Logistics Systems: Design and Optimization (Gerad 25th Anniversary Series)

DESIGN AND OPTIMIZATION

• Essays and Surveys in Global Optimization Charles Audet, Pierre Hansen, and Gilles Savard, editors • Graph Theory and Combinatorial Optimization David Avis, Alain Hertz, and Odile Marcotte, editors • Numerical Methods in Finance Hatem Ben-Ameur and Michele Breton, editors • Analysis, Control and Optimization of Complex Dynamic El-Kebir Boukas and Roland Malhame, editors • Column Generation Guy Desaulniers, Jacques Desrosiers, and Marius M. Solomon,

• Statistical Modeling and Analysis for Complex Data Prob Pierre Duchesne and Bruno Remillard, editors

• Performance Evaluation and Planning Methods for the N eration Internet Andre Girard, Brunilde Sanso, and Felisa Vazquez-Abad, editor • Dynamic Games: Theory and Applications Alain Haurie and Georges Zaccour, editors • Logistics Systems: Design and Optimization Andre Langevin and Diane Riopel, editors

• Energy and Environment Richard Loulou, Jean-Philippe Waaub, and Georges Zaccour, e

DESIGN AND OPTIMIZATION

Edited by

ANDRE LANGEVIN GERAD and Ecole Polytechnique de Montreal

DIANE RIOPEL GERAD and £cole Polytechnique de Montreal

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The objective function (2.19) minimizes the sum of the fixed fa cation costs, the shipment costs from the supply points (plant facilities, the variable facility throughput costs and the routi to the customers. Constraint (2.20) requires each customer exactly one route. Constraint (2.21) imposes a capacity restri each vehicle, while constraint (2.22) limits the length of each rou straint (2.23) requires each route to be connected to a facility. straint requires that there be at least one route that goes from V (a proper subset of the points P that contains the set of facility sites) to its complement V, thereby precluding routes t visit customer nodes. Constraint (2.24) states that any route node i G P also must exit that same node. Constraint (2.25) st a route can operate out of only one facility. Constraint (2.26) de flow into a facility from the supply points in terms of the total that is served by the facility. Constraint (2.27) restricts the put at each facility to the maximum allowed at that site and flow variables and the facility location variables. Thus, if a not opened, there can be no flow through the facility, which in constraint (2.26)) precludes any customers from being assigne facility. Constraint (2.28) states that if route k G K leaves node i G / and also leaves facility j G J, then customer i G be assigned to facility j G J . This constraint links the vehicl variables (Zijk) and the assignment variables (Yij). Constraint (2.32) are standard integrality and non-negativity constraints. Even for small problem instances, the formulation above is a mixed integer linear programming problem. Perl solves the pro ing a three-phased heuristic. The first phase finds minimum co The second phase determines which facilities to open and how

attempts to improve the solution by moving customers between and re-solving the routing problem with the set of open facilit The algorithm iterates between the second and third phases unt provement at any iteration is less than some specified value. W and Bai (2002) propose a similar two-phase heuristic for the and test it on problems with up to 150 nodes. Like the three-layer formulation of Perl, two-layer locatio formulations (e.g., Laporte, Nobert and Pelletier, 1983; Lapo bert and Arpin, 1986; and Laporte, Nobert and Taillefer, 1988 are based on integer linear programming formulations for th routing problem (VRP). Flow formulations of the VRP often sified according to the number of indices of the flow variable: if a vehicle uses arc (i,j) or X^ — 1 if vehicle k uses arc (z size and structure of these formulations make them difficult to ing standard integer programming or network optimization tec Motivated by the successful implementation of exact algorithm partitioning-based routing models, Berger (1997) formulates a location/routing problem that closely resembles the classical fixe facility location problem. Unlike other location/routing probl formulates the routes in terms of paths, where a delivery vehicle be required to return to the distribution center after the final is made. The model is appropriate in situations where the deliv made by a contract carrier or where the commodities to be deli perishable. In the latter case, the time to return from the last to the distribution center is much less important than the time facility to the last customer. Berger defines the following notat

Inputs and sets.

