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Planning and coordination of production and distribution facilities for multiple commodities. (English) Zbl 1001.90026

Summary: We study an integrated logistics model for locating production and distribution facilities in a multi-echelon environment. Designing such logistics systems requires two essential decisions, one strategic (e.g., where to locate plants and warehouses) and the other operational (distribution strategy from plants to customer outlets through warehouses). The distribution strategy is influenced by the product mix at each plant, the shipments of raw material from vendors to manufacturing plants and the distribution of finished products from the plants to the different customer zones through a set of warehouses. First we provide a mixed integer programming formulation to the integrated model. Then, we present an efficient heuristic solution procedure that utilizes the solution generated from a Lagrangian relaxation of the problem. We use this heuristic procedure to evaluate the performance of the model with respect to solution quality and algorithm performance. Results of extensive tests on the solution procedure indicate that the solution method is both efficient and effective. Finally a ‘real-world’ example is solved to explore the implications of the model.

MSC:

90B30 Production models
90C59 Approximation methods and heuristics in mathematical programming
90C11 Mixed integer programming
90B50 Management decision making, including multiple objectives

Software:

GAMS
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References:

[1] Agnihotri, S.; Narasimhan, S.; Pirkul, H., An assignment problem with queuing time cost, Naval research logistics, 37, 231-244, (1990) · Zbl 0711.90024
[2] Aikens, C.H., Facility location models for distribution planning, European journal of operational research, 22, 263-279, (1985) · Zbl 0583.90022
[3] Beasley, J.E., Lagrangean heuristics for location problems, European journal of operational research, 65, 383-399, (1993) · Zbl 0768.90045
[4] Bhatnagar, R.; Chandra, P.; Goyal, S.K., Models for multi-plant coordination, European journal of operational research, 67, 141-160, (1993)
[5] Brown, G.G.; Graves, G.W.; Honczarenko, M.D., Design and operation of a multicommodity production/distribution system using primal goal decomposition, Management science, 33, 1469-1480, (1987)
[6] Cohen, M.A.; Lee, H.L., Strategic analysis of integrated production – distribution systems: models and methods, Operations research, 6, 216-228, (1988)
[7] Fisher, M., The Lagrangian relaxation method for solving integer programming problems, Management science, 27, 1, 1-18, (1981) · Zbl 0466.90054
[8] Fleischmann, B., Designing distribution systems with transport economies of scale, European journal of operational research, 70, 31-42, (1993) · Zbl 0800.90398
[9] GAMS, 1994. Generalized Algebraic Modeling Systems. The Scientific Press
[10] Garey, M.R.; Johnson, D.S., Computers and intractability: A guide to the theory of NP-completeness, (1979), Freeman San Francisco · Zbl 0411.68039
[11] Gavish, B., On obtaining the ‘best’ multipliers for a Lagrangian relaxation for integer programming, Computers and operations research, 5, 55-71, (1978)
[12] Geoffrion, A.M.; Graves, G.W., Multicommodity distribution system design by benders decomposition, Management science, 20, 822-844, (1974) · Zbl 0304.90122
[13] Held, M.; Wolfe, P.; Crowder, H.P., Validation of subgradient optimization, Mathematical programming, 5, 62-68, (1974) · Zbl 0284.90057
[14] Klicenwicz, J.; Luss, H., A Lagrangian relaxation heuristic for capacitated facility location with single-source constraints, Journal of operational research society, 37, 495-500, (1986) · Zbl 0588.90025
[15] Krarup, J.; Pruzan, P.W., The simple plant location problem: survey and synthesis, European journal of operational research, 12, 36-81, (1983) · Zbl 0506.90018
[16] Lee, C.Y., A cross-decomposition algorithm for a multi-product, multi-type, facility location problem, Computers and operations research, 20, 527-540, (1993) · Zbl 0774.90054
[17] Moon, S. 1987. An application-oriented review of developments in mathematical models and solution algorithms for production – distribution system design problems. WPS 87-07-01. Department of Decision Sciences, The Wharton School, Philadelphia, PA
[18] Neebe, A.W.; Rao, M.R., An algorithm for the fixed-charge assigning users to sources problem, Journal of operational research society, 34, 1107-1113, (1983) · Zbl 0521.90075
[19] Pirkul, H.; Schilling, D., The maximal covering location problem with capacities on total workload, Management science, 37, 233-248, (1991) · Zbl 0732.90045
[20] Pyke, D.; Cohen, M., Multiproduct integrated production – distribution systems, European journal of operational research, 74, 18-49, (1994) · Zbl 0803.90072
[21] ReVelle, C.; Laporte, G., The plant location problem: new models and research prospects, Operations research, 44, 864-874, (1996) · Zbl 0879.90130
[22] Sridharan, R., A Lagrangian heuristic for the capacitated plant location problem with single source constraints, European journal of operational research, 66, 305-312, (1993) · Zbl 0771.90062
[23] Tragantalerngsak, S.; Holt, J.; Ronnqvist, M., Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem, European journal of operational research, 102, 611-625, (1997) · Zbl 0951.90561
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