A model and methodologies for the location problem with logistical components. (English) Zbl 0994.90089

Summary: This paper significantly extends traditional facility location models by introducing several logistical cost components such as holding, ordering, and transportation costs in a multi-commodity, multi-location framework. Since location and logistical costs are highly inter-related, the paper provides an integrated model, and seeks to minimize total physical distribution costs by simultaneously determining optimal locations, flows, shipment compositions, and shipment cycle times. Two sophisticated heuristic methodologies, based on Lagrangian relaxation and simulated annealing, respectively, are provided and compared in an extensive computational experiment.


90B80 Discrete location and assignment
90B06 Transportation, logistics and supply chain management
49M30 Other numerical methods in calculus of variations (MSC2010)
Full Text: DOI


[1] Masters JM, Lalonde BJ. The 1988 Ohio State University survey of career patterns in logistics. Annual Conference Proceedings, Council of Logistics Management, vol. 1. 1988. p. 23-50.
[2] Ballou, R., Business logistics management, (1999), Prentice-Hall Upper Saddle River, NJ
[3] Bowersox, D.J.; Closs, D.J., Logistical management, the integrated supply chain process, (1996), McGraw-Hill New York, NY
[4] Blumenfeld DE, Burns LD, Daganzo CF, Frick MC, Hall RW. Reducing logistics costs at general motors. General Motors Research Report-5334, General Motors, Warren, MI, 1986.
[5] Klincewicz, J., Solving a freight transport problem using facility location techniques, Operations research, 38, 1, 99-109, (1990) · Zbl 0715.90044
[6] Benjamin, J., An analysis of inventory and transportation costs in a constrained network, Transportation science, 23, 2, 177-183, (1989)
[7] Goyal, S.K., Determination of optimum packaging frequency of items jointly replenished, Management science, 21, 4, 436-443, (1974)
[8] Russell, R.M.; Krajewski, L.J., Coordinated replenishments from a common supplier, Decision sciences, 23, 3, 610-632, (1992)
[9] Syam, S.; Shetty, B., A heuristic algorithm for the capacitated inventory grouping problem, Decision sciences, 27, 4, 711-733, (1996)
[10] Sridharan, R., The capacitated plant location problem, European journal of operational research, 87, 203-213, (1995) · Zbl 0914.90180
[11] Geoffrion, A.; Graves, G.W., Multicommodity distribution system design by benders decomposition, Management science, 20, 822-844, (1974) · Zbl 0304.90122
[12] Pirkul, H.; Jayaraman, V., A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution, Computers & operations research, 25, 869-878, (1998) · Zbl 1042.90580
[13] Garey, M.R.; Johnson, D.S., Computers and intractability: a guide to the theory of NP-completeness, (1979), Freeman San Francisco, CA · Zbl 0411.68039
[14] Kirkpatrick, S.; Gelatt, C.D.; Vecchi, M.P., Optimization by simulated annealing, Science, 220, 671-679, (1983) · Zbl 1225.90162
[15] Wilhelm, M.R.; Ward, T.L., Solving quadratic assignment problems by ‘simulated annealing’, IIE transactions, 19, 1, 107-119, (1987)
[16] Righini, G., A double annealing algorithm for discrete location/allocation problems, European journal of operational research, 86, 3, 452-468, (1995) · Zbl 0914.90228
[17] Fisher, M.L., An applications oriented guide to Lagrangian relaxation, Interfaces, 15, 10-21, (1985)
[18] Held, M.; Wolfe, P.; Crowder, H., Validation of subgradient optimization, Mathematical programming, 6, 66-68, (1974) · Zbl 0284.90057
[19] Polyak, B., A general method for solving extremum problems, Soviet mathematics doklady, 1, 593-597, (1967) · Zbl 0177.15102
[20] Geoffrion, A.M., Lagrangian relaxation for integer programming, Mathematical programming, 2, 82-114, (1974) · Zbl 0395.90056
[21] Nemhauser, G.L.; Wolsey, L.A., Integer and combinatorial optimization, (1988), Wiley New York, NY · Zbl 0469.90052
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