Pji set of feasible paths from candidate distribution center j G Cjk0- cost of serving the path k G Pj aJik: 1 if delivery path k G Pj visits customer i G /; 0 if not

Decision variables. jk

~

J 1, [0,

if path k G Pj is operated out of distribution cente if not.

Note that there can be any number of restrictions on the feasi in set Pj] in fact, the more restrictive the conditions impose are, the smaller the cardinality of Pj is. Restricting the total the paths, Berger formulates the following integrated locatio

minimize

subject to ^

y\>^ aaj\kfc^fc v == 1 jk

A kt

i /] X X 10. Capacity requirements (Wrennal, 2001) V X 11. Daily activity level (Reed, 1961) X 12. Work schedule (Reed, 1961) V X X 13. Location of utilities and auxiliaries (including maintenance, repair, housekeeping, and fixed f X X 14. Storage facilities (including raw materials, work-in-progres and finished goods) X 15. Procedures and controls X 16. Safety (materials, equipment, personnel) E. Building X X 1. Location on site and orientation V X X 2. Building size and shape X X 3. Construction type X X 4. Structural design V X X 5. Docks and doors — number, opening, size, location, heigh V X X 6. Floors — numbers, condition, load capacity, type of floorin resistance (e.g., to shock, abrasion, heat, vibration, humid solvents, salt, water, etc.), color, sanitary, odourless, stati electricity, sound absorbent (Muther, 1973), and flatness (Sule, 1994) X X 7. Walls characteristics, inside and outside (Sule, 1994) V X X 8. Possible use of mezzanines, balconies, basement, roof X X 9. Ceiling height X X 10. Overhead load capacity X X 11. Columns — location and spacing X X 12. Windows (type, location, size) X X 13. Space availability and characteristics, including limits (Re 1 X X 14. Elevators, ramps LZ X X 15. Loading and unloading facilities V X X 16. Aisle requirements — quantity, type, location, width V X X 17. Aisle congestion (Heragu, 1997) X 18. Safety requirements X X 19. Expansion possibilities

7

Elements by theme

s

F. Site X X X X X

1. 2. 3. 4. 5.

X X X

6. 7. 8.

X X

9. 10.

X

11.

Size and location Topography, including slope of the land Transportation facilities (road, rail, air, water) Expansion possibilities Weather conditions (prevailing wind, southern exposure, North light) Surroundings, including adjacent plants (dirt, fumes, etc.) Available power Within plant conditions (e.g., spread of contaminating ma winter draft, glare from welding arcs, vibrations) Existing buildings Regulations — governments, city, building codes, and for company (Heragu, 1997), including on waste disposal Company's own impact on the community (e.g., noise, ha traffic)

G. Personnel X 1. Number X X 2. Movement X X 3. Working conditions (e.g., lighting, ventilation, heating, no vibration and temperature, natural light, fresh air, colors; Sule, 1994) X X 4. Provision for fire protection — extinguishers, sprinkler sys exits, etc. X X 5. First aid facilities V V X X 6. Aisle location and width V X X 7. Desired location of personnel services areas (entrances, lo room, food service, etc.) X 8. Supervisory requirements V 9. Personnel characteristics problems X a. Available workers with proper skills (Tompkins et al., X b. Training capability (Tompkins et al., 2003) X c. Disposition of redundant workers (Tompkins et al., 200 X d. Job description changes (Tompkins et al., 2003) X e. Union contracts (Tompkins et al., 2003) X f. Work practices (Tompkins et al., 2003) X X 10. Safety H. Miscellaneous X 1. Nature of business and economic cyclic effects (Reed, 1961 X 2. Company policies, including make or buy policy (Reed, 19 X X 3. Flexibility X 4. Degree of automation (Tompkins et al., 2003) X 5. Software requirements (Tompkins et al., 2003)

Acknowledgements This work was supported by the Canad ural Sciences and Engineering Council and by the Fonds de sur la nature et les technologies — Quebec.

