1 The values of the two lottery tickets in Chapter 1 were obtained from what respondents said they would be willing to pay. This survey represents a stated choice survey (Louviere, et. al. 2000), whereas asking recent vehicle buyers what brand they purchased within a market segment and at what price is an example of a revealed choice survey. The differences between the stated choice and the revealed choice surveys were described in detail in Chapter 2, a key feature of the stated choice survey being that it can assess the added value for a proposed new feature in contrast to a revealed choice survey, which is limited to products and features already in use. Respondents to a stated choice survey can be given several new alternatives and asked to select their preferred choice. The expectation is that the respondent’s action will reflect his or her behavior given the same choices in the marketplace. Of course it is important for respondents to be able to evaluate a new feature if a verbal description is insufficient. Graphical, Ordinary Least Square (OLS), Lack Of Fit (LOF) and Maximum Likelihood Estimates (MLE) are four methods that can be used to analyze the outcomes of a stated choice survey. The simplest stated choice survey is binary, between A or B. For example, a respondent may be asked to choose between buying the baseline A or the alternative B. If such a survey is offered to 1000 respondents, total demand is fixed at 1000. If the choice was between buying or not buying, which was the case for the lottery ticket survey in Chapter 1, total demand would not be fixed. If one choice was buy and the second choice was “other,” total demand would not be fixed because “other” includes buy as well as not buy. As discussed in Chapter 2, minimization of cognitive stress is important in a survey as it reduces the likelihood of respondents replacing reasoned choices with oversimplified heuristics or simply not completing the survey because it is too tedious (Arentze, et. al., 2003; Caussade, et. al., 2005; DeShazo and Fermo, 2002). The Direct Value (DV) stated choice survey is designed to minimize cognitive stress on respondents by giving respondents the simplest choice, which is between a fixed baseline at a fixed price and a single alternative offered over a small range of prices (Cook, 2005, pp. 39-52). In keeping with the findings from Prospect Theory, the DV method holds the baseline constant when making paired comparisons. One challenge in seeking survey simplicity is not to compromise statistical accuracy. Another challenge is not to overlook possible interactions.

1

All of the steps listed in this section for computing value, its standard deviation, and degrees of freedom have been automated in spreadsheet templates available from the publisher’s webpage http://www.springer.com/978-1-84628-964-4. See Appendix C.

Analyzing Stated Choice Surveys

35

The most common form of the DV survey has only one attribute that differs between the baseline and the alternative. However, a Conjoint DV survey can be generated in which multiple attributes differ between the baseline and the alternative but the choice set remains binary. In contrast to the standard Conjoint survey (see Appendix D), price is not treated simply as another attribute in the Conjoint DV survey but is varied over a range for each choice set. An application of a Conjoint DV survey is considered in Case Study 8. The baseline choice will often be represented with a subscript using either the number 0 or the letter A, and the alternative will be noted with a dummy subscript i , which can be a number (1, 2, 3, …) or a letter (B, C, D, …). The survey seeks to find the “neutral price” PN for the alternative where half of the respondents choose the alternative and the other half choose the baseline priced at P0 . The difference, PN − P0 , is equal to the value difference, Vi − V0 , between the alternative and baseline. This important property was discussed in relation to Equation (1.2) in Chapter 1. 3.2.1 Graphical Analysis of a DV Survey When the logit model2 is used to evaluate the outcomes of the survey, the neutral price and thus the value difference between the alternative and the baseline can be determined from a “logit plot” of Ln( fi / f 0 ) versus the price difference Pi − P0 as shown in Figure 3.1. As stated above, the price of the alternative is equal to the neutral price at the point where fi = f 0 . When this condition holds, Ln( fi / f 0 ) is equal to 0. The value difference Vi − V0 given by the price intercept Ln( fi / f 0 ) = 0 in Figure 3.1 is seen to be $996. Three additional features should be looked for in logit plots. One is how well the model (as represented by the line) fits the general trend in the points. For example, does the trend show significant curvature making the line a poor representation? If the line is a reasonable representation, is the degree of scatter of the points about the line large or small? A plot of the residuals (differences between the points and the model) is also useful in assessing data quality. The third feature to look for is whether the neutral price is within or outside the range of points. If it is outside the range, confidence in the extrapolated result for value is compromised.

2

The logit model is described in Appendix A.

36


5 4 3

Ln(fi/f0)

2 1 0 -1

$996

-2 -3 -4 -$1,500 -$1,000 -$500

$0

$500

$1,000 $1,500 $2,000 $2,500 $3,000

P i-P 0

Figure 3.1. Logit plot of Ln( f i / f 0 ) on the y-axis versus price of alternative i relative to the baseline price on the x-axis. The value difference Vi − V0 is $996.

3.2.2 Level 2 OLS Regression Analysis of a DV Survey The key results to be extracted from a DV survey are the value of the alternative relative to the baseline, the standard deviation of the relative value, and the price coefficient equal to -1 times the slope of the logit plot. Because demand is fixed in the DV survey, the specific price coefficient is β '' , Equation (A.23). Choosing a price range for the alternative that places the neutral price close to the center of the range is best for measuring the value of the alternative relative to the baseline. An appropriate price range for the alternative with this property can be estimated from a preliminary survey. However, there is an exception to this rule. For example, the value of the automatic transmission for a sporty automobile is not uniformly perceived as an economic good in that not everyone would take it if offered for no extra charge versus the manual transmission baseline. (See Case Study 9.) The survey for this option needs to answer two questions: “What fraction of buyers would choose the automatic transmission over the manual if offered at no extra charge, and how do these buyers value it versus the manual baseline?” These questions can be answered in a DV survey that uses an increasing price range for the option that starts from an initial price equal to the baseline price for the manual. The resulting fractional outcomes are renormalized by dividing through by the fraction of respondents that select the automatic at no extra charge. The neutral price is then computed from the renormalized outcomes, which is used to compute the value of the automatic transmission option relative to the manual baseline.


37

If ni (q) respondents out of n(q) total respondents to a DV survey chose alternative i for trial (choice set) q, the mean value of the choice probability for the population can be estimated using the sample frequency fi (q ) = ni (q) / n(q) . Thus, the logit model utility difference relative to the baseline is given by: ⎧ U i (q) − U 0 ⎛ fi (q) ⎞ ⎪⎪ Ln ⎜ ⎟ ≡ Yi ,o (q ) = ⎨ ⎝ f 0 (q) ⎠ ⎪ ⎪⎩ β '' ⎡⎣Vi − V0 − ⎡⎣ Pi (q ) − P0 ⎤⎦⎤⎦

(3.1)

where the utility, value, and price of the alternative are U i (q) , Vi , and Pi (q ) , respectively, and the utility, value, and price for the baseline are U 0 , V0 , and P0 . If the price of the alternative in Equation (3.1) is adjusted to PN , where respondents in aggregate are indifferent to the two choices, the value difference between the two alternatives, Vi − V0 , is simply equal to their price difference, PN − P0 : Vi − V0 = PN − P0

(3.2)

which proves the relationship discussed earlier and shown in Figure 3.1. The theoretical estimate of the variance for the utility difference between alternative i and the baseline choice 0 is given by the general, multinomial form: ⎛ ⎛ f (q) ⎞ ⎞ ⎤ 1 ⎡ 1 − f 0 (q ) 1 − f i (q ) + + 2 ⎥ (3.3) VAR ⎜ Ln ⎜ i ⎟ ⎟⎟ = VAR (Yi ,0 (q ) ) ≅ ⎢ ⎜ f ( q ) n ( q ) f ( q ) f ( q ) i ⎠⎠ ⎣ 0 ⎦ ⎝ ⎝ 0

Equation (3.3), which was derived from the leading terms in a Taylor expansion for the variance of Ln ( fi (q ) / f 0 (q ) ) , is accurate for large sample sizes n(q) . It incorporates the multinomial expressions for the variance and covariance for the factors fi (q ) and f 0 (q ) , the number 2 coming from the covariance. When the problem is binary with fi = f and f 0 = 1 − f , Equation (3.3) reduces to the better known form: ⎛ ⎛ f (q) ⎞ ⎞ 1 VAR ⎜⎜ Ln ⎜ ⎟ ⎟⎟ = VAR (Y (q) ) ≅ n(q ) f (q )[1 − f (q)] ⎝ ⎝ 1 − f (q) ⎠ ⎠

(3.4)

The variances given by Equations (3.3) and (3.4) represent variances of the mean of the utility differences equal to a sample variance s 2 (q) divided by n(q) having n(q) − 1 df (degrees of freedom).

38


Consider the problem of determining the relative values of vacation locations B and C relative to the baseline vacation location A. Two surveys are required using the DV method, one for B versus A as shown in Figure 3.2 and one for C versus A as shown in Figure 3.3. For simplicity, only the simulated outcomes of the DV survey in Figure 3.2 will be analyzed here. On setting fi = f B = f for the binary choice set, Equation (3.1) yields six, linear simultaneous equations of the form: ⎡1 ⎢ ⎢1 ⎢1 ⎢ ⎢1 ⎢1 ⎢ ⎢⎣1

PB (1) − PA ⎤ ⎡ Ln( f (1) /(1 − ⎥ ⎢ Ln( f (2) /(1 − PB (2) − PA ⎥ ⎢ PB (3) − PA ⎥ ⎡ α ⎤ ⎢ Ln( f (3) /(1 − =⎢ ⎥ PB (4) − PA ⎥ ⎣⎢ − β ''⎦⎥ ⎢ Ln( f (4) /(1 − ⎢ Ln( f (5) /(1 − PB (5) − PA ⎥ ⎥ ⎢ PB (6) − PA ⎥⎦ ⎣⎢ Ln( f (6) /(1 −

f (1)) ⎤ f (2)) ⎥⎥ f (3)) ⎥ ⎥ f (4)) ⎥ f (5)) ⎥ ⎥ f (6)) ⎥⎦

(3.5)

The first matrix on the left represents the design matrix [X]. The elements of the next matrix having two rows and a single column represents the two unknowns α = β '' (VB − VA ) and − β '' . The value difference VB − VA can be computed once

α and β '' have been determined. For simplicity, price was entered into this matrix as a positive quantity, which is why the price coefficient was entered into the vector of unknowns as - β '' . The six rows by one column matrix on the right is the outcomes vector [Y] for the utilities as computed from the logit model. The OLS solution to Equation (3.5) is given by:

[ λ ] = [ XS ][ Y ]

(3.6)

where [ λ ] is the vector of unknowns, which for this problem is given by: ⎡ α ⎤

[ λ ] = ⎢ − β ''⎥

⎣ ⎦ The matrix [ XS ] in Equation (3.6) is referred to here as the “solution” matrix

given by −1

[ XS ] ≡ ⎡⎣[ X '][ X]⎤⎦ [ X '] The matrix

[ X ']

(3.7)

is the transpose of the design matrix. The elements of the

solution matrix are written as ωij (q) in which the double index ij is used to denote that, in general, a given attribute i can have multiple levels j . The index q refers to the trial number (choice set) which ranges from 1 to z (equal to six for this problem). In the spreadsheet computations, [X], [XS], and [Y] were given the


39

not-bolded array names of X, XS, and Y, respectively, in the spreadsheet. This naming convention is followed throughout unless otherwise noted.

Trials

Location A

Location B

1 $2,000

Select one

$1,000

2 $2,000

Select one

$1,500

3 $2,000

Select one

$2,000

4 $2,000

Select one

$3,000

5 $2,000

Select one

$4,000

6 $2,000

Select one

$5,000

Figure 3.2. DV Survey form for assessing the value of vacation location B relative to baseline location A

Trials

Location

Location

A

C

1 $2,000

Select one

$1,000

2 $2,000

Select one

$2,000

3 $2,000

Select one

$3,000

4 $2,000

Select one

$4,000

5 $2,000

Select one

$5,000

6 $2,000

Select one

$6,000

Figure 3.3. Second DV survey for assessing the value of vacation location C versus A

The OLS regression solution represented by Equation (3.6) can have different levels of assumptions for arriving at the statistical properties of the coefficients. The standard assumption (called Level 1 here) is that the population variances S 2 (q) are constant over the q trials. This leads to two ways of estimating S 2 (q) . One is based upon a pooled variance computed as a sample df weighted-average of the measured sample variances s 2 (q) . The df for the pooled variance itself is equal to the summation of n(q) − 1 over the z trials. The other is based upon a LOF variance computed as a summation of the z differences squared between the actual and model outcomes, the result being divided by the LOF df equal to z − 2 . The model outcomes vector, [YModel], is given by:

[ YModel ] = [ X][ λ ]

(3.8)

40


However, the assumption of a constant population variance is not supported for most problems of interest. Consequently, a less restrictive Level 2 set of OLS assumptions (Cook, 2005, pp. 137-146) will be used here as follows3: (1) The population variances for the trials are assumed to differ and therefore the sample variances are not pooled. (2) The sample variances for the trials are computed using formulas based upon the binomial or multinomial distribution as required. (3) The statistical distribution for the parameters of interest are expected to be approximately normal as a result of the Central Limit Theorem. (4) The df for the variance of each coefficient for each attribute of interest are computed using Satterthwaite’s (1946) method. (5) Satterthwaite’s approximate t-test is used. The spreadsheet form for the design matrix [X] and the simulated outcomes for the fractions choosing locations A and B are shown in Table 3.1. (The convention is used here of listing the unknown coefficients at the top of the column in the design matrix whose elements are multiplied by the unknowns.) The elements of vector [VarY] are the variances of [Y] given by Equation (3.4). The OLS solution for the unknowns is the [OLSC] vector shown in Table 3.2. The standard deviations (standard errors) sij , which are elements of the vector [SD] in Column X, were computed by taking the square root of the variances4 given by: sij2 =

z

ωij2 (q ) s 2 (q )

q =1

n( q )

∑

= MMULT(XS^2,VarY)

(3.9)

The convention of showing the spreadsheet expression to the right of the mathematical expression is used in Equation (3.9) and elsewhere. The sample size n(q) for trial q does not appear in the spreadsheet expression because the elements of [VarY] are the variances of the sample mean [Y]. The variance sij2 is computed from a weighted sum of the sample variances in Equation (3.9). Thus, it follows from the Central Limit Theorem that the distributions for the OLS coefficients are approximately normal. The OLS coefficients are assumed to follow Satterthwaite’s approximate t-distribution when the sample size is finite. The elements of Satterthwaite’s df vector, [df], are computed as: ⎡ sij2 ⎤ dfij = ⎣ ⎦ dij

3

2

=(SD^4)/d

(3.10)

All references to the OLS method in what follows implicitly impose the Level 2 assumptions for brevity unless noted otherwise. 4 The taking of the square root of a variance commonly results in a standard deviation and this is why we prefer not to use the conventional term “standard error.”


41

The term dij in Equation (3.10) is an element of vector [d] in Table 3.2 given by: dij =

z

ωij4 (q ) s 4 (q )

∑ n (q)[n(q) − 1] q =1

2

=MMULT(XS^4,VarY^2/(n-1))

(3.11)

The number of respondents is assumed to be n(q) = 100 for each trial q . Note that the Satterthwaite df are 151 and 206 in Table 3.2, which, although well below the pooled df of 594, are large in that the normal distribution could be substituted for the t-distribution without any consequence. This will always be true for large national surveys. Satterthwaite’s approximate t-statistic comes into play when the number of respondents are small as in preliminary and focus group surveys. Thus, the above method works across the full range of respondents. Excellent agreement was found between Level 2 OLS predictions and Monte Carlo simulations for both the binomial and Poisson distributions (Cook, 2005, pp. 311-323). The OLS computations in Table 3.2 used the theoretical variances given by Equation (3.4) to compute the standard deviations of the coefficients. The implied assumption is that the logit model is the correct underlying description of the outcomes. It is critical to check this assumption using a logit plot of the utilities versus the price of the alternative minus the price of the baseline as shown in Figure 3.1 to confirm that the points are uniformly distributed about the line. In this example, the distribution of points is quite good. But situations can arise when the logit model poorly represents the data; a good example being when there are two camps, one which has a positive value for the alternative and a second of similar size, which has a negative value for it. The theoretical variances given by Equation (3.4) should also be checked against the LOF variance using the F-ratio test. If the LOF variance is judged to be significantly higher than the theoretical estimate, the LOF result should be used. Although the LOF results are not included for this specific problem, they are generated automatically in the templates. Table 3.1. The design matrix [X] for assessing the value of vacation location B versus A is located in Area O78:P83 N

O

P

Q

R

S

T

Ln(fB/fA)

76 77

Trials

α

−β′′

fA

fB

VarY

Y

78

1 2 3 4 5 6

1 1 1 1 1 1

-1000 -500 500 1500 2000 2500

0.019 0.083 0.163 0.747 0.901 0.943

0.981 0.917 0.837 0.253 0.099 0.057

0.5362 0.1308 0.0733 0.0529 0.112 0.1866

3.943 2.396 1.637 -1.083 -2.207 -2.809

79 80 81 82 83 84 85

Cell S78 =1/(n*(R78*(1-R78))) (drag down)

86

Cell T78 =LN(R78/Q78) (drag down)

42


Satterthwaite’s approximate t-statistics are listed in Column AA of Table 3.2 and the pairwise errors (PWE) are listed in Column AB. The experiment-wise errors (EWE) listed in Column AC were computed using Bonferroni’s approximate method, which for this problem is simply two times the PWE. (See Mendenhall and Sincich, 1995, p. 895.) Table 3.2. Computations of the coefficients and their statistics for the value of B relative to A using the OLS method V 92 93 94

A

W

X

Y

Z

AA

AB

AC

OLSC

SD

d

df

t

PWE

EWE

2.6E-01

3.2E-05

151

7.3

9.9E-12

2.0E-11

1.7E-04

3.9E-18

206

-11.5 4.0E-24

8.0E-24

1.919 α −β′′ -1.93E-03

AE

AF

Value

996

95 96 97

OLSC =MMULT(X,Y)

df =SD^4/d

SD =SQRT(MMULT(XS^2,VarY))

98

t =OLSC/SD

99

d =MMULT(XS^4,VarY^2/(n-1))

Cell AF93 =-W93/W94

AAB93:AB94 =TDIST(ABS(t),df,1) Cell AC93 =2*AB93 (drag down)

3.2.3 Computing the Standard Deviation and df of Value in a DV Survey Once the unknown coefficients in Equation (3.6) are determined, their ratio given by α / β '' is equal to the value difference between the alternative and baseline:

α = ⎡V − V ⎤ β '' ⎣ i 0 ⎦

(3.12)

It follows from Equation (3.2) and (3.12) that5: PN = P0 − α /(− β '')

(3.13)

The variance of the neutral price, PN , in Equation (3.13) is the same as the variance for value, and for large sample sizes, n, the variance of PN is given by: Var ( PN ) = Var (Vi − V0 ) ≅

Var (α ) 2α Cov(α , − β '') α 2Var ( β '') − + (− β '') 2 (− β '')3 ( − β '') 4

(3.14)

When the general double index notation ij is used for the coefficients, the covariance of ij and kl is given by:

5

It is important to keep track of the sign for the price coefficient as the matrix algebra solution with positive prices yields not β '' but − β '' , which is the quantity that enters into the computations for the variance of value.


Cov(ij , kl ) =

∑ω

ij

(q )ωkl (q )Var (Y (q ))

43

(3.15)

q =1, N

Recall that ωij (q) is element ij in column q of the solution matrix. If Var (Y (q ) ) was equal to one over the q trials, then Equation (3.15) would generate the ijkl element of the unit variance variance-covariance matrix under the heading of COV in Column AT of Table 3.3. The solution matrix [XS] for the vacation problem is shown in Area AM87:AR88 in Table 3.3. For this problem ij in Equation (3.15) is α , and kl is β '' . The elements of the vector [XSAlphaBeta] are equal to the products ωα (q )ωβ (q) taken from the solution matrix, which are used to compute the covariance defined in Equation (3.15). The products given by ωα (q )ωβ (q) are computed in Row AM90:AR90. When summed, they yield in Cell AT90 the symmetric off diagonal elements in the unit variance, variance-covariance matrix. The standard deviation of value equal to $85.6 is computed in Cell AP91. Value, computed in Cell AF93 in Table 3.2, is equal to $996. Thus, the t-statistic for value is 11.7 (= 996/85.6). Table 3.3. The [XS] solution matrix (Area AM87:AR88) and the elements of the covariance vector [XSAlphaBeta] AL 85 86 87 88 89 90 91 92

AM

AN

AO

AP

Solution Matrix XS 1 2 3 4 1.9E-01 1.1E-01 α 3.2E-01 2.8E-01 6.8E-05 −β -1.9E-04 -1.4E-04 -3.4E-05 XSAlphaBeta -6E-05 -3.8E-05 -6.607E-06 7.4691E-06 CovAlphaBeta = -3.55E-05 SDValue = dfValue = VarValue 7.32E+03

AQ

AR

5 6.8E-02 1.2E-04

6 2.5E-02 1.7E-04

AS

αα ββ

8.04E-06 4.31E-06 −αβ 85.6 413

93

XS =MMULT(MINVERSE(MMULT(TRANSPOSE(X),X)),TRANSPOSE(X))

94

XSAlphaBeta =AM87*AM88 (drag across)

95 96 97

COV 0.2 1.0E-07 -8.5E-05

CovAlphaBeta =MMULT(XSAlphaBeta,VarY) VarValue =X93^2/W94^2-2*W93*CovAlphaBeta/(W94)^3+W93^2*X94^2/W94^4 SDValue =SQRT(VarValue)

98

AT87 =SUMSQ(AM87:AR87)

99

AT88 =SUMSQ(AM88:AR88) AT90 =SUM(AM90:AR90)

100

AT

dfValue see Table 3.4

The df for the variance of value is estimated most simply by using Satterthwaite’s method in conjunction with the inverse logit plot with price on the y-axis and the logit function on the x-axis. When the variance for the logit function given by Equation (3.4) is divided by β '' squared, the result is equal to an effective variance for price in the inverse logit plot.

44


The linear set of equations in matrix form that connect the parameters in the inverse logit plot is shown in Equation (3.16) for the binary model. The approximation described above for converting the variance of the logit function into an effective price variance for the inverse plot should have minimal impact on the computation of the df for the variance of value, which is the function of interest. In this regard, value and β '' computed from the inverse plot, Equation (3.16), were $993 and 0.00197, respectively, which are close to the findings for these parameters from the regular logit plots, Equation (3.5). The first matrix on the left side of Equation (3.16) consists of six rows by two columns and represents the design matrix [XI] for the inverse logit arrangement. The solution matrix derived from it is [XIS]. The numerical results for these two matrices are shown in Table (3.4) which was taken from the spreadsheet used in the analysis of this problem. With the spreadsheet array names X and XS replaced by XI and XIS, respectively, the vector of standard deviations [SD] were computed in Table 3.4 by taking the square root of Equation (3.9) and the elements of the vector [d] was computed using Equation (3.11). Finally, the df for value equal to 413 was computed from Equation (3.10) in Cell AO125 Table 3.4. This result was then copied into Cell AP92 in Table 3.3, which was in the same worksheet. ⎡ ⎢1 ⎢ ⎢ ⎢1 ⎢ ⎢ ⎢ ⎢1 ⎢ ⎢ ⎢1 ⎢ ⎢ ⎢1 ⎢ ⎢ ⎢ ⎢1 ⎣

⎛ f (1) ⎞ ⎤ Ln ⎜ ⎟⎥ ⎝ 1 − f (1) ⎠ ⎥ ⎛ f (2) ⎞ ⎥⎥ Ln ⎜ ⎟ ⎝ 1 − f (2) ⎠ ⎥ ⎡ PB (1) − PA ⎤ ⎥ ⎢ ⎥ ⎛ f (3) ⎞ ⎥ PB ( 2 ) − PA ⎥ ⎢ Ln ⎜ ⎟⎥ ⎝ 1 − f (3) ⎠ ⎥ ⎡ V ⎤ ⎢ PB ( 3) − PA ⎥ ⎥ ⎢ ⎥=⎢ ⎛ f (4) ⎞ ⎥ ⎣ −1/ β ''⎦ ⎢ PB ( 4 ) − PA ⎥ Ln ⎜ ⎟⎥ ⎢ P ( 5) − P ⎥ A ⎝ 1 − f (4) ⎠ ⎥ ⎢ B ⎥ ⎥ 6 − P P ⎢ ( ) B A⎥ ⎛ f (5) ⎞ ⎥ ⎣ ⎦ Ln ⎜ ⎟⎥ − 1 (5) f ⎝ ⎠ ⎥ ⎛ f (6) ⎞ ⎥ Ln ⎜ ⎟⎥ ⎝ 1 − f (6) ⎠ ⎦

(3.16)


45

Table 3.4. Computation of the df for value using Satterthwaite’s method with the inverse logit plot with price on the y-axis and the logit function on the x-axis AL 111

AM

AN

1 2 3 4 5 6

Value 1 1 1 1 1 1

-1/Beta 3.94 2.40 1.64 -1.08 -2.21 -2.81

Value -1/Beta

1 0.1362 0.0973

Value -1/Beta

SD 86 45

XI

112 113 114 115 116 117

AO

AP

AQ

AR

2 0.1492 0.0558

3 0.1556 0.0355

4 0.1784 -0.0374

5 0.1878 -0.0675

6 0.1928 -0.0837

d 1.3E+05 2.0E+04

df 413 197

118 119 120 121

XIS

122 123 124 125 126

3.2.4 LOF Estimate of the Standard Deviation of Value The templates also use the LOF method to estimate the standard deviation of value using an inverse logit plot with price on the y-axis and the logit function on the xaxis. The reason for this is that the standard deviation for value computed from the square root of the variance given by Equation (3.14), as stated earlier, is correct only if the logit form is a representative model for the data, which may not always be the case. Thus, the conservative approach is to take the larger of the two standard deviations as being representative. Value and the price coefficients are also computed in the templates using the MLE method, which is described at the end of this chapter and used in Case Studies 2 and 10.

3.3 The Multinomial Stated Choice Survey The vacation location problem just considered using the DV method with two separate surveys can also be analyzed using a single multinomial survey as shown in Figure 3.4 in which respondents are asked to select one of three choices listed in each trial (choice set).6 The dollar amounts represent the prices of the vacations at each location. For this particular example, interactions should not be present

6

In contrast to Figures 3.2 and 3.3, the survey design in Figure 3.4 does not rigorously support the making of binary comparisons to a common baseline due to the baseline price not being fixed.

46


because the choices are mutually exclusive. From the structure of the prices shown in Figure 3.4, the relative value of C to A is expected to be higher than B relative to A. This tentative conclusion might follow from a small, preliminary survey. Each trial in the survey shown in Figure 3.4 will generate in the aggregate three fractional responses: f A , f B , and fC . These fractions in turn generate two logit model outcomes that are coupled to the unknown coefficients α, α′, and β′′ for each trial by the expressions: Y (q ) ≡ Ln ( f B (q ) / f A (q ) ) = α − β '' ( PB (q ) − PA (q ) )

(3.17)

Y '(q ) ≡ Ln ( f C (q ) / f A ( q ) ) = α '− β '' ( PC (q ) − PA ( q ) )

(3.18)

and

where PA (q ) , PB (q) , and PC (q) are, respectively, the prices of A, B, and C for trial q.

Trials 1

Location A $1,000

Vacation Prices Location Location B C $2,000 $3,000

Select one 2

$1,000

$3,000

$4,000

3

$2,000

$2,000

$4,000

4

$2,000

$3,000

$3,000

Select one

Select one

Select one

Figure 3.4. The choice model example contains four choice sets for measuring the values of vacation locations of B and C relative to location A. The check marks simulate a typical response.


47

The above equations can be arranged into a single, consolidated set given by: ⎡1 ⎢1 ⎢ ⎢1 ⎢ ⎢1 ⎢0 ⎢ ⎢0 ⎢0 ⎢ ⎣⎢ 0

0 $1, 000 ⎤ ⎡ Y (1) ⎤ ⎥ ⎢ Y (2) ⎥ 0 $2, 000 ⎥ ⎢ ⎥ ⎢ Y (3) ⎥ 0 $0 ⎥ ⎥⎡ α ⎤ ⎢ ⎥ 0 $1, 000 ⎥ ⎢ Y (4) ⎥ ⎥ ⎢ α' ⎥=⎢ 1 $2, 000 ⎥ ⎢ Y '(1) ⎥ ⎥ ⎢⎣ − β ''⎥⎦ ⎢ ⎥ 1 $3, 000 ⎥ ⎢Y '(2) ⎥ ⎢Y '(3) ⎥ 1 $2, 000 ⎥ ⎥ ⎢ ⎥ 1 $1, 000 ⎦⎥ ⎣⎢Y '(4) ⎦⎥

(3.19)

The eight rows by three columns matrix on the left side of Equation (3.19) is the design matrix [X] for this problem. The first four prices shown in the third column of the design matrix are the differences in price between B and A in Figure 3.4. The fifth through eighth prices are the differences in price between C and A. Because the prices of the alternatives less the prices for the baseline were entered into this matrix as a positive quantity for simplicity, the price coefficient must be entered into the vector of unknowns as - β '' similar to what was done in the DV study earlier. The single column matrix on the RHS represents the outcome vector [Y] . Its elements are Y (q ) for the first four trails and Y '(q ) for the last four trials.7 The spreadsheet representation of the design matrix and the simulated outcomes are shown in Table 3.5. A simulated random sample of n = 100 respondents was again used. The columns of the design matrix are headed by the respective unknown coefficients associated with the columns. The computations used in the spreadsheet are shown at the bottom of the Table 3.5. The variances shown in Column L as [VarY] were computed from Equation (3.3). The model coefficients are computed in the standard manner for a set of linear simultaneous equations: ⎡ α ⎤ ⎢ α ' ⎥ = XS Y ⎢ ⎥ [ ][ ] ⎢⎣ − β ''⎥⎦

7

(3.20)

The consolidated form design matrix [X] in Equation (3.19) can be split into two separate linear systems with one for Y ( q ) and the other for Y '( q ) each having four rows and two columns.


48

Table 3.5. The spreadsheet display of the design matrix and the outcomes for the simulated stated choice experiment E

F

48 49

G

H

I

Design Matrix

J

K Outcomes fB first four then fC Y

L

50 Trials

α

α'

-β''

fA

51

1

1

0

1000

0.3500

0.3400

-0.0290

0.05798

52

2

1

0

2000

0.7500

0.0900

-2.1203

0.12444

53

3

1

0

0

0.0800

0.7900

2.2900

0.13766

54

4

1

0

1000

0.1100

0.0800

0.2700

0.21591

55

1

0

1

2000

0.3500

0.3100

-0.1214

0.06083

56

2

0

1

3000

0.7500

0.1600

-1.5449

0.07583

57

3

0

1

2000

0.0800

0.1300

0.4855

0.20192

58

4

0

1

1000

0.1100

0.8100

1.9966

0.10325

VarY

59

Area K51:K58 = Y =LN(J51/I51) (drag down) Area L51:L58 = VarY =((1-I51)/I51+(1-J51)/J51+2)/n (drag down)

60 61

The solution matrix [ XS ] for this problem is shown in Table 3.6. The spreadsheet expression for [ XS ] is shown at the bottom of Table 3.6. Satterthwaite’s df in

Column R of Table 3.7 are close to the maximum of 396 (=4×99) because the variances in Column L of Table 3.5 are not far apart. (The maximum df is not 8×99 because of the four zeros in each of the α and α ' columns.) The pairwise errors (PWE) are listed in Column T. The experiment-wise errors (EWE) in Column U were again computed using Bonferroni’s approximate method. The values for locations B and C relative to A, which are listed in Column W, were computed by dividing α and α ' by β '' . The analysis of another multinomial stated choice survey is given in Case Study 3.

[ ]

Table 3.6. The solution matrix XS

67 68 69 70 71 72 73

F

G

H

I

J

K

L

M

N

α α' -β''

1 0.25 0 0

2 0 -0.5 0.00025

3 0.5 0.5 -0.00025

4 0.25 0 0

1 0 0.25 0

2 -0.25 -0.25 0.00025

3 0 0.25 0

4 0.25 0.75 -0.00025

Area G68:N70 = XS =MMULT(MINVERSE(MMULT(TRANSPOSE(X),X)),TRANSPOSE(X))


49

Table 3.7. Computations of the unknown coefficients, standard deviations, Satterthwaite’s df, t-statistics and approximate pairwise and experiment-wise errors. Column W shows the values of the vacation locations relative to location A. N 50

O

P

Q

R

S

T

U

OLSC

SD

d

df

t

PWE

EWE

V

51

α

2.091 2.5E-01 1.5E-05

270

8.3

1.9E-15

5.6E-15

52

α' -β''

4.180 3.8E-01 5.8E-05 -2.0E-03 1.7E-04 2.0E-18

363 379

11.0 -12.0

1.0E-24 1.6E-28

3.0E-24 4.8E-28

PWE Cell U51 Cell W51 Cell W52

=TDIST(ABS(t),df,1) =T51*3 (drag down) =-O51/O53 =-O52/O53

53

W

VB-VA = $1,052 VC-VA = $2,103

54 55 56 57 58 59

OLSC SD d df t

=MMULT(XS,Y) =SQRT(MMULT(XS^2,VarY)) =MMULT(XS^4,VarY^2/(n-1)) =SD^4/d =OLSC/SD

3.4 Maximum Log Likelihood Estimate The MLE method provides a more robust solution than the OLS in analyzing stated choice surveys using the logit model. The MLE is particularly advantageous when the fraction of respondents selecting a specific choice is zero or one as in Case Study 10 or when tests are censored (e.g. a fatigue test stopped before failure). In practice, a maximum log likelihood estimate (MLLE) is used because it simplifies the computations by converting a product of terms into their sum. The MLLE expression for the logit model is given by: fij ( q ) ⎞ ⎛ ⎡ ⎤ = ∑ ⎢ ∑∑ f ij (q ) Ln fîj (q) ⎥ max L ≡ Ln ⎜ ∏ ⎡ fîj (q) ⎤ ⎟ ⎦ ⎜ i, j ,q ⎣ ⎟ q ⎢ i j ⎣ ⎦⎥ ⎝ ⎠

(

)

(3.21)

In the double index notation, i refers to the type of attribute and j refers to its level, the double summations being over the N (q) terms in the choice set (trial), q . The function fij (q) is the observed fraction of respondents choosing attribute i at level j in trial q , the summation over q being over the 1 to z trials. This function appears in the exponent of the top expression because it is proportional to the frequency that attribute ij was selected by the respondents. The function fˆ (q) is the model estimate of f (q) given by: ij

ij

fîj ≡

(

)

Exp β '' ⎡⎣Vij − Pij (q) ⎤⎦ ∑∑ Exp β ''⎣⎡Vlm − Plm (q)⎦⎤ l

m

(

)

(3.22)

50


The model estimate can be computed by using the spreadsheet’s Solver function, which resides on the Tools menu, to find the maximum of the log likelihood. The MLLE solution to the multinomial choice survey of Figure 3.4 is shown in Table 3.8. For completeness, the prices and fractions for the vacation locations are recreated in Tables 3.9 and 3.10 in formats that support the MLLE procedure.8 The first step in solving for the unknown coefficients α1 , α 2 , and α 3 (spreadsheet names AEst, BEst, and CEst, respectively) was to generate initial estimates for them located in Cells X13:X15 in Table 3.8. Then α and α ' are computed using the relations α = α 2 − α1 and α ' = α 3 − α1 . Because α and α ' are computed relative to α1 , this coefficient was fixed at 0 for the computations. The initial estimate of β '' named BetaEst was entered into Cell X16. The value of B relative to A given by VB − VA is equal to α / β '' and the value of C relative to A given by VC − VA is equal to α '/ β '' . The exponentials of the estimated utilities are computed for each trial (Rows 13 through 16) in Columns AA through AC, respectively, in Table 3.8 for vacation locations A through C. The outcomes are then summed for each trial in Column AD to form the denominator in Equation (3.22). The estimated fractions, fˆ , for i

i = A → C are noted as Est fi . In Columns AA through AC for Rows 20 through 23, the logs of these functions are multiplied by their respective experimental outcomes f i .

The log likelihoods for each trial listed in Column AD are formed by summing across the entries in Rows 20 through 23. The log likelihoods for each trial in Column AD are then summed to form the total log likelihood estimate in Cell AD24. Once the initial estimates and the computations have been set up in this manner, Solver is selected from the Tools pull-down-menu and instructed to maximize the outcome in Cell AD24 by adjusting the initial estimates entered for BEst, CEst, and β '' in Rows 14 through 16 of Column X. Caution is advised in accepting a Solver solution for the unknown coefficients as Solver may find subsidiary, local maxima. It is worth the effort to obtain first the OLS solutions and take, as a rule of thumb, 80% of the OLS coefficients as the initial estimates for starting the MLLE solution. This should assure that the correct maximum is found. The MLLE results for VB − VA , VC − VA , and β '' are close to the OLS results in Table 3.7. Using the MLLE model results Ln( fˆ / fˆ ) representing the means of i

A

the utilities of i = B or C relative to A, computations of R 2 termed the coefficient of determination showed that the solution given in Table 3.8 explained better than

8

The spreadsheet used for solving this problem named MLLE and OLS Analysis of Vacation Survey is included in the templates. It can be used as a guide for setting up MLLE solutions for other multinomial problems.


51

97% of the variance in the utilities, R 2 being computed from the variation between the model and actual means given by9:

∑ ∑ ⎡⎢⎣ Ln ( ( fˆ (q) / fˆ (q) ) − Ln ( ( f (q) / f i

A

i

i = B ,C q

R2 = 1 −

∑∑

i = B ,C q

⎡ ⎡ ⎢ Ln ( ( fi (q) / f A (q) ) − Avg ⎢ ⎢⎣ ⎢⎣ j = B ,C

A

(q ) ) ⎤⎥ ⎦

2

⎤⎤ Ln ( f j (q ) / f A (q ) ⎥ ⎥ ⎥⎦ ⎥⎦

∑ ∑( ( q

))

2

(3.23)

In summary, both the Level 2 OLS method and the MLLE method can be run on a spreadsheet and they provide similar results for the unknown coefficients for problems that can be reasonably represented using the logit model. However, the MLLE method usually requires special software to compute the asymptotic standard deviations (standard errors) for the coefficients. Nevertheless, the standard deviations computed from the Level 2 OLS model from the square root of Equation (3.3) should be close to those from the MLLE model as both use large sample size asymptotic approximations. (See Case Study 2.) If the logit model is not an accurate representation of the outcomes, then the MLLE and the OLS methods will give poor estimates for the standard deviation of the coefficients. As already discussed in this chapter, graphical methods should be used to check the validity of using the logit model for representing the outcomes of a survey. Table 3.8. MLLE results and computations for the multinomial vacation locations survey W

X

MLLE Coeff.

11 12

1 2 3 4

17 18 19 20 21 22 23

9

Trial 1 2 3 4

0.14 0.14 0.02 0.02

AC

AD

EXP(UB)

EXP(UC)

Sum EXP(U)

0.14 0.02 0.14 0.02

0.16 0.02 0.02 0.16

MAXIMIZE

16

1006 2068

Trial EXP(UA)

AB

25

15

VB-VA = VC-VA =

AA

24

14

0.00 1.99 4.10 1.98E-03

Z

0.43 0.18 0.18 0.20 Sum fi × fB × fC × fA × Ln(Est f A) Ln(Est f B) Ln(Est f C) Ln(Est fi ) -0.40 -0.39 -0.31 -1.10 -0.20 -0.20 -0.34 -0.73 -0.18 -0.20 -0.27 -0.66 -0.26 -0.19 -0.18 -0.62 -3.11

13

AEst BEst CEst β''

Y

The outcome for R2 computed from the variation of the means from the OLS model about the actual means was identical to the MLLE result to two decimal places.

52


Table 3.9. Prices for the vacation locations survey are recreated in a convenient format for the MLLE analysis AB 2 3

Trial 1 2 3 4

4 5 6 7 8

AC

AD

AE

Vacation Prices Location Location Location A B C $1,000 $2,000 $3,000 $1,000 $3,000 $4,000 $2,000 $2,000 $4,000 $2,000 $3,000 $3,000

Table 3.10. Fractions selecting the vacation locations survey are recreated in a convenient format for the MLLE analysis

4 5 6 7 8

AG Trial 1 2 3 4

AH fA 0.35 0.75 0.08 0.11

AI fB 0.34 0.09 0.79 0.08

AJ fC 0.31 0.16 0.13 0.81

3.5 Summary o o o

o

The DV method represents an uncomplicated form of the stated choice survey and as a consequence it should minimize cognitive stress. There should be minimal loss of accuracy because it offers greater flexibility in the selection of the number of prices for consideration. The Level 2 OLS method can be used to analyze binary and multinomial stated choice surveys using a spreadsheet without the need for special software required by the MLE method. The computations have been automated using the spreadsheet templates, which can be downloaded from the publisher’s webpage: http://www.springer.com/978-1-84628-964-4.

3.6 Supporting Case Studies Case Study 2: Simulated Survey of Boston to Los Angeles Flights Case Study 3: Analysis of a Multinomial Stated Choice Survey Case Study 7: Value of Interior Noise in a Luxury Automobile Case Study 8: Quantifying the Trade-off between Acceleration Performance and Fuel Economy Case Study 9: Value of Mustang Options Case Study 10: Simulated Survey of Choice between Auto and Transit Bus Modes


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3.7 Exercises 3.1 Discuss why politicians often spend more time describing their opponent's weaknesses to the electorate than listing their own strengths? 3.2 Your friend visited an antique store and purchased a chair for $550. Another antique dealer across the street saw your friend loading the chair into her car and walked over and asked if she would sell the chair to him. Assume that she was willing to sell the chair. Discuss what her asking price might be. 3.3 You are the chief product planner for the next all new model for the Ford Mustang. You need to reduce the variable cost by $200 to reach the target cost. A member of the planning group has suggested eliminating the automatic window regulators, which are standard equipment on the current model and cost $225 per car. Discuss how you would evaluate the quantitative business case for this suggested action. 3.4 You are in charge of developing the next model of your company's laptop computer, which sells for $1,200. (a) Construct a preliminary DV survey for measuring the value of reducing the weight of the current laptop computer from six to four pounds. Your guess is that the value of the weight save would be $150. (b) Discuss how you would select a convenience sample of 30 respondents from the company to take the survey. (c) Discuss how you would administer the preliminary survey. 3.5 Assume that in Exercise 3.4, the preliminary value found was $200 for reducing by two pounds the weight of the current model laptop. (a) Develop the final DV survey for this exercise assuming that you want to have the standard deviation less than $20. You expect to use the survey with series of focus groups having 25 participants in each. (b) Discuss how you would organize and run a focus group. (c) How many focus groups will you need? (d) How will you deliver the survey to minimize anchoring? 3.6 Derive the expression for the variance of the neutral price given by Equation (3.14). Discuss why the variance of the neutral price is equal to the variance of the value difference between the alternative and the baseline. 3.7 A DV survey (below) was run with 9 prices for the alternative. The price of the alternative was the same as the price of the baseline for trial 1. Determine the value of the alternative by those that considered it an economic good. Use the DV 9 Binary Template for the analysis. Hint: Handle the singularity for trial one by first ignoring it and solving for the economic good fraction for trial 1 using the MLLE worksheet. Then use this fraction for trial 1 in the input data to obtain the economic good value using the Level 2 OLS solution. You should find that the Level 2 OLS solution for value is 57.30 and its standard deviation is 2.24.

54


From DV Survey Baseline Alternate Price Prices P Trial P0 50 50 1 50 60 2 50 70 3 50 100 4 50 110 5 50 120 6 50 130 7 50 140 8 50 150 9

1-f 0.2 0.32 0.44 0.52 0.56 0.68 0.72 0.84 0.88

Initial data f 0.8 0.68 0.56 0.48 0.44 0.32 0.28 0.16 0.12

n 100 100 100 100 100 100 100 100 100

Converted to Economic Good f 1-fEG fEG n 0 1 100 0.15 0.85 100 0.3 0.7 100 0.4 0.6 100 0.45 0.55 100 0.6 0.4 100 0.65 0.35 100 0.8 0.2 100 0.85 0.15 100

3.8 Derive Equation (3.3) for the variance of the utility difference between i and j for a sample size n(q). Hint: Look up Multinomial Distribution on Wikipedia as you will need to know the variance and covariance relations for the multinomial distribution. 3.9 Use the SC 4 Template Multinomial to evaluate the multinomial vacation problem in Chapter 3 by dividing it into two separate problems, one for the value of B to A and one for the value of C to A. Compare the OLSC coefficients and values with those in Table 3.7. 3.10 You are interested in the added value relative to the baseline vehicle for improvements in (1) fuel economy as measured by mpg and in (2) acceleration performance as measured by the time to go from 0 to 60 mph at full throttle. The baseline vehicle has fuel economy of 20 mpg, 0 to 60 mph time of 10 seconds, and a price of $20,000. Set up three survey forms to make this assessment as follows: (A) Design the first survey as a classical conjoint analysis survey based upon an L4(23) OA. Use the first column for fuel economy, the second for acceleration performance, and the third for price. Let the two fuel economies be 20 and 30 mpg. Let the two accelerations be 10 and 6 seconds, and let the two prices be $20,000 and $30,000. (B) Design two DV surveys. Design the first to assess the added value of 30 versus 20 mpg and design the other to assess the added value of 10 versus 6 seconds for the 0 to 60 mph times. (C) Design two surveys in which respondents are asked to write-in their maximum willingness to pay for an improvement. Design the first to assess the maximum willingness to pay for an improvement in fuel economy from 20 to 30 mpg and design the other to assess the maximum willingness to pay for a reduction in 0 to 60 mph acceleration time from 10 to 6 seconds. (D) Next you should take each of the above surveys as a respondent and discuss the level of cognitive stress you sensed for each and any other factors you deem important in regard to completing each survey.