References

Abdinnour-Helm, S. and Hadley, S.W. (2000). Tabu search based heuristics floor facility layout. International Journal of Production Research, 38:3 Abdou, G. and Dutta, S.P. (1990). An integrated approach to facilities la expert systems. International Journal of Production Research, 28:685Aiello, G. and Enea, M. (2001). Fuzzy approach to the robust facility lay certain production environments. International Journal of Production 39:4089-4101. Akinc, U. (1985). Multi-activity facility design and location problems. M Science, 31:275-283. Al-Hakim, L.A. (1991). Two graph-theoretic procedures for an improve to the facilities layout problem. International Journal of Production 29:1701-1718. Al-Hakim, L.A. (1992). A modified procedure for converting a dual graph layout. International Journal of Production Research, 30:2467-2476. Al-Hakim, L.A. (2000). On solving facility layout problems using genetic a International Journal of Production Research, 38:2573-2582. Anjos, M.F. and Vannelli, A. (2002). A New Mathematical Programming for Facility Layout Design. Working paper. Apple, J.M. (1963). Plant Layout and Materials Handling. The Ronald P pany. Apple, J.M. (1977). Plant Layout and Materials Handling, 3rd edition. Joh Sons Inc. Armour, G.C. and Buffa, E.S. (1963). A heuristic algorithm and simulation to relative location of facilities. Management Science, 9:294-309. Askin, R.G. and Standridge, C.R* (1993). Modeling and Analysis of Man Systems. John Wiley & Sons. Azadivar, F. and Wang, J.J. (2000). Facility layout optimization using simu genetic algorithms. International Journal of Production Research, 38:4 Badiru, A.B. and Arif, A. (1996). FLEXPERT: Facility layout expert sy fuzzy linguistic relationship codes. HE Transactions, 28:295-308. Balakrishnan, J. and Cheng, C.H. (1998). Dynamic layout algorithms: A st art survey. OMEGA —International Journal of Management Science, 26 Balakrishnan, J. and Cheng, C.H. (2000). Genetic search and the dynam problem. Computers and Operations Research, 27:587-593. Balakrishnan, J., Cheng, C.H., and Conway, D.G. (2000). An improved exchange heuristic for the dynamic plant layout problem. International Production Research, 38:3067-3077. Balakrishnan, J., Cheng, C.H., Conway, D.G., and Lau, C. M. (2003a) genetic algorithm for the dynamic plant layout problem. International Production Economics, 86:107-120. Balakrishnan, J., Cheng, C.-H., and Wong, K.-F. (2003b) FACOPT: a us FACility layout OPTimization system. Computers and Operations Re 1625-1641. Banerjee, P., Montreuil, B., Moodie, C.L., and Kashyap, R.L. (1990). A reasoning-based interactive optimization methodology for layout design tional industrial engineering conference proceedings, pp. 230-235. Banerjee, P., Montreuil, B., Moodie, C.L., and Kashyap, R.L. (1992a). A of interactive facilities layout designer reasoning using qualitative patte