55

3.11 Convert the DV 8 Binary Template to a DV 7 Binary Template. This requires some familiarity with Excel in terms of re-entering array names and formulas for revised areas. As an aid to the process, first look at each column, copy the expression used, and paste it above the column. Some array names will involve multiple columns and rows. When the first change is made, look over all worksheets to see where diagnostics appear. It is also suggested that you first convert the DV 8 Binary Template to the DV 6 Binary Template as that template already exists and thus you can cross-check your progress and see how possible errors were generated. If you use the prices, results for f, and n given below, you should find value equal to 55.32 and the SD equal to 4.65.

1 2 3 4 5 6 7

From DV Survey Baseline Alternate Price Prices P0 P 50 30 50 40 50 70 50 100 50 110 50 120 50 130

Trial 1 2 3 4 5 6 7

[X] Design Matrix Base P-P0 (α) (−β'') 1 -20 1 -10 1 20 1 50 1 60 1 70 1 80

1-f 0.1 0.2 0.3 0.4 0.5 0.6 0.7

f 0.9 0.8 0.7 0.6 0.5 0.4 0.3

n 78 50 100 20 80 80 80

3.12 This is a team effort exercise to assess the value of adding a second rear sliding door on a minivan using the DV survey provided below. Each student should make four copies of the survey form and ask two females and two males to fill it out. Note gender of each respondent for each survey. If a potential respondents has already participated in the survey for another student, find another respondent. Collect the responses from all students and determine the added value of the door for all respondents, for just males, and for just females. Analyze the results using the DV 5 Binary Template forms and discuss findings for value and its statistics. Is the value difference between males and females significant? What is the fraction of respondents that view the door as an economic good?

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SURVEY You are ready to purchase a minivan and are deciding between the baseline minivan on the left and the alternative on the right, which has a fourth door (a second rear sliding door) and is offered over a range of prices. For each of the five comparisons, select either the vehicle on the left or the one on the right

Without 4th door

With 4th door

$20,000

Select one

$20,000

$20,000

Select one

$20,500

$20,000

Select one

$21,000

$20,000

Select one

$21,500

$20,000

Select one

$22,000

Circle Gender: Male Female

3.13 A multinomial survey for four vacation locations and their prices is listed below for a two-day stay. Also shown are the fractions of respondents that selected each location for each trial. The number of respondents for each trial was 100. Determine the values and their standard deviations of alternatives 1, 2, and 3 relative to the baseline 0. Determine the price coefficients. Hint: Use one SC 8 Multinomial Template for each relative value determination. Vacation Location 0

1

2

3

f0

f1

f2

f3

1

$1,000

$1,200

$1,200

$1,200

1

0.0451

0.0823

0.6638

0.2088

2

$1,000

$1,200

$1,200

$1,500

2

0.0521

0.0567

0.8697

0.0215

3

$1,000

$1,200

$1,800

$1,200

3

0.1627

0.2345

0.0996

0.5032

4

$1,000

$1,200

$1,800

$1,500

4

0.3794

0.2938

0.1555

0.1713

5

$1,000

$1,500

$1,200

$1,200

5

0.0614

0.0187

0.7428

0.1771

6

$1,000

$1,500

$1,200

$1,500

6

0.0572

0.0119

0.8908

0.0400

7

$1,000

$1,500

$1,800

$1,200

7

0.2744

0.0518

0.1440

0.5298

8

$1,000

$1,500

$1,800

$1,500

8

0.2648

0.0585

0.3468

0.3299

3.14 Given the demands and prices for the six brands shown below for the years 2001, 2002, and 2003, develop the value trends using the Value Trend template. Show the trend lines for Brands 1 and 6.


Brand number 1 2 3 4 5 6

2001 Brand name A B C D E F

Demand 50000 75000 60000 100000 120000 40000

Price 40000 35000 45000 45000 45000 55000


2003 Brand name A B C D E F


Demand 70000 80000 60000 95000 110000 41000

2002 Brand name Demand 70000 A 80000 B 60000 C 95000 D 110000 E 41000 F

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Price 45000 35000 46000 45000 45000 41000

Price 46000 35000 46000 45000 45000 41000

3.15 Show that the sum of Di in Equation (A.10) over all N is equal to a constant total demand DT* and independent of the values and prices of the competing products. 3.16 The simulated DV survey below had a relatively small sample size of 15 respondents. The simulated number Chevrolet selections are shown on the right. Analyze and compare the results for value and its standard deviation using the linear model and the logit model. What difficulties did you face and how did you work around them? Assume you are in the market to buy a new mid-sized sedan. For each paired comparison, select the Dodge vehicle on the left or the Chevrolet vehicle on the right. The two sedans are built to identical specifications. Dodge

Chevrolet

PRICE $20,000

Select One

Number PRICE selecting $18,000 15

$20,000

Select One

$19,000

14

$20,000

Select One

$20,000

12

$20,000

Select One

$21,000

11

$20,000

Select One

$22,000

2

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3.17 Reanalyze the outcomes in Exercise 3.16 using the MLLE model first to establish a result for f for the first trial using the appropriate template. Then use the first trial result for f from the MLLE to compute the OLS coefficients, value and the standard deviation of value. Compare the outcomes with those found in Exercise 3.16.

3.8 References Arentze T, Borgers A, Timmermans H, DelMistro R (2003) Transport stated choice responses: effects of task complexity, presentation format and literacy. Transportation Research E 39:229-244 Caussade A, Dios Ortuzar J, de Rizzi LI, and Hensher DA (2005) Assessing the influence of design dimensions on stated choice experiment estimates. Transportation Research B 39: 621-640 Cook HE and Wu A (2001) On the valuation of goods and selection of the best design alternative. Research in Engineering Design 13:42-54 Cook HE (2005) Design for six sigma as strategic experimentation. ASQ Quality Press, Milwaukee, WI DeShazo JR and Fermo G (2002) Designing choice sets for stated preference methods: the effects of complexity on choice consistency. Journal of Environmental Economics and Management 44:123-143 Kahneman D and Tversky A (1979) Prospect theory: an analysis of decisions under risk, Econometrica 47:263-291 Louviere JJ, Hensher DA, and Swait JD (2000), Stated choice methods. Cambridge University Press, Cambridge, UK Mendenhall W and Sincich T (1995) Statistics for engineering and the sciences 4th ed.. Prentice Hall, Engle wood Cliffs, NJ Norvell E (2004) The history of dirty politics. http://silverchips.mbhs.edu/inside.php?sid=3929 Satterthwaite FE (1946) An approximate distribution of estimates of variance of components. Biometrics Bulletin 2:110-114

4 Product Planning and Systems Engineering

Synopsis Product planning and systems engineering are two sides of the same coin. The resulting plan is both a financial and technical document. Value propositions need to be understood for the As-Is condition and developed for the proposed To-Be state. Proposed To-Be technical improvements need to be translated into forecasts of demand, price, cash flow, and return on investment. Differences between forecast and actual performance represent opportunities for learning how to improve the models. The tools now exist to begin to move virtual design upstream to the planning stage to reduce the need for the costly and time consuming build and test of physical prototypes. Validation of virtual models should be made against the performance of systems that are in production because prototype systems are often not built to production level materials, processes, and parts.

4.1 Nature of a System A system is an integrated set of subsystems that generate a response for a given set of inputs from the environment (exogenous) or from within the system itself (endogenous). Living systems exist because their evolutionary processes have successfully countered competing systems. The mountain goat has evolved to survive in an environment that is too harsh for most lowland predators. Present day man-made systems exist because of successful non-random, continuous improvements driven by economic factors and enabled by technological advancements. Aircraft have improved markedly from Wilbur Wright’s flight of 900 feet at a speed of 10 mph to today’s jumbo jets carrying 400 passengers 9000 miles at speeds over 560 mph. Thus, both living and man-made systems survive by adding value in timely and cost effective ways vis-à-vis competing systems.

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Inputs to the desktop computer system shown in Figure 4.1 can come from the keyboard or scanner. Outputs are generated by the printer and monitor. If the desktop system is connected to other systems by a local or wide area network, it can also send outputs to other systems and receive inputs from them, thereby forming a network of systems as illustrated in Figure 4.2. The automobile in Figure 4.3 is networked to systems for supply, repair, refueling, and roadways. Commercial aircraft are networked to airports, overhaul and repair facilities, and the air traffic control system. Printer

Tower

Monitor

Scanner Keyboard Figure 4.1. The subsystems that form the desktop computer system

System

Figure 4.2. Almost all systems are networked to other systems either electronically and/or physically

Product Planning and Systems Engineering

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Dealer networks are particularly critical because dealers have direct contact with customers. Dealers of large, complex, and costly earth moving machines add considerable value to their customer’s purchase through their deep knowledge regarding which machine is best for a specific task. Thus, system designers need to look inwards to understand how subsystem design affects system behavior and outwards to understand how the system is best configured for seamless integration across its networks.

Figure 4.3. Elements of the automotive network

4.2 Transitioning to Total Virtual Design and Development Intense competition is driving major manufacturing industries toward the virtual design of components and subsystems to achieve higher value, lower cost, and reduced time to market. Total Virtual Design and Development (TVD2), which eliminates the need for prototype hardware, is a long range, ultimate goal. Replacement of the prototype-based design, manufacturing, verification, and service process by TVD2 is of course risky and management must devise a wellthought-out and carefully crafted transition plan to manage risk. Thus far, aircraft companies are ahead of the automotive companies in applying virtual design and engineering (Gould, 2005). This has not been without setbacks, however. The Airbus A380 program has lost a year or more resulting in substantial lost profit due to file incompatibility between Catia design software Versions 4 and 5 from Dassault Systèmes (Newton, 2006; Rothman, 2006).

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There is a sound, logical, three-step path to TVD2: Step 1. Verify that the system level prototypes can be replaced by accurate system level simulation. Step 2. Verify that subsystem prototypes can be replaced by simulation. Step 3. Verify that component prototypes can be replaced by simulation. This path is logical because if component prototypes were eliminated first, then neither subsystem level nor system level prototypes could be built! Thus, the immediate challenge for any company planning to reach TVD2 is to verify that it has the suite of simulation software for reliably predicting the outcome of each test it currently runs using full system hardware. Accurate system level simulation is critical because customers only care about system level product attributes that are Critical-To-Value (CTV). Early virtual design efforts began with the use of computer simulation to model the behavior of certain components for stress level and fatigue life. Progress has generated simulations for crash energy management, heat flow, combustion, current flow, electronic cross talk, power requirements, and new molecular structures for pharmacological applications. Computer modeling of this nature has led to a reduction in the amount of prototype hardware needed to support product development and sped up the overall design and development process. For example, the development of excellent graphics software has allowed automotive firms to reduce but not fully eliminate their need for clay models as the belief persists that only a real three-dimensional view provides the correct perspective for assessing visual appeal. Importantly, the speed of computer simulation allows many more alternatives to be considered within a design of experiments formalism than with prototype hardware. Although computer simulation is commonplace today in support of component design, prototype hardware is still used for final verification of design intent in many industries. As long as prototypes dominate the overall design and development process, the fidelity of virtual design to mimic actual production component and system behavior can be less than perfect. This limits the progress in reaching the opportunities offered by TVD2 because successful TVD2 requires very high fidelity in virtual models at all levels of design: component, subsystem, and system. System level virtual design needs much more attention because, as already discussed, system level prototypes need to be eliminated first along the path to TVD2. Another reason for more attention at the system level is that it should improve the competitiveness of the requirements transmitted from system level designers to the subsystem designers shown in Figure 4.4. These requirements initiate the design process and determine how the system will perform and be accepted in the marketplace. Designers at the subsystem and component levels, of course, need to understand the system level issues and participate in setting the requirements. For example, a first tier supplier of a major subsystem to an OEM will have a distinct advantage versus its competitors if it fully understands the system level needs of the OEM and its customers. Such a supplier can churn its system simulation software to identify the range of improvements that it can make to the system level


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attributes of importance to the OEM’s customers. This gives the supplier the insight needed to structure its development program so that it generates, ahead of its competitors, the most competitive subsystem for the OEM’s future product. For example, a jet engine manufacturer needs to have a keen and full understanding of the needs of the airframe manufacturer, the airlines, and their passengers. With this knowledge, the engine supplier structures its research and development program such that it will gain an advantage over the competitors that wait for a list of specifications from the airframe manufacturer. To make system level virtual design and ultimately TVD2 a reality, system designers as well as first tier subsystem suppliers should have the following capabilities fully supported by a suite of virtual design and manufacturing tools: 1. A keen understanding of customer needs, spoken and unspoken, and a sixth sense of what competitors are likely to do over the short and long range. 2. A methodology must be in place for designing products that are robust against variation. This includes a process for continuously improving and validating the accuracy of the full set of computer generated transfer functions used to quantify how a design change at the component and subsystem levels will affect each CTV attribute at the system level. 3. Timely access to a market research data base that shows how changes in the CTV attributes as diagramed in Figure 4.5 affect the fundamental and bottom-line metrics. 4. A high confidence level in the planning process so that once a decision is made it rarely needs to be revisited. 5. Means for capturing things learned throughout the design, build, service, and disposal cycle and a process for smartly applying things learned to the next generation of products. 6. A commitment to continuing profitability based upon timely, continuous improvement in the product’s total value to the customer and society while controlling costs so that affordable price points are offered to the intended customers. Of course, these same capabilities are needed with prototype-based development using a mix of analytical and hardware based tools and tests. Capabilities, 2 and 3 have not been well-honed at this juncture at many firms because, as stated above, they rely upon prototype hardware for design validation. Capability 5, learning, is dependent upon the ability to make sound, quantitative forecasts and to compare them against actual market results. Although forecasts are made as part of all business plans, the degree of rigor in support of the numbers is often weak. Consequently, little can be learned when the financial targets are missed or the target price has to be changed dramatically. Capability 6, the need for an unchanging message grounded in the fundamental metrics, must be the same message to those within and outside the company.

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System

Subsystem A

Subsystem B

Subsystem B

Component B.1 Component B.2 Component B.3

Figure 4.4. This diagram shows the division of the system into subsystems and components. Key requirements flow from the system designers to those responsible for each of the subsystems, who in turn send key requirements to the component designers.

Forecast changes in value, cost, timing, and cash flow.

Figure 4.5. A schematic illustration of translating a proposed design change to changes in the attributes at the system level of importance to the customer and finally to the fundamental and bottom-line metrics


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4.3 Analyzing the As-Is/To-Be Transition using an Automotive Example 4.3.1 As-Is The starting point for value driven product planning and systems engineering is an assessment of the As-Is condition, which includes understanding how the existing product (1) meets customer needs relative to competition, (2) meets the returns expected by financial stakeholders, and (3) meets the societal requirements for environmental impact. The discovery of how the product should best be redesigned to meet these needs, expectations, and requirements in the future represents the To-Be process. The approach to value driven product planning will be illustrated here by considering the problem of a major upgrade of an existing automotive brand, noted as Brand A, which competes against four other brands in its segment, Brands B, C, D, and E, making N = 5 . The first step is to determine the trends in the total values of the competing products over the past several years using Equation (A.8), which can be evaluated in an automated manner using the template described in Appendix C with N=5.1 Value trend analysis showed that Brand C was the value leader with a significant value lead over Brand A, whose baseline demand, value, price, and cost was 150,000, $52,000, $25,333, and $20,000, respectively. The next step is to determine the likely source of Brand C’s total value advantage by converting the differences in the major CTV attributes between Brands A and C into value differences.2 The outcomes for this step are shown in Table 4.1. Brand C is seen to have approximately a $1,700 value advantage per vehicle over Brand A. It does not necessarily follow, however, that Brand C has an edge in demand or profits unless the value differences were generated in a cost effective manner. To complete the As-Is study, a cost breakdown by component and subsystem is generated to assess the differences between competitors in net value, equal to value minus cost. Also the current lead-time from the approval of a new design concept to the start of production should be documented. The costs and investment levels are best estimated by analysts using a part-by-part teardown and assessment study of the Brand C vehicle versus Brand A. They can also be estimated in a directional manner using the process described in Case Study 12. Lead-times are generally obtainable from industry publications. The results must then be carefully examined to understand why the costs and lead-times differ. When better practices are discovered they should be adopted.

1

The use of Equation (A.8) to evaluate the trends in the total values of minivans are provided by Case Study 5 and by Cook and Wu (2001). The total value trends in mid-sized sedans examined by Cook (2006, pp. 109-122) showed that there was a substantial negative correlation to the J.D. Power Vehicle Dependability Index which is computed from the number of repairs over the first three years of operation. 2 The methods for computing the values from the attributes are described in Appendix B.

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Table 4.1. The As-Is condition showing the major CTV attributes that differ between Brands A and C and the resulting value differences created3

A. Fuel economy (miles/gal) B. Front leg room (mm) C. Interior noise (dBA at 70 mph) D. Reliability (repairs over 5 years) E. Range (miles) F. Acceleration (time 0 to 60 mph) G. Shoulder room (mm) H. Head room (mm) I. Turning radius (ft)

Attribute Vehicle Vehicle A C 22 24 1140 1164 68 64 4 6.05 317 346 9 10 1440 1450 960 952 35 33 Total

Value C minus Value A $909 $540 $1,535 -$1,039 $57 -$441 $109 -$239 $268 $1,699

4.3.2 To-Be The starting point for the To-Be product plan is an assessment of how to overcome the value advantages of C shown in Table 4.1. The value differences shown were computed from the relationships given in Appendix B. Brand C is seen to have over a $1,500 value advantage due to its lower interior noise level. Brand A is seen to have over a $1,000 value advantage due to its fewer repairs. A thorough search also needs to be made to assure that one or more important attributes have not been overlooked. Attributes considered unimportant to customer value in the past, may offer new opportunities today. The search can be aided by noting that all products, independent of their class, can acquire the same set of generic CTV attributes at the system level, Table 4.2 (Cook and Gill, 1993). Products in different classes highlight certain attributes while suppressing others so that special demographic needs for a market niche are met at the system design level. Serious consideration of a wider range of generic attributes for possible implementation encourages out-of-the-box thinking and discovery of entirely new products and product variants. For example, in the past, the design of ski bindings and boots were unique between alpine and telemark (free heel) equipment. New bindings and boots are now available that can accommodate either technique depending on which is best for the current snow and terrain conditions and the mood and skills of the skier. Most cars today are designed to a fixed ride height. But shocks can be designed so that the ride heights could be increased to aid low speed travel over trails normally restricted to SUVs. Temperature controlled cup-holders are an example of a convenience that aids in providing for the sense of taste by making beverages not only convenient for use in a car but more delicious.

3

Reliability loss was computed conservatively using Equation (B.11).


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Consideration of the To-Be possibilities led to nine categories for potential actions, which are shown as A through I in Table 4.3. However, no explicit proposals surfaced for changing head room, shoulder room, and turning radius. Actions listed under one category can affect other CTV attributes. For example, the proposed material changes, A.4 through A.6, impacted not only fuel economy but also noise, reliability, range, and acceleration performance.4 The estimated value changes are shown in Table 4.4. When two or more actions are combined, the linear assumption is made here initially, which is that the value changes due to changes in the CTV attributes are additive. However, once an initial assessment has been made to identify the actions that look very promising from the financial analysis, attribute combinations suspected of having interactions can be evaluated Computer simulation can be used to compute the interactions and corrections can then be made to the expected CTV attributes and values as needed. The value curve in Figure 4.6 shows how improvements in fuel economy translate into improvements in value relative to the 22 mpg baseline for $2.89/gal fuel. (A quadratic approximation to Equation (B.7) is used over the limited range shown.) The front leg-room value curve shown in Figure 4.7 was used for converting changes in front leg room to changes in value relative to the 1140 mm baseline. (A quadratic approximation to Equation (B.8) was used over the limited range.) The interior noise value curve shown in Figure 4.8 was computed from Equation (B.10.). The value for a change in the number of repairs over five years was computed using Equation (B.11). The value changes for range and 0 to 60 mph acceleration performance shown in Figures 4.9 and 4.10, respectively, were computed from Equations (B.13) and (B.14). In computing range, time was valued at $30/hr for a tank volume of 18 gallons. Acceleration performance was expressed in terms of the log of the average acceleration as humans react to force as a psychophysical variable (Falmagne, 1986, p. 1.31). The value curve peaks at an acceleration time of 2 seconds based upon the assumption that safety concerns begin to dominate the thrill of acceleration at this point. When there is insufficient time to develop a value curve of interest based upon market research, an intuitive curve can be constructed as described in Appendix B in which a jury is used to estimate the ideal and critical levels of the attribute and the fraction of time that the attribute is important when the product is in use. These parameters are then substituted into Equation (B.2) to generate the intuitive value curve. The decision as to which proposed actions should be considered for implementation requires assessing their impact on the bottom-line metric used by the firm for judging investments. A break-even period of less than three years is used here for simplicity. The use of a break-even requirement for decision making is also not uncommon in practice. Another assumption for this example is that the total investment can not exceed $350 million.

4

The projections shown are directional estimates for purposes of demonstration.

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Table 4.2. Incomplete list of potential generic CTV attributes for any product. (Source: Gill MR and Cook HE (1993) On system design. Research in Engineering Design 4:215-226, Table 7, © 1993 Springer-Verlag, with kind permission of Springer Science and Business Media.) A. Five Senses a. Visual excitement b. Odor c. Sound and noise d. Feel e. Taste B. Time between events (product functioning) a. Between spatial locations b. From input to output c. Learning: start to completion d. From start-up to completion e. From shut down to off f. From off to store C. Time between events (product malfunction) a. Between failures b. From failed to fixed c. Useful life D. Friendliness a. Comfort b. Ergonomics c. Mental effort required E. Robustness: tolerance for a. Humidity b. Heat c. Vibration d. Dust e. Cold f. Snow g. Operator differences h. Shelf life

F. Generalized dimensions a. Volume b. Weight c. Moment of inertia d. Length e. Diameter f. Width g. Height G. Legal/ethics a. State and Federal laws b. Foreign laws c. Moral laws H. Safety to user and others a. Risk of injury b. Risk of loss of life c. Ability to warn of hazardous condition I. Environmental a. Ability to recycle b. Earth impact c. Water impact d. Electromagnetic impact e. Direct impact on people and biomass J. Costs a. To operate b. To repair c. Downtime losses d. Life-cycle disposal costs


Table 4.3. Potential actions for improving the CTV attributes of Brand A

Projected Attribute Changes Fuel economy Leg room Noise Reliability Range repairs miles mpg mm dBA

Potential Actions A. Mainly Fuel economy A.1 Lightweight valves 0.2 A.2 Reduced piston friction 0.5 A.3 Low loss tires 0.5 A.4 M aterial A BIW 2 A.5 M aterial B BIW 1 A.6 M aterial C BIW 2 B. Mainly Front Leg Room B.1 Cab forward 0.1 B.2 Thin seat backs 0.1 C. Mainly Interior Noise C.1 Sound Deadening M astic -0.2 C.2 Reduced wind noise 0 C.3 Low noise tires 0.1 C.4 3.9 L V6 engine -2 D. Mainly Reliability D.1 Improved DOE methods 0 D.2 Virtual design 0 D.3 Improved SPC 0 E. Mainly Range E.1 Fuel tank size + 2 gal -0.043 E.2 Fuel tanks size +3 gal -0.064 F. Mainly Acceleration See A, C, and E 0 G. Mainly S houlder Room No actions 0 H. Mainly Head Room No actions 0 I. Mainly Turning Radius No actions 0

0 to 60 Accel sec

0 0 0 0 0 0

-0.2 -0.2 0 0.2 0.2 -0.4

0.2 0 0 0.1 0 0

2.88 7.2 7.2 28.8 14.4 28.8

0 -0.1 -0.1 -1.0 -0.5 -1

10 15

-0.5 0.2

0 0.2

1.44 1.44

0 0

0 0 0 0

-1 -1 -0.5 0.5

0 0 0 0

-2.88 0 1.44 -28.8

0.1 0 0 -0.66

0 0 0

0 0 0

-0.5 -1 -1

0 0 0

0 -0.1 0

0 0

0 0

0 0

33.04 50.64

-0.018 -0.026

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

69

70


Table 4.4. Estimated value changes for improving the CTV attributes of Brand A

Fuel Econ A. Mainly Fuel economy A.1 Lightweight valves $96 A.2 Reduced piston friction $237 A.3 Low loss tires** $237 A.4 M aterial A BIW* $908 A.5 M aterial B BIW* $467 A.6 M aterial C BIW* $908 B. Mainly Front Leg Room B.1 Cab forward $48 B.2 Thin seat backs $48 C. Mainly Interior Noise C.1 Sound Deadening M astic -$97 C.2 Reduced wind noise $0 C.3 Low noise tires** $48 C.4 3.9 L V6 engine -$1,014 D. Mainly Reliability D.1 Improved DOE methods $0 D.2 Virtual design $0 D.3 Improved SPC $0 E. Mainly Range E.1 Fuel tank size + 2 gal -$21 E.2 Fuel tanks size +3 gal -$31 F. Mainly Acceleration See A, C, and E

Estimated Value Change Total Leg ReliValue room Noise ability Range Accel Change $0 $0 $0 $0 $0 $0

$83 $83 $0 -$84 -$84 $166

-$101 $0 $0 -$51 $0 $0

$6 $14 $14 $53 $27 $53

$0 $44 $44 $439 $220 $439

$83 $378 $295 $1,266 $631 $1,566

$273 $392

$207 -$84

$0 -$101

$3 $3

$0 $0

$530 $258

$0 $0 $0 $0

$409 $409 $207 -$211

$0 $0 $0 $0

-$6 $0 $3 -$59

-$44 $0 $0 $291

$263 $409 $257 -$992

$0 $0 $0

$0 $0 $0

$253 $507 $507

$0 $0 $0

$0 $44 $0

$253 $551 $507

$0 $0

$0 $0

$0 $0

$47 $67

$8 $12

$34 $47

* Either A.4, or A.5, or A.6, or baseline mild steel body. **Either A.3 or C.3 or baseline tire


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NPV versus 22 mpg base

$5,000 $4,000 y = -13.189x2 + 1060.8x - 17005

$3,000 $2,000 $1,000 $0 -$1,000 -$2,000 20

25

30

35

Fuel economy (mpg) Figure 4.6. Value changes for fuel economy relative to a 22 mpg baseline for $2.89/gal fuel

$1,500 y = -0.2323x2 + 559.28x - 335668 Value relative to baseline

$1,000 $500 $0 -$500 -$1,000 -$1,500 -$2,000 1080

1100

1120

1140

1160

1180

1200

Front leg room (mm)

Figure 4.7. Value changes for front leg room versus a 1140 mm baseline

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$59,000 $58,000 $57,000

Value

$56,000 $55,000 $54,000 $53,000 $52,000 $51,000 $50,000 40

45

50

55

60

65

70

75

Interior noise (dBA) Figure 4.8. Value of interior noise versus a 68 dBA baseline

-$300 y = -0.0035x2 + 4.1696x - 1653.6

Value

-$400 -$500 -$600 -$700 -$800 200

250

300

350

400

450

500

Range in miles Figure 4.9. Value of vehicle range is negative because it is an operational cost. Improvements in range versus a baseline will, of course, add value to the vehicle.


73

$56,000 $54,000 $52,000 Value

$50,000 $48,000 $46,000 $44,000 $42,000 $40,000 1

1.5

2

2.5

3

3.5

4

Ln(88/t0,60 ) Figure 4.10. Acceleration value for family sedans shown as a function of the psychometric acceleration force

The financial metrics for each proposed action including break-even time are shown in Table 4.5, price and demand changes being computed from Equations (A.13) and (A.1), respectively. Lightweight material A.5 (Material B) was chosen for the BIW application because its breakeven time of 1.01 years is better than the other two.5 All of the proposed actions listed as “No” in the last column of Table 4.5 were a result of either an estimated negative impact on annual revenue or a breakeven time greater than three years. The proposed actions for adding value in Table 4.6 are ranked by their time to break-even. Their cumulative impacts on price and annual revenue are shown in Figures 4.11 and 4.12, respectively, as a function of cumulative added investment. The cumulative added revenue shows diminishing returns with added investment, the cab forward design showing marginal added revenue for the amount of added investment. Whether or not this simulated investment would be wise in the real automotive marketplace rests on whether cab forward offers appealing styling opportunities as it would be difficult for competitors to counter the design change in a timely manner because of the major tooling investment and lead-time required to duplicate it. Thus, a value assessment of design appeal without and with the cab forward design is needed to provide a final assessment of the proposed To-Be redesign. Except for cab forward, most customers walking through a show room may not recognize the improvements in reliability, fuel economy, and acceleration performance. It is important that the company use its marketing resources to

5

BIW (Body-in-white) is automotive jargon for the materials that form the structure of the body of the vehicle. Seats, trim, wiring, windows, window regulators, carpets, mirrors, glass, etc. are not included.

74


inform potential buyers of these improvements. The added price must not be out of the affordable range for the market segment. In other words, value and cost (and thus price) cannot arbitrarily be increased while keeping the product affordable within the original segment. Moreover, it may be a challenge for a brand in one segment to move to a higher segment and be accepted there as a valid member. The computations of the change in value with changes in the automotive CTV attributes considered above have been automated, the template being described in Appendix C. Because value curves are concave, a net loss of value occurs when CTV attributes exhibit variation in production, an issue first described by Taguchi in his formulation of the loss function. These losses are not considered in the templates. However, they have been explored in detail elsewhere as part of the design of experiments formalism (Cook, 2005, pp.165-173). Table 4.5. List of financial metrics and time to break-even for the potential actions. The “Consider” column represents the tentative decision to implement or not to implement, using a 1 or 0, respectively. Time Annual Revenue Investto Consider Est. Price Demand Change ment Break 0 No Cost Change Change Millions Millions Even 1 Yes A. Mainly Fuel economy A.1 Lightweight valves A.2 Reduced piston friction A.3 Low loss tires** A.4 M aterial A BIW* A.5 M aterial B BIW* A.6 M aterial C BIW* B. Mainly Front Leg Room B.1 Cab forward B.2 Thin seat backs C. Mainly Interior Noise C.1 Sound Deadening M astic C.2 Reduced wind noise C.3 Low noise tires** C.4 3.9 L V6 engine D. Mainly Reliability D.1 Improved DOE methods D.2 Virtual design D.3 Improved SPC E. Mainly Range E.1 Fuel tank size + 2 gal E.2 Fuel tanks size +3 gal

$30 $55 $70 $215 $300 $298 $844 $1,042 $300 $455 $1,000 $1,266

790 4,593 -77 6,297 4,933 8,447

$7.95 $46.20 -$0.78 $63.33 $49.61 $84.95

$50.00 $5.00 $5.00 $100.00 $50.00 $100.00

6.29 0.11 -6.45 1.58 1.01 1.18

0 1 0 0 1 0

7,910 861

$79.55 $8.66

$200.00 2.51 $30.00 3.46

1 0

$0 $200

$249 $227

$290 $60 $310 $400

$277 -410 -$4.12 $1.00 $224 5,203 $52.33 $10.00 $285 -786 -$7.91 $1.00 -$254 -20,765 -$208.84 $100.00

$0 -$300 $40

$119 $100 $259

3,778 12,688 6,960

$38.00 $127.60 $70.00

$50 $60

$42 $54

-241 -188

-$2.43 -$1.90

-0.24 0.19 -0.13 -0.48

0 1 0 0

$2.00 0.05 $40.00 0.31 $2.00 0.03

1 1 1

$0.50 -0.21 $0.50 -0.26

0 0


75

Table 4.6. Rankings of tentative actions according to break-even time Annual Net Annual Revenue Invest- Time to Est. Est. Price Demand Change ment Break Action Value Cost Change Change Millions Millions Even D.3 Improved SPC $507 $40 $259 6,960 $70 $2 0.03 D.1 Improved DOE methods $253 $0 $119 3,778 $38 $2 0.05 A.2 Reduced piston friction $378 $70 $215 4,593 $46 $5 0.11 C.2 Reduced wind noise $409 $60 $224 5,203 $52 $10 0.19 D.2 Virtual design $551 -$300 $100 12,688 $128 $40 0.31 A.5 M aterial B BIW $631 $300 $455 4,933 $50 $50 1.01 B.1 Cab forward $530 $0 $249 7,910 $80 $200 2.51

$1,800

Cumulative added price

$1,600 $1,400 $1,200 $1,000 $800 $600 $400 $200 $0 $0

$50

$100

$150

$200

$250

$300

$350

6

Cumulative added investment (10 $) Figure 4.11. Trend of the cumulative price change versus cumulative investment

4.3.3 Learning Assume that the company building and selling Brand A implemented all of the actions listed in Table 4.6. Because it has provided quantitative estimates for the value improvements, the company should follow-up to verify whether or not the predicted total value change was actually seen in the marketplace. The actual or revealed total value for the change from the prior As-Is design to the upgraded ToBe design can be computed using Equation (A.8), the same expression used for computing the value trends for the As-Is analysis. The amount of improvement found should then be compared to the forecast total improvement of $3,259. Before making the comparison, however, it is important to confirm that the projected attribute changes agree with the attribute changes found in the actual product manufactured.

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Cumulative added revenue (106 $)

$500 $450 $400 $350 $300 $250 $200 $150 $100 $50 $0 $0

$50

$100

$150

$200

$250

$300

$350

6

Cumulative added investment (10 $) Figure 4.12. Trend of the cumulative added revenue versus cumulative investment

Although the computation of total value of the product given by Equation (A.8) does not depend directly on the values of its competitors, it is directly dependent upon the number of competing products, N . Care needs to be taken in arriving at this number because although there may be 10 vehicles in the segment, the majority of customers may consider fewer than this in making a purchase decision. One method for estimating N is to solve for it from Equation (A.5) which gives N = ηC / ε C . In this expression, ηC is the self price elasticity and ε C is the elasticity of average demand when all N change price by the same amount. Of course the two elasticities have to be obtained from independent econometric studies. Another method is to rank the competing brands by sales and set N equal to the maximum number of brands that, in concert, have up to but no more than, say, 80% of the total demand. Another more rigorous approach is to survey randomly selected buyers to determine how many brands each considered on average in making their purchase decision (McConville 1996). The results of the comparison between the forecast for the change in value and the actual change in value computed from Equation (A.8) can be used to test the validity of the value model used in generating the forecast. If the discrepancy is too large to be simply from statistical uncertainty, the source of the error needs to be found. Errors in forecasting can arise if CTV attributes are impacted by a design changes not included in the To-Be analysis. For example, value may be in error if an exterior design change is made to improve fuel economy by reducing aerodynamic drag, but the analysis of its impact on visual appeal was not included. Or perhaps the value forecast for the exterior design change was captured using surveys that utilized computer renderings that did not adequately represent the impact of the change. To know if this occurred, the forecast needs to be re-


77

evaluated by comparing the value of the actual new vehicle with the actual prior vehicle using the DV method. Consider an attribute such as reliability, which is heavily influenced by the prior experience of the user. Consequently, improvements in reliability may take four or five years for potential buyers to recognize unless the company significantly extends warranty coverage. Even if a company’s product reliability is sub-par, a bold action would be to extend the warranty period because this converts a value problem, which some companies have trouble quantifying, to a cost problem, which they are likely much better at solving. Nevertheless, if sufficient effort is made in developing quantitative forecasts and discovering and correcting sources of error, in time the company will learn how to make more accurate forecasts in the future, which should provide a wider scope of benefits. This includes investing in the right technologies and a better demand forecast, which allows planners to set optimal production facilities requirements and supply chain schedules. Planners also need to see if their price and profitability forecasts were near their targets. Such projections, as already noted, are error prone but important as they hone a firm’s ability to forecast actions of competitors, which can be a major factor in arriving at the right product plan. 4.3.4 Robustness to All Types of Variation Classical robust design (Taguchi and Wu, 1980) involves finding cost effective ways of minimizing variation in the CTV attributes.6 Taguchi’s design of experiments methods are primarily structured to provide robustness against variability at the component level. This well-known approach represents robustness against endogenous variation and the tools widely used for making such improvements are statistical process control and design for six sigma. System designers also need to consider robustness against exogenous variation arising from changes in the operating environment. A critical exogenous variable for any market is the appearance of a new, strong competitor that has targeted your business and market. Caterpillar quickly recognized that it had a serious threat from Komatsu and successfully countered by reducing its cost structure even though it involved a bitter strike. The US auto companies did not recognize the severity of the threat from Japanese and later Korean manufacturers early enough to counter effectively and protect their markets. The price of fuel is a critical exogenous variable for airline and automotive manufacturers. Airbus has had to modify its wide-body design to counter the speed and fuel efficiency of Boeing’s 777 and new 787. Manufacturers of large pickups and SUVs have seen sales and profits drop precipitously as oil moved beyond $60 per barrel. New technologies such as fuel shut off at idle, displacement on demand, hybrid, and diesel power are being targeted for SUVs and pickups as a result. Would a careful economic robustness analysis show that these technologies should have been in the market earlier as optional features? Would it have been more profitable for automotive planners to have hedged a few years ago by

6

In Taguchi’s terminology these are the attributes that influence the cost of inferior quality.

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manufacturing and marketing smaller, more fuel efficient products as options alongside the larger products offered? Hybrid and diesel vehicles discussed in Case Study 4 are examples of products that help hedge against the increases in the price of fuel and legislated reductions in atmospheric pollution. Many automotive companies are now also studying vehicles powered by fuel cells even though they may not appear in production for 15 years. 4.3.5 Sourcing New Technology There are several ways to source subsystems and components that are purchased from a supply base independent from the company selling the final product. An often used method is to give all potential suppliers the stated requirements including those for performance, quality (including process capability), and delivery. The bid then goes to the supplier that offers the lowest price provided that its subsystem or component has been verified to meet all of the stated requirements. This approach, however, can limit overall product appeal and profitability because the creativity of the supply base may not be sufficiently challenged. The base may be better challenged by providing it with the minimum acceptable level of the performance specifications for the subsystem or component. As part of this process, each potential supplier is given the set of transfer functions that couples the performance of the specific subsystem or component to the critical attributes at the system level. Each supplier is also given the curves and algorithms that couple changes in the system level attributes to changes in value. The bid is then awarded to the supplier whose subsystem or component is projected to give the largest result for value minus purchase price. In this manner, the supply base is challenged to provide high value as well as a low price. For example, automobile tires influence many system level attributes including interior and exterior noise levels, ride quality, handling, safety, and operating cost. The radial tire was a critical breakthrough technology, which improved upon every CTV attribute that a tire can affect. The first radial tires on a US built car were introduced on the Lincoln Continental and the Mark III in 1968 but chairman of the company was deeply concerned initially about putting these new tires on the company’s top two vehicles. To paraphrase his one-on-one meeting in the design studio with the executive in charge, the chairman bluntly asked, “Who was responsible?” The executive’s response was “Sir, I was and let me tell you why.” Once the chairman heard the major improvements in performance generated by the radial tires, he along with his concerns quickly left the studio. The executive’s response was what Carlson and Wilmot (2006, p. 103) would term the “elevator pitch” needed to describe and defend this new, innovative technology in a succinct and clear manner. Challenged at the highest level, the executive was cool under fire because he was fully confident in his decision. Thus, began the start of the spectacular rise in radial tires on US made vehicles. Suppliers have different methods of pricing their technologies. Cost plus a profit margin is one of the simplest approaches. Pricing to obtain a desired return on investment is another. A formal study of supplier pricing can be made starting with Equation (A.13), which shows how the OEM prices assuming a Nash


79

equilibrium vis-à-vis its N − 1 competitors. When the simplifying assumption is made that the competitors of the OEM of interest will not change their costs or values, Equation (A.13) can be written as:

δ P = ψ V δ V +ψ C δ C

(4.1)

In this expression δ V and δ C represent the added value and added cost, respectively, of the supplier’s new technology. If the OEM does not have added variable costs for implementing the technology, then δ C is equal to the supplier’s price, PS . The coefficients ψ V and ψ C computed from Equation (A.13) are listed in Table 4.7. Note that ψ V + ψ C = 1 . Table 4.7. A listing of the coefficients in Equation (4.1) as a function of the total number of competitors N 1 2 3 4 5 6 7 8 9 10

ψV 0.500 0.533 0.536 0.533 0.530 0.527 0.525 0.523 0.521 0.519

ψC 0.500 0.467 0.464 0.467 0.470 0.473 0.475 0.477 0.479 0.481

When the value and cost changes are relatively small, the variational form of Equation (1.3) can be used to estimate the change in the OEM’s cash flow:

δ A ≅ K ⎡⎣P0 − C0 ⎤⎦[δ V − δ P ] + D0 [δ P − δ C ] + δ F + δ M

(4.2)

Using the expression for the variation in price from Equation (4.1), we find that the change in cash flow is given by:

δ A ≅ K ⎡⎣ P0 − C0 ⎤⎦ψ C ⎡⎣δ V − PS ⎤⎦ + D0ψ V ⎡⎣δ V − PS ⎤⎦ + δ F + δ M

(4.3)

The supplier’s cash flow is given by:

AS ≅ D ⎣⎡ PS − CS ⎦⎤ + δ FS + δ M S

(4.4)

In Equation (4.4), D is the demand for the OEM’s product with the supplier’s new technology and it is given by:

80


D = D0 + Kψ C ⎣⎡δ V − PS ⎦⎤

(4.5)

The OEM’s cost δ C is assumed equal to the supplier’s price, PS , for the new technology. The term CS in Equation (4.4) is the supplier’s variable cost. The cash flow for a supplier and its OEM are shown in Figure 4.13 as a function of the supplier’s price of the new technology to the OEM. If they shared net cash flow equally, then the supplier’s price would be $62.80. The assumptions used in the computations were that δ V = $100 and CS = $12 in conjunction with the baseline parameters from Section 1.4 with N = 6 For simplicity, fixed costs and investment were taken equal to zero. In this example, the supplier had no competitors. A directional estimate for price as a function of the number of suppliers competing for the business can be made using Figure 1.6. When the number is one, two, three, four, etc. competing suppliers, the prices are 100%, 83%, 75%, 70%, 66%, etc. of the single competitor price. $14.00 $12.00

Profit OEM Profit Supplier

6

Profit (10 $)

$10.00 $8.00 $6.00 $4.00 $2.00 $0.00 $0

$20

$40

$60

$80

$100

Price of new technology (P S) Figure 4.13. Profits for the OEM and its supplier as a function of the supplier’s price of the new technology to the OEM


81

4.4 Summary o

o

o o

o

o o

The logical progression to total virtual design and development is to first eliminate the need to build full system prototypes, then eliminate the need to build subsystem prototypes, and finally eliminate the need to build component prototypes. Before each step can be completed the software for replacing the prototype builds must be validated against production parts and subsystems. System design begins with an assessment of the As-Is condition. This includes an assessment of how well the existing product is meeting the needs of all stakeholders including the customer, the company, dealers, governments, stockholders, and the rest of society. Only when the product’s As-Is condition is understood, should the To-Be plan be developed. As part of the To-Be plan, the firm needs to forecast the demand, price, and profitability of the new product based upon improvements in the CTV attributes, costs, investment and estimates of what competitors are likely to do. Once sufficient production has been generated, forecasts should be compared to actual market outcomes. The sources of discrepancies between the forecasts and the actual behavior must be identified and corrections made. Lessons learned are applied to the next generation product. Potential customers need to be made aware of the value improvements to the product through timely advertising and marketing. The sourcing of new technology from suppliers needs to reward both high value and low purchase price.

4.5 Supporting Case Studies Case Study 4: The Market for Hybrid and Diesel Mid-sized Sedans Case Study 5: Revealed Values: Minivan Trends Case Study 11: Assessing Relative Brand Value Case Study 12: Value and Cost Benchmarking a Yogurt Market

4.6 Exercises 4.1 Choose a historical period (state the starting year and an ending year) and review the improvements in the theory of computation and technological improvements in the speed of computation over that period. Discuss what you believe were the four most important events (theory and/or technology) and when did they occur. So do you observe continuous improvement? (See White 1996)

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4.2 Develop an intuitive value curve for the weight of a cell phone. Choose the ideal and critical weights and the exponential weighting factor. Describe how you arrived at the parameters. Take the baseline weight and price to be 4 ounces and $250, respectively. Use the log of weight as the attribute instead of weight itself in developing the value curve. 4.3 Develop an intuitive value curve for the talk time battery life of a cell phone. Choose the ideal and critical lifetimes and the exponential weighting factor. Describe how you arrived at the parameters. Take the baseline talk time and price to be 4.2 hours and $250, respectively. 4.4 Develop an intuitive value curve for the standby time battery life of a cell phone. Choose the ideal and critical lifetimes and the exponential weighting factor. Describe how you arrived at the parameters. Take the baseline standby time and price to be 200 hours and $250, respectively. 4.5 Develop an intuitive value curve for interior width of an automobile. Choose the ideal and critical lifetimes and the exponential weighting factor. Describe how you arrived at the parameters. Take the baseline interior width to be 53 inches and the vehicle price to be $25,000. 4.6 Develop an intuitive value curve for exterior width of an automobile. Choose the ideal and critical lifetimes and the exponential weighting factor. Describe how you arrived at the parameters. Take the baseline exterior width to be 65 inches and the vehicle price to be $25,000. Note that the exterior width should be assumed to be independent of the interior width in developing the value curve. The problem of the coupling of exterior and interior width is given in Exercise 4.7. 4.7 Assume that the exterior width of an automobile is equal to the interior width plus 12 inches. On doing this, combine the value curves for interior and exterior width from Exercises 4.6 and 4.5, respectively using Equation (B.5). Plot the combined value curve and determine the optimum exterior width. 4.8

Describe the network for the owners of a private home.

4.9 Discuss the opportunities and risks for changing the design and development of a new commercial aircraft from prototype supported development to virtual supported development using computer simulation. 4.10 Assume that you are in charge of a company that is a first tier jet engine supplier to commercial aircraft companies. Discuss why it is important to be fully knowledgeable about the full system requirements of your immediate customer (airframe company), as well as the airlines that will fly the plane and their customers.