Banerjee, P., Zhou, Y., and Montreuil, B. (1992b). Conception d'ame d'installations : Optimisation par induction genetique. Technical R 66, Groupe de recherche en gestion de la logistique, Faculte des s Tadministration de l'Universite Laval. Banerjee, P., Zhou, Y., and Montreuil, B. (1997). Genetically assisted op of cell layout and material flow path skeleton.//i? Transactions, 29:277 Barbosa-Povoa, A.P. Mateus, R., and Novais, A.Q. (2001). Optimal two-d layout of industrial facilities. International Journal of Production Re 2567-2593. Barbosa-Povoa, A.P., Mateus, R., and Novais, A.Q. (2002). Optimal 3D industrial facilities. International Journal of Production Research, 40:1 Baykasoglu, A. and Gindy, N.N.Z. (2001). A simulated annealing algorith namic layout problem. Computers and Operations Research, 28:1403Bazaraa, M.S. (1975). Computerized layout design: A branch and bound AIIE Transactions, 7:432-438. Benjaafar, S. and Sheikhzadeh, M, (2000). Design offlexibleplant layouts. actions, 32:309-322, Boswell, S.G. (1992). TESSA — A new greedy heuristic for facilities layou International Journal of Production Research, 30:1957-1968. Bozer, Y.A., Meller, R.D., and Erlebacher, S.J. (1994). An improvement-ty algorithm for single and multiple-floor facilities. Management Science, 4 Butler, T.W., Karwan, K.R., Sweigart, J.R., and Reeves, G.R. (1992). An model-based approach to hospital layout. HE Transactions, 24:144-152 Cambron, K.E. and Evans, G.W. (1991). Layout design using the analytic process, Computers and Industrial Engineering, 20:211-229. Castell, C.M.L., Lakshmanan, R., Skilling, J.M., and Banares-Alcantara, Optimisation of process plant layout using genetic algorithms. Com Chemical Engineering, 22.S993-S996. Castillo, I., and Peters, B A. (2002). Unit load and material-handling con in facility layout design. International Journal of Production Research 2989. Castillo, L and Peters, -B.A. (2003), An extended distance-based facility la lem, International Journal of Production Research, 41:2451-2479. Cedarleaf, J. (1994). Plant Layout and Flow Improvement. McGraw-Hill B pany Inc. Chen, C.-W. and Sha? D.Y. (1999). A design approach to the multi-objecti layout problem. International Journal of Production Research, 37:117 Cheng, R. and Gen. M. (1998). Loop layout design problem in flexible man systems using genetic algorithms. Computers and Industrial Engineeri 61. Cheng, R,, Gen, M., and Tosawa, T. (1996). Genetic algorithms for desi layout manufacturing systems. Computers and Industrial Engineering, 3 Chhajed, D., Montreuil, B., and Lowe, T.J. (1990). Flow network manufacturing systems layout. Technical Report 90-12, Faculte des s l'administration de l'Universite Laval. Chiang, W.-C. (2001). Visual facility layout design system. International Production Research, 39:1811-1836. Chiang, W.-C. and Chiang, C. (1998). Intelligent local search strategies facility layout problems with the quadratic assignment problem formu

Chiang, W.-C. and Kouvelis, P. (1996). An improved tabu search heuristi ing facility layout design problems. International Journal of Production 34:2565-2585. Chittratanawat, S. and Noble, J.S. (1999). An integrated approach for f out, P/D location and material handling system design. International Production Research, 37:683-706. Chwif, L., Pereira Barretto, M.R., and Moscato, L.A. (1998). A solution to layout problem using simulated annealing. Computers in Industry, 36:1 Cimikowski, R. and Mooney, E. (1997). Proximity-based adjacency determ facility layout. Computers and Industrial Engineering, 32:341-349. Das, S.K. (1993). A facility layout method for flexible manufacturing syste national Journal of Production Research, 31:279-297, Deb, S.K. and Bhattacharyya5 B. (2003). Facilities layout planning based multiple criteria decision-making methodology. International Journal of Research, 41:4487-4504. Delmaire, H., Langevin, A., and Riopel, D. (1995a). Evolution Sy the Quadratic Assignment Problem, Technical Report G-95-24, Les C GERAD, Montreal, Canada. Delmaire, Hr) Langevin, A., and Riopel, D. (1995b). Le probleme d'implantation d'usine: une revue. Technical Report G-95-09, Les C GERAD, Montreal, Canada. Delmaire, H., Langevin, A., and Riopel, D. (1997). Skeleton-based faci design using genetic algorithms, Annals of Operations Research, 69:85 Drezner, Z. (1987), A heuristic procedure for the layout of a large number o Management Science, 33:907-915. Dutta, K;N. and Sahu, S. (1982). A multigoal heuristic for facilities design MUGHAL. International Journal of Production Research, 20:147-154. Dweiri, F. (1999). Fuzzy development of crisp activity relationship charts fo layout. Computers and Industrial Engineering, 36:1-16. Dweiri, F. and Meier, FA. (1996). Application of fuzzy decision-making i layout planning. International Journal of Production Research, 34:320 Evans, G.W., Wilhelm, M.R., and Karwowski, W. (1987). A layout desig employing the theory of fuzzy sets. International Journal of Production 25:1431-1450. Fortenberry, JLC. and Cox,