83

4.11 You are in charge of selecting and purchasing the new brake system for a new vehicle. What information do you need to give about the vehicle each to each of the several companies that are potential suppliers? Discuss how you will make your decision using value and price analysis. 4.12 Given the prices and values of the four vehicles below, compute their Cournot costs (demand is for one month, July 2006). Discuss the issues in taking these specific results as being correct for variable cost. Time

Brand number 1 2 3 4

Elasticity

Period

N

εC

Jul-06

4

1

Brand name A B C D

Demand 41892 38048 17669 17516

Price $22,558 $21,778 $20,587 $21,625

Value $45,819 $44,623 $40,113 $41,113

4.7 References Carlson CR and Wilmot WW (2006) Innovation the five disciplines for creating what customers want. Crown Business, New York Cook HE (2006) The role of demand modeling in product planning. In: Chen W, Lewis K, and Schmidt L (eds.) Decision Making in Engineering Design. ASME Press Cook HE (2005) Design for six sigma as strategic experimentation, ASQ quality Press, Milwaukee, WI Cook HE and Wu A (2001) On the evaluation of goods and selection of the best design alternative. Research in Engineering Design 13:42-54 Cook HE and Gill MR (1993) On system design. Research in Engineering Design 4:215-226 Falmagne J (1986) Psychophysical measurement and theory. In: Boff K, Kaufman L, and Thomas J (eds.) Handbook of perception and human performance Vol. 1. John Wiley and Sons, New York Gould L (2003) What auto can learn from aero: simulating without prototypes. Automotive Design and Production 10, http://www.autofieldguide.com/articles/100309.html McConville GP (1996) Developing value relationships for automotive attributes. M.S. Thesis, Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign Newton RS ( 2006) Lessons for all CAD users from the Airbus Catia debacle. Sept. 29, AEC News.com, http://aecnews.com/articles/2035.aspx

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Rothman A (2006) Airbus vows computers will speak same language after A380 delay. Sept 29, Bloomberg, http://www.bloomberg.com/apps/news?pid=20601085&sid=aSGkIYVa9IZk Taguchi G and Wu Y (1980) Introduction to off-line quality control. Central Japan Quality Association, Nagoya White S. (1996) A brief history of computing. http://trillian.randomstuff.org.uk/~stephen/history/timeline.html

Case Study 1 Value Speculation in a Stock’s Price

Insight: The price and demand of a stock clearly illustrates how valuations differ between buyers and sellers and how “irrational exuberance” can arise with negative consequencies.

CS1.1 Buyers and Sellers Traders in a company’s stock can be divided into two segments, “buyers” who value the stock on the high side and “sellers” who value it somewhat lower. Demand functions exist for each, which, for simplicity, are shown as linear functions of price in Figure CS1.1. Sellers will sell when price exceeds their valuation VS of $11, and buy if it is less than VS . Buyers will buy when the price is below their valuation, VB , of $13 and sell when it is above VB . Thus, depending on the price of the stock, the so-called buyers can sell and sellers can buy. For simplicity, trading in this stock is assumed to be independent of the values and prices of other stocks. Buyers and sellers succumb to speculation by adding value to the stock if its price is increasing with time or by reducing value if its price is decreasing. This type of speculation is readily modeled by adding a term proportional to the time rate of change of price, dP dt , to VS and VB . Also, in making a buy or sell decision, traders may not have information that is up to date because orders are placed after reviewing price behavior and analysts’ reports generated at some prior point in time. Thus, the total value of the stock for the seller can be written as: VS = V0, S + c

dP dt

(CS1.1) t*

86


The term V0,S is the true value of the stock to the seller and the constant c represents the strength that the rate of change of price contributes to value in the mind of the seller and buyer. The prior time at which the rate of change of price was evaluated is t * . Similarly for buyers we have

VB = V0, B + c

dP dt

(CS1.2) t*

CS1.2 Demand for a Speculative Stock Thus, the sellers demand function for the speculative stock is given by: ⎡ dP DS = K ⎢V0, S + c dt ⎣

⎤ − P⎥ t* ⎦

(CS1.3)

and the buyers demand function is given by: ⎡ dP DB = K ⎢V0, B + c dt ⎣

⎤ − P⎥ t* ⎦

(CS1.4)

At market equilibrium, price is constant and DS ≡ − DB equilibrium price is given by: PEq = ⎡⎣V0, B + V0, s ⎤⎦ / 2

It follows that the

(CS1.5)

Equation (CS1.5) is simply another form of the monopoly relation in that the transaction price is equal to one-half of the sum of the values to the buyer and seller as discussed in Chapter 1. The simplest governing equation for price in a dynamic market not in equilibrium sets the relative change in price with time proportional to the total demand for the stock, which is equal to the sum of the demand for buyers and sellers (Cook, 1997, pp. 48-54): P(t + δ t ) − P (t ) = a ' δ t ⎡⎣ DS + DB ⎤⎦ / N Sh P (t ) ⎡ dP = aδ t ⎢ PEq + c dt ⎣

⎤ − P⎥ t* ⎦

(CS1.6)

Value Speculation in a Stock’s Price

87

In Equation (CS1.6), N Sh is the number of shares outstanding, a ' is a dimensionless rate constant, and a = 2a ' K / N Sh . The behavior of price with time can be determined using the spreadsheet to solve Equation (CS1.6) numerically. Not surprisingly, the behavior of price with time is highly dependent upon the speculative coefficient c in Equation (CS1.6).

CS1.3 Gold Mining Stock Hypothetical Example Assume that the stock of interest is for a gold mining company. At time zero, the stock was at an equilibrium price of $4. Then the company announced that it had discovered a major new lode. This increased the true value of the stock to $12 but the price does not simply move instantaneously to this point but increases in a diffusive manner from $4 to $12 according to Equation (CS1.6) because it takes time for the market to reflect upon and adjust to the new reality. When c = 0 (no speculation), the numerical solution gives a smooth transition as shown in Figure CS1.2.1 Stock demand, as shown in Figure CS1.3, is such that no transactions occur before time equal to 3 because price is sufficiently low that all so-called sellers want to buy. However, when time has reached six, there are equal numbers of buyers and sellers and price in Figure CS1.2 has stabilized to PEq . 25 Demand Sellers Demand Buyers

20

Demand

15 10 5 0 -5 -10 $0

$2

$4

$6

$8

$10

$12

$14

$16

PriceA

Figure CS1.1. Linear demand curves assumed for sellers and buyers

For all of the computations, a = 0.1 , δ t = 0.04 , and the time for evaluating the derivative of price with time was 0.28 prior to the time that an order was made.

1

88


When the coefficient c is increased from 0 to 0.7, the stock price overshoots somewhat as shown in Figure CS1.4 and then decays in an oscillatory manner to PEq . When the coefficient c is increased to 1.1, Figure CS1.5, the stock price exhibits a strong overshoot of PEq followed by a crash. The overshoot is caused by dP / dt being positive initially. As the price runs past PEq , a downward pull appears which slows down the rate of price growth and eventually stops it. As s price starts to fall, dP / dt becomes increasingly negative, which drives the speculative value and the price down at an ever increasing rate well past PEq to almost zero. If the numerical solution were extended, the strong overshoot and crash would simply keep repeating in a cyclical manner. If traders learn from their irrational exuberance, the cycle does not repeat and price settles in at $12.

CS1.4 Summary o o o

Two necessary conditions are needed to generate a crash of a stock according to the model used here. Speculative value being added to the stock in proportion to the rate of change of price with time is one condition. Old information being used to assess the time rate of change of the stock’s price prior to the purchase is the second condition.

$14 $12

Price

$10 $8 $6 $4 $2 $0 0

1

2

3

4

5

6

Time

Figure CS1.2. The price behavior with time for a jump in the value of a stock from $4 to $12 for no speculation, c = 0

Value Speculation in a Stock’s Price

89

10.00 8.00

Sellers Buyers

Demand

6.00 4.00 2.00 0.00 -2.00 -4.00 0

1

2

3

4

5

6

Time

Figure CS1.3. The demand for sellers and buyers as a function of time for c = 0

$16 $14 $12 Price

$10 $8 $6 $4 $2 $0 0

1

2

3

4

5

6

Time

Figure CS1.4. The price behavior with time for a jump in the value of a stock from $4 to $12 for modest speculation, c = 0.7

90


$35 $30

Price

$25 $20 $15 $10 $5 $0 0

1

2

3

4

Time

Figure CS1.5. The price behavior with time for a jump in the value of a stock from $4 to $12 for strong speculation, c = 1.1

CS1.5 References Cook HE (1997) Product management: value, quality, cost, price, profits, and organization. Kluwer Academic, Amsterdam

Case Study 2 Simulated Survey of Boston to Los Angeles Flights

Insight: When aggregate data follow the logit model, survey outcomes computed using the Level 2 Ordinary Least Squares method compare well with results from the maximum likelihood method.

CS2.1 Experimental Design Louviere, et. al. (2000, pp. 103-110) simulated a survey in which respondents reviewed 16 independent flights from Boston to Los Angeles. Each trial presented an independent binary choice for selecting or rejecting a flight having a mix of numerical and categorical (0 or 1) attributes as follows: 11 Fare: $300, $400, $500, $600 21 Departure at 8 am (no = 0; yes = 1) 22 Departure at 9 am (no = 0; yes = 1) 23 Departure at 12 noon (no = 0; yes = 1) 31 Time of flight: 4, 5, 6, or 7 hrs

41 Number of stops: (none = 0; one =1) 51 Entertainment Audio (no = 0; yes = 1) 61 Entertainment Video (no = 0; yes = 1) 71 Meals: Yes or no (no = 0; yes = 1) 81 Airline: United = 1; Delta = -1

The resulting design matrix [XX] is shown as part of Table CS2.1. The double indexed columns for the attributes are defined above except for the baseline defined as 0. The 2 pm departure is denoted by -1s in the departure time columns, which makes the baseline for departure times zero. The continuous variables of fare and trip time are in columns 11 and 31, respectively. There are also four levels of departure time but they appear as three separate columns because the variable is taken to be categorical. The remaining five categorical columns, excluding the baseline column, have two levels, 0 or 1. The resulting design is an L16(43,25) orthogonal array (OA), which can be constructed from the base L16(45) OA by converting two of the four level columns into five two level columns.1 One

1

Orthogonal arrays are discussed in Appendix F.

92


additional two-level column could be added but the design would then be fully saturated. A total of 100 respondents were used in the simulations, the fractions f for each trial being shown in Column P. The elements of the utility difference vector [Y] relative to not-buy were computed as Ln( f /(1 − f )) and the elements of the variance vector, [VarY], were computed from Equation (3.4). The solution matrix, [XXS], is shown in Table CS2.2. The spreadsheet expression used to compute the solution matrix is shown at the bottom of Table CS2.2. Table CS2.1. The design matrix [XX] is located in Area E8:O23. The columns f, Y, and VarY are, respectively, the fraction selecting the trial, the utility difference and its variance.

D E 7 Trial 0 8 1 1 9 2 1 10 3 1 11 4 1 12 5 1 13 6 1 14 7 1 15 8 1 16 9 1 17 10 1 18 11 1 19 12 1 20 13 1 21 14 1 22 15 1 23 16 1

F

G H

I

J

K

L M N O

P

Q

R

11 21 22 23 31 41 51 61 71 81 f Y 300 1 0 0 4 0 0 0 0 -1 0.80 1.386 300 0 1 0 5 1 0 1 1 -1 0.60 0.405 300 0 0 1 6 1 1 0 1 1 0.50 0.000 300 -1 -1 -1 7 0 1 1 0 1 0.30 -0.847 400 1 0 0 5 0 1 0 1 1 0.60 0.405 400 0 1 0 4 1 1 1 0 1 0.50 0.000 400 0 0 1 7 1 0 0 0 -1 0.20 -1.386 400 -1 -1 -1 6 0 0 1 1 -1 0.35 -0.619 500 1 0 0 6 1 0 1 0 1 0.10 -2.197 500 0 1 0 7 0 0 0 1 1 0.15 -1.735 500 0 0 1 4 0 1 1 1 -1 0.40 -0.405 500 -1 -1 -1 5 1 1 0 0 -1 0.20 -1.386 600 1 0 0 7 1 1 1 1 -1 0.30 -0.847 600 0 1 0 6 0 1 0 0 -1 0.05 -2.944 600 0 0 1 5 0 0 1 0 1 0.10 -2.197 600 -1 -1 -1 4 1 0 0 1 1 0.15 -1.735

VarY 0.063 0.042 0.040 0.048 0.042 0.040 0.063 0.044 0.111 0.078 0.042 0.063 0.048 0.211 0.111 0.078

Table CS2.2. Solution matrix [XXS] F 30 31 32 33 34 35 36 37 38 39 40 41 42 43

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

ij 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1.1 0.4 0.1 0.0 0.3 0.5 -0.1 0.0 -0.2 -0.3 0.2 0.1 -0.9 -0.3 0.0 0.1 11 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 21 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 22 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 23 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 -0.1 -0.1 0.2 -0.1 31 -0.1 0.0 0.0 0.1 0.0 -0.1 0.1 0.0 0.0 0.1 -0.1 0.0 0.1 0.0 0.0 -0.1 41 -0.1 0.1 0.1 -0.1 -0.1 0.1 0.1 -0.1 0.1 -0.1 -0.1 0.1 0.1 -0.1 -0.1 0.1 51 -0.1 -0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 -0.1 -0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 61 -0.1 0.1 -0.1 0.1 -0.1 0.1 -0.1 0.1 0.1 -0.1 0.1 -0.1 0.1 -0.1 0.1 -0.1 71 -0.1 0.1 0.1 -0.1 0.1 -0.1 -0.1 0.1 -0.1 0.1 0.1 -0.1 0.1 -0.1 -0.1 0.1 81 -0.1 -0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 0.1 0.1 -0.1 -0.1 -0.1 -0.1 0.1 0.1 Area G31:V41 = XXS =MMULT(MINVERSE(MMULT(TRANSPOSE(XX),XX)),TRANSPOSE(XX))

Simulated Survey of Boston to Los Angeles Flights

93

CS2.2 OLS Solution with Satterthwaite’s df and Approximate tTest The elements of the utility coefficient vector, [OLSC] and their standard deviations, [SD] are listed in Columns AC and AE, respectively, in Table CS2.3. The dollar values listed in Column AD were computed by dividing the elements of the [OLSC] vector by minus one times the coefficient for the fare. The relative value of the 2 pm departure (not shown) is minus $35.24. The standard deviations were computed from the variances given by Equation (3.4). The elements of the column vector, [d], were computed using Equation (3.11) and the elements of Satterthwaite’s [df] were computed using Equation (3.10). The df, although large, are much smaller than the pooled df equal to 1584 (=16×99). As the number of trials (choice sets) increases, the df increases and this aids in improving sensitivity. However, this is offset somewhat by the conversion of pairwise error (PWE) in Column AI to experiment-wise error (EWE) in Column AJ using Bonferroni’s method. The EWE compensates for the fact that when more and more coefficients are evaluated, it becomes likely that random fluctuations will indicate that an experimental coefficient is deemed significant using PWE even though the coefficient for the population may in fact be zero. Table CS2.3. Outcomes for the OLS solution using Satterthwaite’s df and approximate ttest AA AB AC 44 45 ij OLSC 46 0 0 4.120 47 Fare 11 -0.008 48 8 21 0.568 49 9 22 -0.187 50 12 23 -0.116 51 Time 31 -0.379 52 Stops 41 -0.024 53 Audio 51 0.256 54 Video 61 0.086 55 Meals 71 0.630 56 Airline 81 -0.157 57 58 OLSC 59 Cell AD48 60 SD 61 d 62 df

AD OLS Values

$75.44 -$24.83 -$15.38 -$50.36 -$3.15 $34.05 $11.39 $83.68 -$20.81

AE

AF

AG

SD 0.410 0.001 0.112 0.126 0.111 0.055 0.132 0.132 0.132 0.132 0.066

d 7.4E-05 2.4E-16 2.7E-07 6.8E-07 2.6E-07 9.3E-09 2.7E-07 2.7E-07 2.7E-07 2.7E-07 1.7E-08

df 385 634 596 375 592 968 1154 1154 1154 1154 1154

AH

AI

AJ

AK Sig. at t PWE EWE 5% 10.0 1.6E-21 1.6E-21 Yes -12.1 1.3E-30 2.0E-29 Yes 5.1 2.8E-07 4.1E-06 Yes -1.5 7.0E-02 1.0E+00 -1.0 1.5E-01 2.2E+00 -6.9 3.8E-12 5.7E-11 Yes -0.2 4.3E-01 6.4E+00 1.9 2.6E-02 4.0E-01 0.6 2.6E-01 3.9E+00 4.8 1.1E-06 1.6E-05 Yes -2.4 9.0E-03 1.4E-01

=MMULT(XXS,Y)

t =OLSC/SD PWE =TDIST(ABS(t),df,1) =SQRT(MMULT(XXS^2,VarY)) Cell AJ46 =(AI46)

=-AC48/$AC$47 (drag down)

=MMULT(XXS^4,VarY^2/(100-1))

=SD^4/d

Cell AJ47 =(16-1)*AH47 (drag down)

94


CS2.3 Solution using Maximum Log Likelihood Estimate The utility coefficients named MLLEC, which were computed using the MLLE method discussed in Chapter 3, are shown in Column AL of Table CS2.4. They are in reasonable agreement with those from the OLS method in Column AC of Table CS2.3 considering the size of the standard deviations. They are in close agreement with the MLLE coefficients reported by Louviere et. al. when their categorical code of 0 listed for Delta is replaced by the -1 actually used in their computations. The MLLE values are listed in Column AM. The relative value of the unlisted 2 pm departure is minus $40.17. Of greater importance is a comparison of the tstatistics in Table CS2.4 (computed here using the OLS standard deviations in Column AE of Table CS2.3) with those in Column AO reported by Louviere et. al. using MLE methods. The standard deviations themselves are compared in Table CS2.5. Considering the nature of the approximations used in both sets of computations, the t-statistics and the standard deviations are also in good agreement. Thus, based upon this comparison, the results of the Level 2 OLS regression with Satterthwaite’s approximate t-test are in relatively good agreement with the outcomes from the MLLE analysis. The coefficients of determination, R 2 , computed from the OLS and MLLE outcomes were also similar, being 0.914 and 0.904, respectively. Table CS2.4. Solution for the utility coefficients computed using the maximum log likelihood estimate (MLLE) method

Simulated Survey of Boston to Los Angeles Flights

95

Table CS2.5. Comparison of standard deviations of the coefficients as computed by Louviere et. al using MLE methods and those taken from Table CS2.3 using OLS methods.

The steps in the spreadsheet computations of the MLLE coefficients are shown in Table CS2.6. The initial estimates of the utility coefficients relative to not buy were named MLLEC and entered into Column AL of Table CS2.4. These were then used to compute the initial estimate of the utilities for each trial named MLLEU in Column AS of Table CS2.6. Next the exponentials named ExpMLLEU in Column AT of Table CS2.6 were computed with the utilities as the arguments of the exponentials. The ExpMLLEU were then used to compute f and 1 − f in Columns AU and AV, respectively, in Table CS2.6. The next step was to compute the elements in the log likelihood summation, which was done by each row in Columns AW, AX, and AY and the outcomes in Column AY were then summed in Cell AY25, which is the cell that was maximized by Solver to arrive at the final MLLE coefficients shown in Column AL of Table CS2.4.

CS2.4 Summary o

o

o

The outcomes from the Level 2 OLS analysis of the simulated survey were in reasonable agreement with the findings of Louviere, et. al. (2000, pp. 103-110), who used the MLE method. Agreement should be expected when the aggregate data is wellrepresented by the logit model and asymptotic expressions are used for computing the variance of the coefficients. If the special software needed to use the MLE is not available, then the Level 2 analysis could be performed using the spreadsheet.

96


Table CS2.6. Key steps in the MLLE solution method for the utility coefficients

AR AS AT AU AV AW AX AY (100-n ) 6 Est. Est. 1-f n x Ln(f ) x Ln(1-f ) 7 Trial MLLEU ExpMLLEU f Sum 8 1 1.096 2.993 0.750 0.250 -23.1 -27.7 -50.8 9 2 0.610 1.841 0.648 0.352 -26.0 -41.8 -67.8 10 3 0.051 1.052 0.513 0.487 -33.4 -35.9 -69.3 11 4 -0.846 0.429 0.300 0.700 -36.1 -25.0 -61.1 12 5 0.511 1.668 0.625 0.375 -28.2 -39.2 -67.4 13 6 -0.295 0.744 0.427 0.573 -42.6 -27.8 -70.4 14 7 -1.534 0.216 0.177 0.823 -34.6 -15.6 -50.2 15 8 -0.664 0.515 0.340 0.660 -37.8 -27.0 -64.8 16 9 -1.380 0.252 0.201 0.799 -16.0 -20.2 -36.2 17 10 -1.976 0.139 0.122 0.878 -31.6 -11.0 -42.6 18 11 -0.250 0.779 0.438 0.562 -33.0 -34.6 -67.6 19 12 -1.269 0.281 0.219 0.781 -30.3 -19.8 -50.2 20 13 -1.241 0.289 0.224 0.776 -44.9 -17.8 -62.6 21 14 -2.158 0.116 0.104 0.896 -11.3 -10.4 -21.7 22 15 -2.558 0.077 0.072 0.928 -26.3 -6.7 -33.0 23 16 -1.811 0.163 0.140 0.860 -29.4 -12.9 -42.3 24 MLLEU =MMULT(XX,MLLEC) 25 ExpMLLEU =EXP(MLLEU) -858.104 26 Area AU8:AU23 =ExpMLLEU/(ExpMLLEU+1) MAXIMIZE 27 Area AV8:AV24 =1/(ExpMLLEU+1) Cell AY25 =SUM(AY8:AY23) 28 Cell AW8 =100*P8*LN(AU8) (drag down) 29 Cell AX8 =100*(1-P8)*LN(AV8) (drag down) 30 Cell AY8 =SUM(AW8:AX8) (drag down)

CS2.5 References Louviere JJ, Hensher DA, and Swait JD (2000) Stated choice methods. Cambridge University Press, Cambridge, UK

Case Study 3 Analysis of a Multinomial Stated Choice Survey

Insight: The outcomes of multinomial surveys can also be analyzed in a straightforward manner using the Level 2 OLS method.

CS3.1 A Simulated Multinomial Survey A simulated multinomial stated choice survey1 is shown in Table CS3.1, which uses the general double index form ij given by 11, 21, 31, and 41.2 It will be used to assess the value of several soft drinks relative to a local brand cola (Cola) when served with a burger and fries. The prices shown are for each drink. The total price of the meal, which should be specified in a true survey, is not shown as it is not needed for this sample problem. The arrangement of prices in Table CS3.1 is based upon an L9 (34 ) OA (nine trials, four factors at three levels each). The total values for the drinks were taken as $5.00, $5.50, $5.25, and $4.75, respectively, for 11, 21, 31, and 41. Experimental error was introduced about these means by modeling each of the values as being normally distributed having a standard deviation of the means of $0.05. The number of respondents was assumed to be 100. Strictly speaking, no baseline is designated in Table CS3.1. If the problem were analyzed using the DV survey approach, the reference drink chosen, Cola, would be a true baseline as it would be offered at the same fixed price in each of three separate surveys. Each would present a several choices between Cola and one of the alternatives offered over a range of five or six prices.

1

The equations for analyzing a stated choice survey are presented in Chapter 3. The double index notation for factors introduced in Appendix D is used here in place of the single index such as A, B, etc. to show how the general notation is used for a simple problem. 2

98


Table CS3.1. Prices of drinks for the hypothetical survey to determine the value of drinks with burger and fries relative to Cola

D E 5 Burger 6 Fries 7 Cola 8 Trial 11 9 1 $2.00 10 2 $2.00 11 3 $2.00 12 4 $2.50 13 5 $2.50 14 6 $2.50 15 7 $3.00 16 8 $3.00 17 9 $3.00

F Burger Fries Shake 21 $2.00 $2.50 $3.00 $2.00 $2.50 $3.00 $2.00 $2.50 $3.00

G Burger Fries Pepsi 31 $2.00 $2.50 $3.00 $2.50 $3.00 $2.00 $3.00 $2.00 $2.50

H Burger Fries Coffee 41 $2.00 $2.50 $3.00 $3.00 $2.00 $2.50 $2.50 $3.00 $2.00

In Table CS3.1, respondents are not asked to review the entire survey before making an entry. They only need to select their optimal choice from one of the four entries provided in a given row and then move to the next. If the survey was presented in a printed form, a respondent would simply circle his or her preference in each row. However, in a classical conjoint survey design, as discussed in Appendix D, respondents are asked to review different attribute levels in every row before force ranking the rows. As the number of rows (choice sets) increase, the cognitive burden on the respondent increases. Because of this, the number of choice sets is often limited to eight or nine. Thus, it is straightforward to sense that the survey in Table CS3.1, which deals with just one row at a time, presents less cognitive stress than the conjoint survey in Table D.1.

CS3.2 Simulation Process The simulation process used to generate the responses assumed the above values and that the fraction of the choices within a row followed a logit model with a price coefficient β '' equal to 2/$, which is the rounded off size for β '' computed from Equation (A.23) for this specific problem. The resulting simulated outcomes for the fractions fi1 are shown in Table CS3.2. The ratios of fi1 / f11 are shown in Table CS3.3 and the variances of the utility differences in Table CS3.4 were computed from the multinomial expression given by Equation (3.3). Each trial in Table CS3.1 results in three equations in the OLS linear regression model for the utility differences, which transforms the design in Table CS3.1 into the expanded design matrix [X] shown in Table CS3.5 having 27 rows and 4 columns. The outcomes [Y], which represent differences in the utilities relative to the 11 baseline, were computed by taking the logs of the entries for 21, 31, and 41

Analysis of a Multinomial Stated Choice Survey

99

in Table CS3.3 and rearranging them into a column. The price differences in column 51 couple − β '' to the outcomes. The nature of the logit model is such that the design matrix [X] can also be split into three subordinate designs of nine rows each by two columns, one column i1 being for the drink with i = 2 → 4 and the other, column 51, for the price coefficient. Each subordinate design would lead to a separate result for − β '' , which could then be averaged. One advantage in splitting the grand design into three is that the SC 9 multinomial template available from the publisher’s web-site could be used to generate the analysis as the templates can handle [VarY] computed from the multinomial expression Equation (3.3). However, the number of alternatives being considered needs to be constant for each row. Thus, the templates can not be used for a presence/absence survey.

Table CS3.2. Simulated selection fractions f i1 associated with the design in Table CS3.1

8 9 10 11 12 13 14 15 16 17

AA Trial 1 2 3 4 5 6 7 8 9

AB 11 0.154 0.326 0.628 0.097 0.149 0.144 0.042 0.049 0.086

AC 21 0.506 0.368 0.188 0.720 0.482 0.144 0.818 0.344 0.198

AD 31 0.250 0.239 0.130 0.160 0.084 0.626 0.067 0.573 0.345

AE 41 0.090 0.067 0.055 0.023 0.284 0.086 0.073 0.034 0.371

Table CS3.3. Ratios of f ij / f i1 computed from Table CS3.2 Trial 1 2 3 4 5 6 7 8 9

11 1 1 1 1 1 1 1 1 1

21 3.30 1.13 0.30 7.44 3.23 1.00 19.61 7.08 2.31

31 1.63 0.73 0.21 1.65 0.57 4.35 1.60 11.79 4.02

41 0.59 0.21 0.09 0.24 1.90 0.60 1.76 0.70 4.32

100


Table CS3.4. Variances of Ln( f i1 / f11 ) from Table CS3.3 as computed from Equation (3.3)

AB AC AD AE 21 Trial 21 31 41 22 1 0.085 0.105 0.176 23 2 0.058 0.073 0.179 24 3 0.069 0.093 0.198 25 4 0.117 0.166 0.529 26 5 0.088 0.185 0.102 27 6 0.139 0.085 0.185 28 7 0.252 0.390 0.376 29 8 0.235 0.223 0.500 30 9 0.167 0.146 0.144 31 32 Cell AC22 =(1/n)*((1-$AB9)/$AB9+ (1-AC9)/AC9+2) 33 (drag across and down) 34

CS3.3 The Level 2 OLS Coefficients The OLS coefficients, [OLSC], and their statistics are shown in Table CS3.6. All are significant at better than 5% EWE. The coefficients were also computed using the maximum log likelihood method (see Chapter 3) and were within 2% of the OLSC results. The values found from the simulated survey for the three drinks relative to Cola were $0.50, $0.24, and -$0.23, which were computed by dividing their respective OLSC coefficients by β '' = 2.002 . These results should be compared to the population relative values of $0.50, $0.25, and -$0.25 and β '' equal to 2 used as input to the simulations.

CS3.4 Summary o

o o

This case study demonstrated how to use the Level 2 OLS model to analyze a multinomial survey for the values of the alternatives relative to the baseline. Each trial in the case study generated N − 1 = 3 equations in the design matrix resulting in 27 linear equations and four unknowns. However, all multinomial problems that can be described by the logit model can also be solved by using separate sets of equations for the coefficients, whose relative values are to be determined. The separate price coefficients found should be averaged. This approach will often be less tedious for large scale problems.

Analysis of a Multinomial Stated Choice Survey

101

Table CS3.5. Columns 21 through 51 represent the design matrix [X]. The outcomes vector represented by the utilities [Y] was computed by taking the logs of the coefficients in Table CS3.3 and rearranging into a single column. The variance vector for the utilities [VarY] was transcribed from Table CS3.4. Shake Pepsi Coffee Trial 21 1 1 2 0 3 0 4 1 5 0

31

41

51

0 1 0 0 1

0 0 1 0 0

0 0 0 0.5 0.5

Y 1.193 0.486 -0.530 0.123 -0.311

VarY 0.085 0.105 0.176 0.058 0.073

6

0

0

1

0.5

-1.575 0.179

7

1

0

0

1

-1.208 0.069

8

0

1

0

1

-1.576 0.093

9

0

0

1

1

-2.437 0.198

10

1

0

0

-0.5

2.007 0.117

11

0

1

0

0

0.501 0.166

12

0

0

1

0.5

-1.415 0.529

13

1

0

0

0

1.173 0.088

14

0

1

0

0.5

-0.570 0.185

15

0

0

1

-0.5

0.644 0.102

16 17 18 19 20

1 0 0 1 0

0 1 0 0 1

0 0 1 0 0

0.5 -0.5 0 -1 0

21

0

0

1

-0.5

0.563 0.376

22

1

0

0

-0.5

1.958 0.235

23

0

1

0

-1

2.467 0.223

24 25 26

0 1 0

0 0 1

1 0 0

0 0 -0.5

-0.358 0.500 0.838 0.167 1.392 0.146

27

0

0

1

-1

1.464 0.144

0.002 1.469 -0.510 2.976 0.468

0.139 0.085 0.185 0.252 0.390

102


Table CS3.6. The Level 2 ordinary least square coefficients, OLSC, and their statistics AH 8 9 10 11 12 13 14 15 16 17

Shake Pepsi Coffee -Beta

AI ij 21 31 41 51

Coeff SD t d

AJ OLSC 1.007 0.481 -0.461 -2.002

AK AL SD t 0.122 8.24 0.135 3.57 0.172 -2.69 0.138 -14.54

AM d 3.12E-07 4.88E-07 1.29E-06 3.47E-07

=MMULT(XS,Y) =SQRT(MMULT(XS^2,VarY)) =OLSC/SD =MMULT(XS^4,VarY^2/(n-1))

AN df 715 671 674 1034

AO PWE 4.08E-16 1.89E-04 3.69E-03 4.89E-44

AP EWE 1.63E-15 7.58E-04 1.48E-02 1.96E-43

df =SD^4/d PWE =TDIST(ABS(t),df,1) EWE =4*AO9 (drag down)

Case Study 4 The Market for Hybrid and Diesel Mid-sized Sedans

Insight: Although the price premiums for hybrid and diesel powered passenger cars can exceed their added value from improved fuel economy, a not insignificant market for these vehicles is forecast over the long term

CS 4.1 Prior Studies Greene, et. al. (2004) studied the long term market for hybrid and (clean) diesel powered vehicles taking into consideration many CTV attributes in addition to fuel economy improvements. With the assumption of wide availability of these types of vehicles beyond 2012, they forecast (see their Figure 15) that the two technologies will hold a combined share of the sedan market of approximately 34%, with diesels taking 21% and hybrids taking 13%. Their forecast for the total light vehicle market was even larger, with diesels taking 23.8% and hybrids taking 16.5%. This contrasts with the sales outcomes for 2006 where hybrids made up only 1.8% of all vehicle sales (Welch 2007). However, Toyota did sell 107,897 Prius vehicles in the US in 2006, which was 20% of the combined sales of Toyota’s Camry and Prius. McManus (2004) reported the results of two surveys, one for hybrids and one for diesels. His findings, which were included in Table 7 of Greene, et. al. (2004), are shown here as logit plots in Figures CS4.1 and CS4.2, respectively, for the hybrid and diesel. The price for the baseline vehicle having a spark-ignition (SI) engine was $25,026. More recently, Ong and Hasselhoff (2005) conducted a willingness to pay survey in the Los Angeles area for hybrids. Their findings are shown in Figure CS4.3. They did not show prices in their survey, but used percentage increments from a non-specified price of a baseline vehicle. Their percentages were converted to the prices shown in Figure CS4.3 using the McManus’ baseline price of $25,026. The price slopes (multiplied by -1), values, and the standard deviations of value extracted from the surveys are summarized in Table CS4.1. For the hybrids, McManus’ (2004) results are listed as Hybrid 1 and those of Ong and Haselhoff (2005) are listed as Hybrid 2. The added values from the surveys for the hybrid

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vehicle in Table CS4.1 are seen to be smaller than the added value for the diesel. It is speculative, but the hybrid technology may still be so new relative to the diesel that its potential merits are being discounted until verified over time in the marketplace. The standard deviations in the fourth column of Table CS4.1 were computed using the Lack Of Fit (LOF) method described in Chapter 3. The standard deviation for Hybrid 1 is seen to be quite large relative to its value of $534, making the Hybrid 2 results preferred even though taken from a local region.

0.5

Ln(f/(1-f))

0

y = -0.0004x + 0.2127 2 R = 0.912

-0.5 -1 -1.5 -2 $0

$1,000 $2,000 $3,000 $4,000 $5,000 $6,000 Price

Figure CS4.1. Logit plot data from McManus survey for willingness to pay for hybrid

1.5 y = -0.0006x + 0.9111 R 2 = 0.9349

1

Ln(f/(1-f))

0.5 0 -0.5 -1 -1.5

$0

$1,000

$2,000

$3,000

$4,000

Price

Figure CS4.2. Logit plot of data from McManus survey of willingness to pay for diesel

The Market for Hybrid and Diesel Mid-sized Sedans

105

CS 4.2 This Study This case study is less comprehensive, focusing only on the mid-sized passenger car market. Also we will consider only the impact of improved fuel economy, which is the key CTV attribute driving the development and purchase of these vehicles. This makes the analysis less thorough but it provides full insight into the major steps involved in making a more comprehensive forecast. CS4.2.1 Comparing Individual NPV Forecasts of Share with Survey Results The values computed from the projected improvements in fuel economy using the NPV model developed in Case Study 8 for this attribute are summarized in Table CS4.2. The baseline fuel economy chosen was the combined city and highway for the 2006 Camry. The improvements in fuel economy for the hybrid and diesel were taken to be 40% and 33%, respectively, which are the percentages used by Green, et. al. The price of fuel was taken to be $1.81 for gasoline and diesel fuels, which represent their averages over the year 2004. The vehicles were assumed to travel 12,000 miles annually. The fuel economy value improvements for the hybrids computed from the NPV model are seen to be around twice the survey value for the Hybrid 2 in Table CS4.1 and outside its three standard deviation range. (The standard deviation for the Hybrid 1 value in Table CS4.1 is too large for a meaningful comparison.) However, the survey value and computed fuel economy value for the diesel are reasonably close. The last two columns in Table CS4.2 compare the market shares predicted by the NPV forecasts versus those from the surveys. The NPV forecasts were computed from the NPV values and added prices in Table CS4.2 and the measured slopes β '' from Table CS4.1. The relatively small percentages for Hybrid 2 are a result of its β '' slopes being larger than the other two thereby generating a greater fall-off in share with price. CS4.2.2 Reference Price for Options A common practice is to compute the price elasticity from the expression for β '' (see Equation (A.23)) and to compare it with the price elasticity for the market segment. This practice can be flawed theoretically because the number of competing products in the survey will usually not be the same as for the market segment. For the surveys here, N = 2 , but N could be as large as 6 or 7 in the actual market segment. Another issue is that the price used in computing the price elasticity is almost always taken to be the full price of the good. However, when considering vehicle options, respondents, as well as buyers, may use instead their perceived value of the option (Cook, 1997, pp. 96-97) as a reference. In fact, a fraction x of buyers may use the price PC as a reference and 1 − x may use their perceived value of the option VOpt as a reference. Thus, another approach is to make use of the quantity VC − PC in the first relation in Equation (A.23) if demand is fixed or the first relation in Equation

106


(A.21) if demand is not fixed.1 For fixed demand with N = 2 , we find that the reference value less the reference price is given by: VC − PC =

4

(CS4.1)

β ''

The findings for VC − PC computed from Equation (CS4.1) using the experimental results for β '' are shown in Table CS4.3. Using the possibility describe above that respondents may be using different references, we can write VC − PC as VC − PC = xPC + (1 − x)VOpt

(CS4.2)

It follows from Equations (CS4.1) and (CS4.2) that the fraction is given by: x = (4 / β ''− VOpt ) /( PC − VOpt )

(CS4.3)

Using the average for VC − PC in Table CS4.3, we find that x = 0.25 , which implies, if the assumptions are correct, that 25% of the respondents used PC as a reference and 75% used the value of the option, VOpt . This approach offers an alternative interpretation to the use of elasticities in explaining the price coefficient.

1

Ln(f/(1-f))

0.5

y = -0.0008x + 0.5946 2

0

R = 0.992

-0.5 -1 -1.5 -2 -2.5 -3 $0

$1,000

$2,000

$3,000

$4,000

Added price Figure CS4.3. Logit plot of data from Ong and Haselhoff survey of willingness to pay for hybrid

1

Recall that VC that is the total value of the product.


107

Table CS4.1. Results from the surveys showing the slope for the negative price coefficient, β '' , value of the alternative power plants, the standard deviation of value, and the three standard deviation ranges computed from lack of fit

Vehicle Survey type β'' value Base SI N/A N/A Hybrid 1 3.98E-04 $534 Hybrid 2 7.81E-04 $762 Diesel 5.86E-04 $1,555

SD Value Value range ± 3 SD LOF low high N/A N/A N/A $631 -$1,358 $2,426 $113 $424 $1,100 $240 $835 $2,275

Table CS4.2. The projections of value and individual market share of an alternative versus the base SI as computed from (1) the NPV of savings from improvements in fuel economy and from (2) the surveys. Fuel costs used for the NPV computations were $1.81/gal.

Annual Vehicle Fuel fuel type Price economy costs Base SI $25,026 28.5 $762 Hybrid 1 $28,946 39.9 $544 Hybrid 2 $28,946 39.9 $544 Diesel $27,976 37.9 $573

Annual savings versus base SI 0 $218 $218 $189

Added Forecast NPV Price % market 9 year versus share horizon Baseline NPV Survey 0 0 N/A N/A $1,507 $3,920 27.7 20.62 $1,507 $3,920 13.2 7.83 $1,309 $2,950 27.7 30.63

Table CS4.3. Reference value less reference price computed from the survey outcomes Vehicle type

VC -PC

Hybrid 1 Hybrid 2 Diesel Avg.=

$10,046 $5,124 $6,826 $7,332

CS4.2.3 Forecasts of Long Term Share of Three Competing Powerplants The projections for long term market share are shown in Table CS4.4 for fuel costs of $1.81/gal. The values and prices of the hybrid and diesel were taken relative to the base SI engine vehicle as a reference. Because demand floats in the actual marketplace, the price coefficient β ' = ( N + 1) /(VC − PC ) was used for the projections with N = 3 and VC − PC = $7,332. The projections from this study are reasonably close to those found by Greene, et. al., which is somewhat fortuitous as only one attribute was considered here. The projections in Table CS4.5 are for fuel costs of $3.00/gal but the added values are still below the added prices.

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Table CS4.4. Projections for market share for passenger cars for the three competing options based upon $1.81/gal fuel

Vehicle Added type Value Price Base SI $0 $0 Diesel $1,309 $2,950 Hybrid $1,507 $3,920

f β' EXP(β'(V-P)) 0.0005 1 0.596 0.0005 0.408 0.244 0.0005 0.268 0.160

Table CS4.5. Projections for market share for passenger cars for the three competing options based upon $3.00/gal fuel

Added Vehicle type Value Price Base SI $0 $0 Diesel $2,169 $2,950 Hybrid $2,498 $3,920

β' EXP(β'(V-P)) 0.00055 1 0.00055 0.653 0.00055 0.460

f 0.473 0.309 0.218

It may seem that the model is incorrect in that a substantial market share is predicted for the diesel and hybrid even though their added values from the surveys were estimated to be less than their added prices. Although a single added value was used to describe the demand behavior in each of the logit plots in Figures CS4.1 through CS4.3, a specific respondent had his or her own willingness to pay for the new technologies and a reasonable percentage were willing to pay more than the added values from the surveys listed in Table CS4.1. However, with the added values from the surveys less than the added prices, it would not make economic sense for a company to eliminate an existing, successful SI vehicle and replace it with either a diesel or hybrid. Instead to reach those respondents who were willing to pay more than the added value from the survey for the hybrid or diesel, the manufacturer should either introduce an all new vehicle or offer hybrid or diesel powered vehicles as options to existing vehicles. But even this approach only makes sense financially if (1) the price of the vehicle is greater than cost or if (2) within a year or so ways will be found to reduce cost to the point that the vehicle is profitable. The Prius likely does not satisfy either of the above conditions in 2006. So, did Toyota make a mistake? Probably not. First of all, the Prius has only had a limited negative impact on Toyota’s laudable bottom-line. Moreover, it immediately boosted Toyota’s image with environmentalists at a time when the company was moving into the large pickup market. Of significant long term importance is the fact that Toyota and its suppliers will be ahead of competitors in learning the intricacies of the special control algorithms and new battery technology required for hybrids, which it can use in future vehicles. By manufacturing the Prius, Toyota will also learn where costs can be reduced. Moreover, if fuel prices continue to increase, added value will exceed costs at a time where there will likely be high demand for vehicles with excellent fuel economy. Finally, the Prius, to Toyota’s advantage, puts pressure on its competitors to develop strong hybrids at a


109

time when some are hard pressed financially. Thus, a positive business case can be made for a product even when the short term case is negative. However, you need a special vision and deep pockets to justify it. As stated earlier, Prius sales in 2006 were 20% of the combined sales of Prius and Camry. This figure may not be far off the long term upper limit penetration expected for hybrid vehicles provided that the price of fuel and the price of hybrids remain close to their 2006 levels.

CS 4.3 Summary o

o

o

o

Significant demand can exist even when the added prices of the hybrid and diesel vehicle are greater than their added value from fuel economy savings. Hybrid and diesel vehicles should not be used to replace successful current brands but should be offered either as optional powertrains to current brands or offered as an entirely new brand as Toyota did with the Prius. The jury is still out as to what the actual long term market share will be for the hybrid and diesel in the US. In 2006, hybrids made up only 1.8% of all vehicle sales. In 2006, Prius sales were 20% of the combined sales of Toyota’s Camry and Prius. The 20% figure likely represents a rough upper limit on the fraction of hybrid sales that can be expected in the long term if availability and confidence in the technology becomes widespread. This assumes that the price of fuel does not change from the average over 2006 and the added price for hybrids holds constant.

CS 4.4 References Greene DL, Duleep KG, McManus W (2004) Future potential of hybrid and diesel powertrains in the us light-duty vehicle market. ORNL/TM-004/181, Oak Ridge National Laboratory, Oak Ridge, TE McManus W (2004) Hybrids and clean diesels: if you build it, will they come? J.D. Power and Associates, Detroit, MI Ong P and Hasselhoff K (2005) High interest in hybrid cars. SCS fact sheet 1, UCLA Lewis Center for Regional Policy Studies Welch D (2007) Why hybrids are such a hard sell? Business Week, March 19:45

Case Study 5 Revealed Values: Minivan Trends

Insight: A key objective of most major product redesigns is to add significant new value. Once production begins, the company should compare its forecast with the observed value improvement to learn how to refine its value modeling capability and plan better products in the future.

CS5.1 Consumers Reveal Preferences when They Buy Consumers reveal their preferences through their choices in the market place. A survey of randomly selected buyers to assess their purchases represents a revealed choice survey. However, not all preferences may be revealed as some desirable features or attributes may not be incorporated in the current goods or services. In addition to revealed choice surveys, reports by firms such as R.L. Polk and J.D. Power and Associates, which document trends in market share and prices, can be used to assess the value trends between competing brands.

CS5.2 Minivan Revealed Value Trends 1998 through 2002 Model Years CS5.2.1 Ford Windstar The revealed trends in total value of six minivans are shown in Figure CS5.1. These were computed from Equation (A.8), which is a self-consistent logit model expression in that it gives the logit model value differences when they are solved for using Equation (A.19). The trends can be computed automatically using the Value Trend Template described in Appendix C. All points are connected by lines to aid the eye. For the computations, the number of competing brands, N , was taken as six and the elasticity, ε C , was set equal to one (Donndelinger and Cook,

112


1997). The average prices and average demands for each year were equated to the average transaction prices and retail sales as supplied by Power Information Network, a division of J.D. Power and Associates. As the prices and sales are proprietary, they are not shown here. The values are in constant 2002 $. The trends for the Ford Windstar and the Honda Odyssey from model years 1998 to 1999 in Figure CS5.1 are of interest here. The Windstar’s value trend is represented by the open circles connected by the heavy dashed line. Its value increased by $2,583 from 1998 to 1999 as a result of its redesign, which included the second rear sliding door (see Chapter 1), new interior and exterior styling, and a 1.2 inch increase in overall width.1 In addition, improvements in city driving range from 360 to 442 miles and highway driving range from 500 to 598 miles were achieved by increasing the fuel tank capacity, but fuel economy was reduced from 20.5 mpg to 20 mpg. However, from 1999 through 2002, few improvements were made to the Windstar and its value trend, not surprisingly, remained flat over that period, as seen in Figure CS5.1.