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The objective is to minimize the total unfinished workload a of each time period. Constraint (7.32) maintains the conser flow of cranes. Constraint (7.33) specifies the number of crane block at the beginning of the first period. Constraint (7.34) that the total number of cranes in all the blocks at the end o period is the same as that at the beginning of the first perio straint (7.35) ensures that at most K cranes can work simul

load finished in block i during period £, where the right sid constraint is the crane capacity available in block i during tha They referred to constraint (7.32)-(7.36) and (7.38) as the cr constraints and to constraint (7.36) as the workload capacity c Cheung et al. (2002) proposed a Lagrangean decomposition solu cedure and a successive piecewise-linear approximation method ing the above mathematical model. Many studies have been carried out on dispatching prime mo as yard trucks (Bish, 1999), straddle carriers (Bose et al., 200 mated guided vehicles (Bish, 2003; Grunow et al., 2004; Kim 1999; Kim and Bae, 2004; Vis et al., 2001), and automatic lifting (van der Meer, 2000). Hartmann (2004) proposed a genetic a to dispatching various handling equipment and manpower in terminals. Holguin-Veras and Walton (1995) proposed methods mating and calibrating the service times of various handling eq in container terminals for use in a simulation program. Yang et a and Vis and Harika (2004) compared the performance of differe of automated vehicles for transporting containers in port conta minals. Evers and Koppers (1996) addressed the traffic control and Qiu and Hsu (2000) discussed the routing problem for container terminals. The following are from the mathematical model that Bish (2 gested. The objective is (1) to determine a storage location unloaded container; (2) to schedule the trip of each container hicle; and (3) to schedule the loading and unloading operatio QCs so as to minimize the total travel time. Two ships were considered, sh~ and sh+, that need unloa loading, respectively, and that are berthed around the same that they can be served by the same set of k vehicles. Let N+ denote the set of containers that will be unloaded from s and the set of containers that will be loaded onto ship sh+, resp Also, let Ci be the element in 7V~. Associated with each conta loaded onto a ship is its current storage location in the yard are is known. Each such container will require a loaded vehicle trip current storage location to the location of ship sh+. Let L+ de set of current storage locations of the containers in set N+. potential storage location in the yard area is reserved for the c of each unloading ship. We are given a set of potential storage reserved for all containers that will be unloaded from sh~, and w this set as L~~. Each unloaded container will require a loaded ve from the location of ship sh~ to its selected storage location.

is, we assume that no container in set N~ can be stored in currently occupied by a container in set 7V+. Let L = L~ U L + . Wi be the subset of L~ where Q can be stacked. In addition to these loaded trips, each vehicle will need to m empty trip between two loaded trips scheduled right after ea on that vehicle, if the destination of the previous loaded trip origin of the next loaded trip are different. Thus, these empty t depend on the sequence of loaded trips on each vehicle. Each container is assigned to exactly one potential storage location loaded trip for an unloaded container is matched with a loaded a loading container in a way of minimizing the total travel dista denote loaded trip i by l{ and the travel time of l{ by in. The following network is constructed to solve the problem. node, with unit supply, is created for each unloaded container And a demand node is created for each location q G L+. Add two copies of trans-shipment node lp and lV) are made for each location p G L"~, in our network. The arc set is given by A = {(a,l'p):

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