Figure CS5.1. Value trends for several minivans from 1998 to 2002 model years in constant 2002 dollars. (Transaction prices and retail demand used in the computations were provided by Power Information Network, a division of J.D. Power and Associates.)

CS5.2.2 Honda Odyssey By the mid 1990s, Honda had developed an excellent grasp of how automotive value is generated through attribute improvements. One example of this new-

1

The base, three door model was also retained.

Revealed Values: Minivan Trends

113

found expertise (and there are others) is the Honda Odyssey value trend in Figure CS5.1, which is represented by the filled triangles connected by the heavy solid line. From the 1998 to the 1999 model years, the value improvement was $7,413, which allowed the Odyssey to move from dead last in value to a competitive position. The Odyssey attributes improvements from 1998 to 1999 included size (a 14.8% increase as measured by length × width), acceleration performance, interior and exterior styles, luggage capacity, and reliability. The zero to 60 mph acceleration time was decreased from 11.3 to 9.5 seconds but the combined fuel economy was decreased from 23.5 to 22 miles/gallon. “Best Buy” recommendations came from a variety of sources as a result of these improvements. Honda continued to add value to the Odyssey leading to a dominant position by 2002.

CS5.3 Learning by Comparing Forecast Value Improvements with Actual Improvements A value conscious company should compare its value forecasts for major redesigns with the observed value improvements after production has begun to discover where it needs to improve its forecasting model. In doing so, it will learn how to make better forecasts and products in the future. However, a major issue in making quantitative comparisons between theoretical, attribute-based value improvements for automobiles is to have a good grasp of the added values for changes in highly subjective attributes such as exterior and interior designs. A series of focus groups can be used to do this with properly designed surveys, but apparently few automotive companies quantify the value improvements associated with appearance, comfort, and ergonomics. If the relative values of these attributes were quantified, then a meaningful analysis of the differences in total value between the vehicles shown in Figure CS5.1 could be made. The lessons learned would show how to improve value modeling, demand, and profits.

CS5.4 Summary o o o

o

Revealed value trends over time for the brands competing within a market segment can be computed from their demand and price trends. Demand is taken to be equal to sales, which is satisfactory as long as there is not a backlog of customers for a given brand. The revealed value improvement for major redesigns should be compared to the forecast improvement to assess the accuracy of the value forecasting tool used. Discrepancies found in the forecasting model should be corrected so that improved forecasts and products can be made in the future. This constitutes part of the learning process needed to remain competitive.

114


CS5.5 References Donndelinger JA and Cook HE (1997) Methods for analyzing the value of automobiles. SAE 1997 Transactions, Journal of Passenger Cars 106:12631281

Case Study 6 Effect of Market Dilution When Value Differs between Competitors

Insight: A company that introduces a new product into a market segment has an attacker’s advantage because it will gain market share from the existing firms. As additional viable competitors enter the market segment, the initial firms inescapably loose additional market share. They must restructure to lower fixed costs to maintain profitability unless the overall market grows sufficiently to absorb the existing capacity.

CS6.1 Competing Products Differ in Value In Chapter 1, the role of market dilution was considered in an idealized state in which the competitors were identical in value, cost, and price. In real markets, differentiation will exist. The problem is re-examined here in which Competitor A starts out as a monopolist. The value of its product is $42,740, which is 0.95 times the value used in Chapter 1. Competitor A is then challenged by competitor B whose product has a value of $47,250, which is 1.05 times the value used in Chapter 1. Thus the value of B exceeds that for A by $4,500 or 10.5%. Finally additional competitors, lumped together as C, enter the market one by one. Each has a value of $45,000, which is mid-way between A and B. The total number of competitors is varied from 1 to 10 and they are assumed to have the same variable cost of $15,000. These numbers loosely apply to automobiles in the upper mid-sized range for family sedans in the North American market. The demand computations were made using the linear model, Equation (A.1), with prices computed from the Cournot/Nash model, Equation (A.12). The negative slope of demand, K , was taken to be 40 units annually per $.

116


CS6.2 Price Trends The price trends of products A, B, and C are shown in Figure CS6.1. The entry of competitor B’s product generates a marked price reduction of $5,225, a drop of over 18%. Annual demand for A shown in Figure CS6.2 falls from 555,000 to 346,000 or 37%. Gross revenue in Figure CS6.3 falls from 7.7 to 2.99 billion $ or 61%. Such large changes are not unexpected when a monopolist is attacked by its first strong and viable competitor.1 With additional entries, A’s losses are exacerbated by its weaker value position. As the total allocated fixed costs for producing 200,000 vehicles annually can exceed $1 billion, net revenue for A can become zero or negative with only four total competitors in the segment. On the other hand, vehicle B can sustain up to seven competitors before reaching a net zero in revenue.

CS6.3 Attackers’ Advantage As shown in Figure 1.8 and discussed in Chapter 1, attackers have an advantage if their products are competitive because they are able to add market share over time at the expense of those already in the market, who must restructure as fast as possible to lower fixed costs. Contractual agreements with workers, however, may limit the amount of restructuring that can be done in a timely manner. Although it is easy to say that the original manufacturers need to make better products to regain share when faced with ever increasing market dilution, better products will only lessen, but not stop the losses until a new equilibrium is reached. The gains by early entrants stimulate new entrants into the market. But the shape of the gross revenue curve in Figures CS6.3 and 1.9 shows that there are diminishing returns as more competitors enter. As profit margins thin with dilution, the firms that survive must be close competitively. Otherwise one superior product would in time bankrupt the others. Once the race to dilution has advanced well into the low return domain, the survivors should sense a strong driving force to reduce dilution through mergers and acquisitions and other forms of cooperation such as the emergence of a price leader. However, federal trade regulators will likely keep N from falling below two or three firms. The lack of severe dilution with N small makes it easier for a firm whose products have lower value and higher costs than its competitors to survive.

1

Of course these market adjustments do not occur immediately with the entry the first competitor, which offers the original monopolist a limited amount of time to restructure.

Effect of Market Dilution when Value Differs between Competitors

Price

$30,000 $28,000

A

$26,000

B

$24,000

C

$22,000 $20,000 $18,000 $16,000 $14,000 0

2

4

6

8

10

Total number of competitors

Figure CS6.1. Price for A, B, and C as a function of the total number of competitors

Annual demand

600,000 500,000

A B

400,000 300,000 200,000 100,000 0 0

2

4

6

8

10

Total number of competitors Figure CS6.2. Annual demand for competitors A and B

117

118


$10 A

Gross revenue in 109 $

$8

B $6 $4 $2 $0 0

2

4

6

8

10

Total number of competitors Figure CS6.3. Gross revenue for A and B as a function of the total number of competitors.

CS6.4 Summary o

o o

o o

If new entrants to a market have comparable products in terms of price and value, they have an attacker’s advantage in that they can gain market share at the expense of those in the market before them. Entering, however, can become speculative with more competitors coming in than the market can sustain profitably. Because the shape of the revenue cure with the number of competitors favors fewer competitors, in time the oversupply of competitors should diminish. Brands that are weaker in value and higher in cost are most likely to fail. Others may be eliminated through mergers and acquisitions. Cooperative behavior among the survivors may also appear in which a price leader emerges to soften competition.

Case Study 7 Value of Interior Noise in a Luxury Automobile

Insight: When the value curve for interior noise of a luxury sedan is normalized by dividing through by its baseline value, the curve should be applicable to other sedan segments.

CS7.1 DV Survey Using a DV survey, Pozar and Cook (1997) showed that the value curve for interior noise in a luxury automobile could be described by an exponentially weighted parabolic value function, as discussed in Appendix B. Their interest was to develop a methodology for assessing the value of noise reduction and they used a convenience survey for this purpose in which the 75 participating respondents were employees of a major automobile company. Thus, the outcomes are directional only. The survey was delivered via a computer screen, as shown in Figure CS7.1. Respondents wore headphones and could listen to the different noise levels of the baseline and alternate luxury vehicles cruising at 70 mph. The noise spectrums used were from a digital recording purchased from Sound Ideas, the frequency distribution being constant for all cases. The noise level of the alternative vehicle was varied from 52 to 78 dBA, whereas the noise level of the baseline was fixed at 66 dBA. A total of 11 different dBA levels were evaluated for the alternative. (One level, equal to 64 dBA, was not included in the analysis as it was an outlier caused by the 2 dBA change from baseline not exceeding the threshold of detection as discussed below.) The respondents were divided into a group of 37 and a group of 38. Each group listened to only one-half of the levels to reduce respondent fatigue. If the respondent’s prior selection was for the alternative, the price of the alternative was automatically increased by the computer. If the prior choice was for the baseline, the price of the alternative was decreased. This process was repeated until the respondent switched his or her preference. For this study, the value of the 62 dBA relative to the 66 dBA baseline was evaluated using the DV 11 Template, which can be obtained from the publisher’s web-site. (The templates and their use are described in Appendix C.) The logit

120


plot from the template is shown in Figure CS7.2. The 62 dBA input data from the 38 respondents are shown in Table CS7.1 as copied from the DV 11 Template. The vector [Y], which represents the utility differences between the 62 dBA alternate and the 66 dBA baseline, is computed as Ln ( f /(1 − f ) ) by the template. The vector [VarY] represents the variances of [Y] and was computed by the template using Equation (3.3).

CS7.2 Level 2 OLS Coefficients The Level 2 OLS coefficients and their statistics given by the template are shown in the box in Table CS7.2. The mean of the value change in going from 66 to 62 dBA and its standard deviation of $1,896 and $155, respectively, are shown in the lower portion of Table CS7.2. The computations in the template for the df for value were made following the method described in Chapter 3 in which Satterthwaite’s df is computed using the statistics from the inverse logit plot.

Figure CS7.1. Computer screen used in the DV survey for the value of interior noise. (Reprinted with permission from SAE Paper 980621 © 1998 SAE International.)

Value of Inerior Noise in a Luxury Automobile

121

2.000

Ln(f/(1-f))

1.500 1.000

y = -0.0007x + 1.3694

0.500

R2 = 0.9697

0.000 -0.500 -1.000 -1.500 -2.000 -2.500 0

1000

2000

3000

4000

5000

P-P 0

Figure CS7.2. Logit plot for assessing value of 66 versus 62 dBA. (Redrawn and reprinted with permission from SAE Paper 980621 © 1998 SAE International.)

Table CS7.1. The design matrix, input data, and selected outcomes for assessing the value of 62 dBA relative to 66 dBA as taken from the DV 11 Template.

[X] Design Matrix Base P-P0 Trial α 1-f −β'' 200 0.197 1 1 800 0.355 2 1 3 1 1200 0.382 4 1 1400 0.461 5 1 2000 0.513 6 1 2400 0.539 7 1 2600 0.592 8 1 2800 0.697 9 1 3400 0.724 10 11

1 1

f 0.803 0.645 0.618 0.539 0.487 0.461 0.408 0.303 0.276

n 38 38 38 38 38 38 38 38 38

Y 1.40 0.60 0.48 0.16 -0.05 -0.16 -0.37 -0.83 -0.96

VarY YModel 0.17 1.22 0.11 0.79 0.11 0.50 0.11 0.36 0.11 -0.08 0.11 -0.36 0.11 -0.51 0.12 -0.65 0.13 -1.09

3800 0.776 0.224 38 -1.24 0.15 4400 0.882 0.118 38 -2.01 0.25

-1.38 -1.81

122


'' Table CS7.2. Level 2 OLS coefficients and statistics for α and − β as taken from the DV 11 Template

Coefficients and Value and Their Statistics TAIL (enter 1 or 2) 2 OLSC SD d α 1.3694 0.23925 0.0000 - β'' -0.000722 0.00010 6.662E-19

CovAlphaBeta VarValue SDValue

0.0000 24011 $155

df 160 150

dfAlphaBeta Value tValue PWE value

t 5.72 -7.22

PWE 5.00E-08 2.48E-11

EWE 1.00E-07 4.95E-11

281 $1,896 Relative to baseline 12.24 6.96E-28

CS7.3 Exponentially Weighted Parabolic Model The full value curve is shown in Figure CS7.3. It has been normalized by dividing through by V0 (taken nominally to be twice the price of $40,000 of the baseline vehicle). The points at 40 and 110 dBA were taken from human factor studies (Woodson, et. al., 1992, p. 606). The point at 110 dBA is shown as zero because it represents the threshold of pain. A maximum is shown at 40 dBA because below this noise level the environment starts to become eerily and uncomfortably quiet. The best fit curve is an exponentially weighted parabola as described by Equations (B.2) and (B.3). The empirical, exponential weighting coefficient, γ , is equal to the slope of a plot of Ln(V / V0 ) versus Ln(ς V ) , where ς V is given by Equation (B.3). Figure CS7.4 shows that γ is 0.59 for interior noise. The tabulated data for the plot are shown in Table CS7.3. The linear plot and high R 2 value shown in Figure CS7.4 supports the use of the exponentially weighted, parabolic function given by Equation (B.2) to describe this value curve. The conjecture is that the weighting factor is proportional to the fraction of time that the attribute is important in the use of the product. From EPA studies, highway driving occupies approximately 40% of time the time spent in a car. Although the theoretical result is not well supported in this case, it is not outlandishly off the actual fraction either. It is important to note that the normalized curve shown in Figure CS7.3 for a luxury sedan can be converted, at least approximately, to the value curve for another family sedan segment by multiplying it by the baseline value V0 for that segment.


123

1.2 1

V/V0

0.8 0.6

Best fit curve From DV survey

0.4 0.2 0 40

60

80

100

120

Noise dBA

Figure CS7.3. The exponentially weighted three point value curve for interior noise at 70 mph. The circled points at 40 and 110 dBA are estimates of the ideal and critical points, respectively, taken from published human factor studies. (Reprinted with permission from SAE Paper 980621 © 1998 SAE International.)

0.100

Ln(V/V0)

0.050

y = 0.5853x - 0.004 2

R = 0.9972

0.000 -0.050 -0.100 -0.150 -0.3

-0.2

-0.1

0.0

0.1

0.2

Ln(ζV)

Figure CS7.4. Plot for determining the exponential weighting coefficient. (Reprinted with permission from SAE Paper 980621 © 1998 SAE International.)

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CS7.4 Prospect Theory Model The values found here can also be interpreted in terms of Prospect Theory gains (when noise is reduced from baseline) and losses (when noise is increased) as shown in Figure CS7.5. The slopes differ by a factor of two, which is not uncommon for a Prospect Theory interpretation. The point off the line at 64 dBA is believed to arise from the fact that the 2 dBA reduction from the baseline was not detectable by most respondents. Thus, given a choice between the baseline and the uncertainty of whether the noise of the alternative was greater or less than the baseline, respondents were biased to stay with the baseline. A bias for the baseline is another finding from Prospect Theory. Table CS7.3. Tabulated outcomes for all 10 alternative noise levels

T rial 1 2 3 4 5 6 7 8 9 10

dB A 52 58 60 62 66 68 70 72 74 78

V-V 0 5204 3590 2723 1896 0 -1451 -3389 -4264 -5564 -9147

Ln(V/ V 0 ) 0.06302 0.04390 0.03347 0.02342 0.00000 -0.01831 -0.04328 -0.05477 -0.07209 -0.12143

Ln( ζV ) 0.11862 0.08004 0.06329 0.04445 0.00000 -0.02590 -0.05449 -0.08598 -0.12063 -0.20067

CS7.5 Comparing the Two Models Thus, we have two interpretations for the value curve for noise examined here. The first interpretation is that the curve fits an exponentially weighted parabolic function that exhibits diminishing returns as noise is reduced. The second interpretation is that the value follows the behavior expected from Prospect Theory for gains versus losses. The two fit the findings equally well. Prospect Theory provides a local but fundamental insight into how value behaves about a given baseline point and explains why value curves should be concave. The exponentially weighted parabolic function is an empirical representation of value, but it covers a wider attribute range from the ideal level where value is a maximum to the critical level where value is zero.

V-V0


$8,000 $6,000 $4,000 $2,000 $0 -$2,000 -$4,000 -$6,000 -$8,000 -$10,000

125

y = -369.93x + 24731 2

R = 0.9781

y = -742.58x + 49001 2

R = 0.9921 50

55

60

65

70

75

80

Noise dBA Figure CS7.5. Plot of value versus noise exhibits a typical Prospect Theory plot of gains versus losses. The point × at 64 dBA is more than 3 standard deviations below the line. We believe that many respondents were unable with confidence to detect that the 64 dBA level was, in fact, a reduction in noise and thus stayed with the baseline. (Reprinted with permission from SAE Paper 980621 © 1998 SAE International.)

CS7.6 Summary o o

o o

The value curve for interior noise in a luxury vehicle was found to follow an exponentially weighted parabolic function. The empirical weighting exponent of 0.59 is in rough agreement with the fraction of time equal to 0.4 that drivers on average spend at cruising speeds. This supports the rule of thumb that the weighting coefficient should be approximately the fraction of time that the attribute is important during the use of the product. The outcomes could also be explained in terms of Prospect Theory’s findings of how value behaves for gains versus losses. The two interpretations are not in conflict. Prospect Theory gives a more fundamental but local explanation for value behavior, whereas the exponentially weighted parabolic function gives a more empirical but non-local description of how value is expected to behave.

CS7.7 References Pozar M and Cook HE (1998) On Determining the relationship between vehicle value and interior noise. SAE Transactions, Journal of Passenger Cars 106:391401

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Tversky A and Kahneman D (1991) Loss aversion in riskless choice: a referencedependent model. Quarterly Journal of Economics 106:1039-1061 Woodson WE., Tillman B, and Tillman PL (1992) Human factors design handbook (2nd ed.). McGraw-Hill, New York

Case Study 8 Quantifying the Trade-off between Acceleration Performance and Fuel Economy

Insight: Employees can be respondents to an initial survey to gain a rapid estimate of the value of a proposed new feature or option without the chance of exposing it to competitors. Care must be taken to select employees who are representative of the demographics of interest.

CS8.1 A Key Auto Trade-off The tradeoff between vehicle acceleration performance and fuel economy must be made with care. One methodology for quantifying the tradeoff was developed by McConville and Cook (1996) with help from colleagues at a major automobile manufacturer. A ten mile test route, which included freeway driving and city driving, was mapped out for evaluating acceleration performance under normal driving conditions. The route is shown schematically in Figure CS8.1. Included in the figure is the length of the route (10 miles), the fraction of time spent accelerating (17%), and the observed speed limits. Also listed are the full throttle acceleration times from 0 to 60 mph for the three vehicles used in the experiment. No full throttle accelerations were made, however, on the test route. A monitor rode in each vehicle to instruct the driver when to accelerate to what speeds and what turns to make to follow the route with normal driving habits. The respondents were a convenience sample of 50 male and 36 female volunteers from the company. Although the convenience sample makes the findings directional, the experiment served the purpose at hand, which was to develop a structured methodology for quantifying the tradeoff. Except for paint color and minor exterior ornamentation differences, the vehicles were identical in make and style. The acceleration performances of the vehicles were specified in terms of their 0 to 60 mph times at wide open throttle. These times were varied for each vehicle by using different engines, different spark advances, and different weight loadings. The respondents were not told of the relative performances of the vehicles.

128


Route length: 10 miles Road speed limits: 25, 35, 45, 50, and 55 Acceleration events: 17% of total time

0 to 60 mph times in seconds: Car A: 16.9 Car B: 12.2 Car C: 10.8

Figure CS8.1. Details of test conditions used to obtain the value of acceleration performance versus fuel economy

CS8.2 Experimental Design The conjoint DV method was used to assess the combined values for acceleration and fuel economy. Respondents were told that the baseline (vehicle) had a stated fuel economy of 22 mpg and a price of $18,000. The experimental design had eight trials. For each trial, respondents were presented with four separate paired comparisons and were asked to choose between the baseline and the alternative for each. Each of the alternatives for a given trial had a fixed fuel economy but a different price. Over the eight trials a total of six prices ($17,000, $18,500, $19,000, $19,500, $20,000, and $21,000) and five fuel economies (18, 20, 22, 24, and 26 mpg ) were evaluated. In contrast to the original analysis by McConville and Cook (1996) which used 0 and 1 categorical variables, coded variables were used here to increase sensitivity. The coded variable for acceleration was equal to the acceleration time minus the mean acceleration time of 13.3 seconds, the quantity divided by 13.3. The coded variable for fuel economy was equal to the fuel economy minus the mean fuel economy of 22 mpg, the quantity divided by 22. The first analytical model examined here used a coded design array that included the acceleration variable squared and the fuel economy variable squared. The coefficient for the fuel economy variable squared was found to be insignificant, however. This variable was then removed, which resulted in the design matrix [X] shown inside the first box in Table CS8.1. The value vector [Y]

Quantifying the Trade-off between Acceleration Performance and Fuel Economy

129

for the trials was computed from the difference between the neutral price found for the trial and the baseline price of $18,000. The last column lists the model values [YModel], which were computed from Equation (3.8) after solving for the four unknown coefficients. Table CS8.1. Shown in the first box is the design matrix used to evaluate the trade-off between acceleration versus fuel economy. Also shown are the outcomes [Y] and model outcomes [YModel].

Trial 1 2 3 4 5 6 7 8 9

Base 1 1 1 1 1 1 1 1 1

Accel 0.271 0.271 0.271 -0.083 -0.083 -0.083 -0.188 -0.188 -0.188

Accel^2 0.0733 0.0733 0.0733 0.0068 0.0068 0.0068 0.0353 0.0353 0.0353

FE 0.000 0.091 0.182 -0.091 0.000 0.091 -0.182 -0.091 0.000

Y $0 $800 $1,250 $1,290 $1,610 $2,000 $1,430 $1,970 $2,500

YModel $178 $683 $1,188 $1,128 $1,633 $2,138 $1,462 $1,967 $2,472

CS8.3 Values of the Attributes Relative to Vehicle A at 22 mpg The coefficients found for the coded variables and their statistical properties are shown in Table CS8.2. The solution matrix [XS] was computed in the standard manner from the design matrix [X] in Table CS8.1. The LOF variance for value was computed using the spreadsheet expression given by: VARLOF = SUMSQ(Y-YModel)/(9-4)

The above result was used for VarY in Equation (3.9) to compute the standard deviations of the value coefficients in Table CS8.2. The four coefficients are seen to be significant at better than 10% EWE. The coefficients for the coded variables in Table CS8.2 were used to compute the relative values for the acceleration and fuel economy variables in their uncoded representations, the results being shown in Table CS8.3. The decrease in acceleration time from 16.9 to 12.2 seconds and to 10.8 seconds is seen to add $1,455 and $2,293, respectively, in value. The reduction in fuel economy from 22 to 18 mpg is seen to reduce value by $1,010; whereas the improvement in fuel economy from 22 to 26 mpg is seen to improve value by the same amount. The coefficient of determination R 2 is 0.994.

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Table CS8.2. Values for the baseline and values of attributes relative to baseline

Base Accel Accel^2 FE

Value Coeff SD t PWE EWE $1,105 $135 8.20 0.000 0.000 -$5,694 $556 -10.23 0.000 0.000 $8,387 $3,234 2.59 0.024 0.073 $5,555 $699 7.95 0.000 0.001

Table CS8.3. Relative values for acceleration time and fuel economy

Accel Relative time Value value -$927 $0 16.9 $528 $1,455 12.2 10.8 $1,367 $2,293

Fuel Relative Econ. value -$1,010 18 -$505 20 $0 22 $505 24 $1,010 26

CS8.4 Exponential Weighting Coefficient for Acceleration Performance Acceleration performance was analyzed in terms of the empirical weighted parabolic function shown in Equations (B.2) and (B.3). The acceleration variable g was computed as Ln(88 / t0,60 ) where t0,60 is the full throttle acceleration time from 0 to 60 mph. Ln(88 / t0,60 ) is proportional to the psychometric intensity of the acceleration force experienced by the driver.

The critical time for t0,60 was

estimated to be 40 seconds which was taken as twice the highest acceleration time found in a search of published results. The ideal acceleration time was taken to be 2 seconds for the family sedan segment. This force is over 1.37 Gs, which is beyond the ability of most passenger car tires to grip the road. The g forces on most roller coaster passengers are around 3 but some exceed this according to Wikipedia (2006). The 0 to 60 mph vehicle acceleration time for 3 g is 0.91 seconds and the driver must be able to avoid spinout resulting from side-to-side torque and road adhesion differences. Roller coasters, of course, run on rails, they have no driver, and passengers are fully restrained, greatly reducing the safety issues. Thus, the ideal acceleration time of 2 seconds for a passenger car is a reasonable level for balancing safety against the thrill of acceleration. Using these parameters, the coefficient γ was computed in Figure CS8.2, which is the same type of plot used to compute this coefficient for interior noise in Figure CS7.6. The result found for γ for acceleration is 0.18 as taken from the equation listed in Table CS8.3. The closeness of this result to the fraction of time

Quantifying the Trade-off between Acceleration Performance and Fuel Economy

131

of 0.17 that respondents spent accelerating during the test drives is entirely fortuitous on noting that the two standard deviation range for γ is from 0.13 to 0.23. Nevertheless, the fact that the range of γ contains the time spent accelerating supports to the rule of thumb that the weighting factor is roughly the fraction of time that the attribute is important during the use of the product.1 0.07 y = 0.1799x - 0.0011

0.06

2

R = 0.9775

Ln(V/V0 )

0.05 0.04 0.03 0.02 0.01 0 -0.01 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Ln(ζV) Figure CS8.2. Plot to determine exponential weighting coefficient for acceleration performance

CS8.5 Time Horizon and Discount Rate for Fuel Economy The discount rate and time horizon for fuel savings were computed from the best NPV fit to the relative value of fuel economy in Figure CS8.3. Fuel economy affects both what is paid at the pump on an annual basis and it also affects the value of time lost at the pump for refueling. The vehicles were assumed to be driven 12,000 miles a year. The price of fuel (at the time of the study) was $1.20 per gal. The value of a person’s time when refueling was assumed to be $0.50 per minute and the time for a single refuel was 6 minutes. The fuel tank volume was assumed to be 15 gallons and the refueling stop was made when the fuel level dropped to 15% of capacity. The best fit of the theoretical NPV was for a time horizon of 9 years with a discount rate of 5.6%. In the original analysis, the best fit was for a time horizon of 7 years with a 5% discount rate. The fuel economy computed from theoretical NPV values for fuel costs and refueling loss of personal time costs in Figure CS8.3

1

The outcome in Case Study 7 also supports this rule of thumb.

132


show a concave function, whereas the experimental findings are linear. Also the time horizon for the best fit is larger than the three to five years we expected. Nevertheless, the discount rate and the time horizon are reasonable for someone who was logical in the economic sense about the true accounting for the NPV for fuel economy over the lifetime of the vehicle. With analytical expressions for both acceleration performance and fuel economy, it is possible to construct a family of curves of constant value with fuel economy on one axis and acceleration time on the other. A set of such plots were made for different prices of fuel by McConville and Cook ( 1996). $1,500

Experiment

$1,000 NPV

$500 $0 -$500 -$1,000

Theory

-$1,500 15

20

25

30

Fuel economy (mpg)

Figure CS8.3. Comparison of experimental fuel economy with the best fit theoretical value computed from the NPV of the annual value lost from fuel costs and time lost in refueling

CS8.6 References McConville G and Cook HE (1996) Examining the trade-off between automobile acceleration performance and fuel economy, SAE Transactions, Journal of Material Manufacturing 105:37-45 Wikipedia (2006) Acceleration due to gravity. http://en.wikipedia.org/wiki/Acceleration_due_to_gravity

Case Study 9 Value of Mustang Options

Insight: When a feature costs more than its added value, it will not be profitable to include it as part of the standard equipment. However, it may be highly profitable to offer it as an option.

CS9.1 DV Survey of Mustang Owners Randomly selected buyers of a Ford Mustang during March and April of 1995 were surveyed as to their willingness to pay for six different options (McConville and Cook, 1997). The purpose of the survey was to examine the differences in effectiveness of three different ways of presenting the survey. One survey was sent to 1000 buyers who were asked to write in the maximum price they would be willing to pay for the option relative to the baseline vehicle. Another survey was sent to 1000 buyers, who were presented with a single price for the option. Three different forms of this survey were sent out. Each set was sent to a different group of 1000 buyers so that a cumulative willingness to pay against three different prices would be generated. The third survey followed the Direct Value (DV) format described in Chapter 3 in which the option was offered at three different prices. This survey was sent to another 1000 buyers. Comparisons to actual price sensitivities suggested that the elasticities found were unrealistically low when respondents were presented with a single price for an option. This led to values that were unrealistically high. There was not a large difference between the outcomes from the write-in and three-price surveys. However, a slight edge was indicated for the three-price, DV survey because its response rate was 27% versus 22% for the write-in survey, suggesting that the write-in survey may have caused slightly more cognitive stress. Also, in a direct comparison against the known take rate for the ABS (anti-lock brake system) option, the three-price DV survey prediction was better than that for the write-in price and single price surveys. The six individual options and their values and standard deviations found using the three price survey are shown in Table CS9.1. These were recomputed here using the DV 3 template described in Appendix C. The results listed for value are

134


from the OLS analysis, which were the same as for the LOF analysis. However, the standard deviations of the OLS analysis were all smaller than those computed from the LOF analysis using inverse logit plots. Thus, the larger LOF standard deviations were entered into Table CS9.1 to have a conservative bias. The discrepancies between the OLS and LOF standard deviations are a result of model error caused by the slight convex curvature seen in most of the logit plots. Table CS9.1. Value of Mustang options and their standard deviations. The values were computed from DV 3 template. The standard deviations were computed using the inverse logit plot with the LOF method because they were all higher than the estimates computed from the asymptotic expression for variance given by Equation (3.3).

Option EG Auto Trans ABS Leather Seats Air Cond Convertible V8

Value $1,743 $908 $549 $1,517 $3,290 $2,751

SD $148 $82 $180 $177 $558 $409

CS9.2 Automatic Transmission Option The output summary from the template is shown in Table CS9.2 for the 49% of the respondents who considered the automatic transmission an economic good. This less than strong preference for the automatic transmission is not surprising for buyers of a sporty, muscle car. The number respondents that saw the automatic transmission as an economic good was divided by 0.49 except for the fraction that chose the automatic transmission at no price penalty, which was set at 0.95 instead of unity to avoid the singularity in the logit function. These fractions are shown against the three prices at the top left of Table CS9.2. The value of this option when all respondents were included was a negative $61, making it very unwise to offer it as standard equipment. The economic good outcomes can be used to estimate how to price the option given its value and cost. An outcome can depend upon (1) whether the option purchase decision was made after independently making the choice to purchase the base vehicle or (2) whether the availability of the option influenced the purchase of the base vehicle and thus increased overall demand. Figure CS9.1 shows the projected revenue per vehicle sold as a function of the price of the automatic transmission option assuming (1). The optimal price is seen to be close to the value of the option of $1,740. Figure CS9.2 shows the projected revenue per vehicle sold for assumption (2), the optimal price being close to one-half of the sum of the option value plus its cost (assumed here to be $1,000) thereby giving a price of $1,371. For simplicity, these computations were made using the linear demand model, Equation (A.1) For relatively inexpensive options, making the option decision after the purchase decision was made is the likely scenario. For expensive options,

Value of Mustang Options

135

particularly if they are unique from a single manufacturer, the coupled purchase is the likely scenario. For this particular problem, there was less than a 1% increase in total demand for the coupled purchase because the added demand for the vehicle with the option took sales from the base vehicle.

CS9.3 Anti-lock Brakes Option The template summary for the ABS option is shown in Table CS9.3. The F-test result at the bottom of the summary sheet shows that the Type I error is very small for rejecting the hypothesis that the variance for value from the LOF model came from a population having the same variance as that computed from the Level 2 OLS method given by Equation (3.4). Note that the price ranges for the automatic transmission in Figures CS9.2 and ABS in CS9.5 are quite different. This reflects the fact that their values were expected to be different based upon a small preliminary survey. The ability to set the target price for each attribute in this manner is an important feature of the DV method. The findings for the ABS in Table CS9.3 are typical of those found for the other options, which are (1) that because of the convexity observed in the logit plot, the theoretical OLS standard deviations for value were less than the standard deviations computed using the LOF method, and (2) that somewhat higher R 2 results were found for the OLS and LOF analyses than for the MLLE analysis. The higher R 2 results should be expected as both the OLS and LOF arrive at their coefficients by minimizing the least square error.

CS9.4 Option Price Elasticities A good question regarding the ease or lack thereof in selling an option is “When considering vehicle options, do buyers use the price of the entire vehicle as a reference or do they use their sense of the value of the option?” Of course some buyers may consider the price of the option one way and others may consider it the other. If the reference price of buyers is the value of the option, Equation (A.19) becomes: Ln( fOpt /(1 − fOpt ) = β ''Opt ⎡⎣VOpt − POpt ⎤⎦

(CS9.1)

Since demand is fixed in the DV method, it follows from Equation (A.23) that:

β ''Opt =

4ε Opt VOpt

(CS9.2)

136


The results for β ''Opt computed from Equation (CS9.2) for the six options are listed in Table CS9.4. Also shown are the option elasticities computed from Equation (CS9.2). The average of the option elasticities of 0.78 supports the view that the reference price is close to the aggregate value of the option. The larger the size of β ''Opt , the smaller is the uncertainty in the value of the option among the respondents. A method for breaking the fraction of respondents into those having the vehicle price as a baseline and those having the option value as baseline is discussed in Case Study 4.

CS9.5 Summary o

o

o

o

o

When respondents to a DV survey regarding Mustang options were asked to choose between a baseline and an option offered at a single price, the resulting elasticities found were unrealistically low making the values of the option unrealistically high. However, realistic values were found for surveys in which respondents were asked either to write in their maximum willingness to pay for an option or to select from binary choices consisting of a fixed price baseline and an alternative that was offered over a range of three prices. When buyers choose an option after deciding to purchase the automobile, the optimal price for the option was found to be approximately equal to its value. The standard deviations for the value of the options were somewhat higher when computed from the LOF method versus the theoretical standard deviations computed from the asymptotic logit model. This was caused by curvature in the logit plots. When the value of an option is higher than its cost, it still may be profitable to offer it as an option. The automatic transmission for sporty cars is a good example of this.


137

Table CS9.2. Template parameters for those respondents that considered the automatic transmission as an economic good Price 0 800 1600

EG f 0.95 0.793 0.582

EG Automatic Transmission Level 2 Linest OLS LOF MLLE 2.8459 2.8459 2.7136 α 0.0016 0.0016 0.0015 β'' Tails 2 2 SD α 0.124 0.220 tα 22.92 12.91 df α 1107 1 SD β'' 0.00010 0.00021 16.46 7.65 t β'' df β'' 1374 1 R^2 0.9832 0.9832 0.9770 Value 1743.47 1743.47 1786.22 SD value 45.69 147.93 t value 38.2 11.8 df value 2540.0 1 PWE value 3.28E-252 F test Type 1 0.00

Average net revenue per vehicle

$300 $200 $100 $0 -$100 -$200 -$300 Value = $1,740

-$400 -$500 $0

$1,000

$2,000

$3,000

$4,000

Price of option Figure CS9.1. Projected revenue per vehicle sold as a function of the price of the automatic transmission option assuming no overall increase in demand

138


Added revenue per car sold

$250 $200 $150 $100 $50 (V+C)/2 $0 $0

$500

$1,000

$1,500

$2,000

Price of Option

Figure CS9.2. Added revenue per car sold assuming that the value and price of the option affects total sales.

Table CS9.3. Template parameters for ABS (anti-lock brake system) Price 300 600 900

α β'' Tails SD α tα df α SD β'' t β'' df β'' R^2 Value SD value t value df value PWE value F test Type 1

f 0.901 0.69 0.539 ABS Level 2 Linest OLS LOF MLLE 3.1070 3.1070 2.9330 0.0034 0.0034 0.0032 2 2 0.149 0.477 20.83 6.52 1233 1 0.00021 0.00074 16.63 4.65 1634 1 0.9558 0.9558 0.9498 908.45 908.45 920.57 17.97 81.69 50.6 11.1 2202.0 1 0.00E+00 5.7E-06


139

Table CS9.4. Option elasticities β'' Option EG Auto Trans ABS Leather Seats Air Cond Convertible V8

-1

($) 0.0016 0.0034 0.0016 0.0045 0.0008 0.0008

Option elasticity 0.71 0.78 0.22 1.69 0.69 0.58

CS9.6 References McConville GP and Cook HE (1997) Evaluating mail surveys to determine the value of vehicle options. SAE Transactions, Journal of Passenger Cars 106:1290-1297

Case Study 10 Simulated Survey of Choice between Auto and Transit Bus Modes

Insight: When the fraction of respondents choosing the alternative is 0 or 1, the maximum likelihood method must be used as singularities appear when using the logit model with the OLS formulation. Nevertheless, for this particular problem, an approach was found, which generated an approximate but insightful Lack Of Fit solution that avoided the singularities.

CS10.1 Maximum Log Likelihood Solution Ben-Akiva and Lerman (1985, pp. 87-92) simulated a stated choice survey in which a single respondent chose between two modes of transportation, auto or transit bus (transit), over a series of 21 different travel times for each. The travel times are shown in Columns D and E in Table CS10.1 for the auto and transit, respectively. The mode selected is the outcome vector [Y] in column F. The index is 1 if the auto mode was selected and 0 if the transit mode was selected. They used a linear-in-the-attributes utility model in which the relative value of the auto to transit was one attribute and the utility of time was the other. The Maximum Log Likelihood Estimates (MLLE) for the coefficients of the utility of the auto versus the transit modes and for the utility of time are listed in Cells M2 and M3, respectively. They were computed using the Solver tool in the spreadsheet.1 The coefficients are identical to three decimal places to those reported by Ben-Akiva and Lerman. The actual values for the coefficients used by Ben-Akiva and Lerman to generate the simulations were -0.25 and -0.05 for the auto mode and transit time, respectively. Thus, for identical times, the transit bus mode would be preferred over the auto. The findings for the two coefficients were used to compute the MLLE model outcomes [YmodelMLLE] in Column G. The logical expression in Cell H8, which is described at the bottom of Table CS10.1, was pulled down to generate the 1

See the general discussion in Chapter 3 on using Solver to generate MLLE solutions.

142


0 or 1 model predictions for the transportation mode. If the probability was greater than 0.5, a one was selected, otherwise it was zero. The two predictions shown with boxes around them (trials 2 and 13) did not agree with the simulated outcomes. The computations used to generate the auto and transit time MLLE coefficients are contained in Columns J through P. Again the specific expressions used are shown at the bottom of Table CS10.1. The logit model numerators in Equation (3.22) are computed in Columns J and K and their contributions to the MLLE function are computed in Columns M and N. Because the outcomes for each fi in each row were either 0 or 1, the MLLE elements in Columns M and N were either zero or finite. Column P sums the two elements in each row. The sum in Cell P30 of the terms in Column P is the MLLE function that Solver maximizes. Table CS10.1. MLLE analysis of simulated auto versus transit choice survey C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

D

E

F

G

H

I

J

K

L

M N Coefficients Auto -0.238 Time -0.053

O

P

Net Mode Log Log Likelihood Auto LikeTravel Time Numerators Elements =1 YmodelPrelihood Auto Transit Y MLLE diction Auto Transit Auto Transit Coeff. 1 52.90 4.40 0 0.057 0 0.047 0.792 0.000 -0.058 -0.058 2 4.10 28.50 0 0.742 1 0.634 0.220 0.000 -1.356 -1.356 3 4.10 86.90 1 0.985 1 0.634 0.010 -0.015 0.000 -0.015 56.20 31.60 0 0.176 0 0.040 0.187 0.000 -0.194 -0.194 4 51.80 20.20 0 0.128 0 0.050 0.342 0.000 -0.137 -0.137 5 0.20 91.20 1 0.990 1 0.780 0.008 -0.010 0.000 -0.010 6 7 27.60 79.70 1 0.926 1 0.182 0.015 -0.077 0.000 -0.077 8 89.90 2.20 0 0.007 0 0.007 0.890 0.000 -0.007 -0.007 9 41.50 24.50 0 0.242 0 0.087 0.272 0.000 -0.277 -0.277 0 0.049 0 0.005 0.099 0.000 -0.050 -0.050 10 95.00 43.50 8.40 0 0.006 0 0.004 0.640 0.000 -0.006 -0.006 11 99.10 1 0.962 1 0.295 0.012 -0.038 0.000 -0.038 12 18.50 84.00 13 82.00 38.00 1 0.071 0 0.010 0.133 -2.648 0.000 -2.648 8.60 1.60 0 0.352 0 0.499 0.919 0.000 -0.434 -0.434 14 15 22.50 74.10 1 0.924 1 0.239 0.020 -0.079 0.000 -0.079 16 51.40 83.80 1 0.815 1 0.051 0.012 -0.205 0.000 -0.205 17 81.00 19.20 0 0.029 0 0.011 0.361 0.000 -0.029 -0.029 1 0.828 1 0.053 0.011 -0.189 0.000 -0.189 18 51.00 85.00 1 0.776 1 0.029 0.008 -0.253 0.000 -0.253 19 62.20 90.10 0 0.016 0 0.005 0.308 0.000 -0.016 -0.016 20 95.10 22.20 1 0.918 1 0.087 0.008 -0.086 0.000 -0.086 21 41.60 91.50 0.476 Cell F29 =AVERAGE(F8:F28) Cell J8 =EXP($M$2+D8*$M$3) -6.166 Cell G8 =J8/(J8+K8) Cell K8 =EXP($M$3*E8) MAXIMIZE Area H8:H28 =IF(YmodelMLLE>0.5,1,0) Cell M8 =F8*(LN(J8/(J8+K8))) Cell N8 =IF(F8=0,1,0)*LN(K8/(J8+K8)) Cell P8 =SUM(M8:N8) (drag down) Cell P30 =SUM(P8:P28)

Simulated Survey of Choice between Auto and Bus Transit Modes

143

Table CS10.2 shows the two coefficients along with their asymptotic standard errors, which were taken directly from Ben-Akiva and Lerman’s analysis.2 Also shown is the t-statistic, which is equal to the coefficient divided by its asymptotic standard error. The conclusion from Table CS10.2 is that the utility coefficient for the auto versus the transit mode, although close to the true result for the population, is not significant from zero and that trip time controls the findings in large part. In Table CS10.3, L(max) is the maximum of the log likelihood and L(0) is the log likelihood with all of the coefficients equal to zero. The two quantities are used to compute the “informal goodness of fit” ρ 2 which is equal to 1 − ( L(max) / L(0)) . The value of ρ 2 can be interpreted as expressing the MLLE prediction in Column H is able to explain 57.6% of the variation in the mode selected Column G. This outcome is low compared to the estimate shown for the traditional R 2 = 0.659 computed as 1-SSE/SSY with SSE and SSY being computed from the sum of the squares described in the standard manner for Cells T11 and T12. Both coefficients were used in the R 2 computations even though the auto coefficient was not significant. Table CS10.2. Ben-Akiva and Lerman’s coefficients for auto and time of travel including the asymptotic standard error (standard deviation) and the t-statistic

T 1 2 3 4 5 6

U

Coefficient estimate Auto -0.238 Travel time -0.053

V Asymptotic standard error 0.7505 0.0206

W

t -0.32 -2.57

Table CS10.3. Incomplete list of MLLE summary statistics S T U 8 L (max) = -6.166 L (0) = -14.556 9 10 ρ^2 = 0.576 SSE = 1.785 11 SSY = 5.238 12 13 R^2= 0.659 14 Cell T10 =1-(T8/T9) 15 Cell T11 =SUMSQ(Y-YmodelMLLE) 16 Cell T12 =SUMSQ(Y-AVERAGE(Y)) 17 Cell T13 =1-T11/T12 18

2

Special software is required to generate the asymptotic standard errors using the MLLE method.

144


CS10.2 LOF Workaround Solution Although the MLLE method can be used with the logit model to analyze problems having discrete 0 or 1 results for f as in Ben-Akiva and Lerman’s simulated survey, the OLS method can not be used because of the singularities. However, the singularities can be avoided by modeling the observed 0 and 1 fractional outcomes directly instead of their logs using the LOF method (see Chapter 3) in conjunction with the design matrix [XX] in Table CS10.4 (area AD8:AF28).3 Table CS10.4. The design array [XX] for the LOF analysis is in Area AD8:AF28. Also shown are the model results for the 0 and 1 outcomes and the LOF prediction. The prediction for trial 13 is enclosed by a box to show that the 0 is incorrect.

AH AI AJ AC AD AE AF AG 7 Trial Baseline Auto Transit YmodelLOF Prediction 8 1 1 0.085 -0.910 -0.1133 0 9 2 1 -0.916 -0.415 0.2099 0 3 10 1 -0.916 0.783 0.9974 1 11 4 1 0.153 -0.352 0.2536 0 12 5 1 0.063 -0.586 0.0998 0 13 6 1 -0.996 0.871 1.0552 1 14 7 1 -0.434 0.635 0.9012 1 15 8 1 0.845 -0.955 -0.1416 0 16 9 1 -0.148 -0.497 0.1574 0 17 10 1 0.949 -0.107 0.4155 0 18 11 1 1.033 -0.828 -0.0576 0 19 12 1 -0.620 0.724 0.9588 1 20 13 1 0.683 -0.220 0.3409 0 21 14 1 -0.824 -0.967 -0.1526 0 22 15 1 -0.538 0.520 0.8255 1 23 16 1 0.055 0.719 0.9573 1 24 17 1 0.662 -0.606 0.0873 0 25 18 1 0.046 0.744 0.9735 1 26 19 1 0.276 0.849 1.0427 1 27 20 1 0.951 -0.544 0.1283 0 28 21 1 -0.146 0.877 1.0608 1 29 30 0.0493 =EstVar Cell AE8 =(D8-Meantime)/Meantime 31 32 Cell AF8 =(E8-Meantime)/Meantime 33 YmodelLOF =MMULT(XX,LOFC) 34 Area AJ8:AJ28 =IF(YmodelOLS

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