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On solving large instances of the capacitated facility location problem. (English) Zbl 1163.90614
Summary: We present two sets of results pertaining to the solution of capacitated facility location problems that are large, especially with regard to the number of customers. One set of results relates to customer aggregation, while another set of results concerns the judicious selection of variable-upper-bounding (VUB) constraints to include in the initial integer-programming formulation.In many real-world instances of facility location problems, cities and towns define customers’ and their demands’. Such problems typically feature large metropolises that have numerous satellite townships whose total population is exceeded (often, greatly) by that of the associated metropolis. We argue that both sets of our results would be relevant in solving such problems. We discuss our computational experiences with reference to a real-world variant of the classical capacitated facility location problem that spurred the results reported here.

##### MSC:
 90B80 Discrete location and assignment 90C10 Integer programming
LINGO; MINTO
Full Text:
##### References:
 [1] Aardal, K.: Capacitated facility location: separation algorithms and computational experience. Mathematical programming 81, 149-175 (1998) · Zbl 0919.90096 [2] Aardal, K.; Pochet, Y.; Wolsey, L. A.: Capacitated facility location: valid inequalities and facets. Mathematics of operations research 20, 562-582 (1995) · Zbl 0846.90088 [3] Aardal, K.; Pochet, Y.; Wolsey, L. A.: Erratum: capacitated facility location: valid inequalities and facets. Mathematics of operations research 21, 253-256 (1996) · Zbl 0856.90063 [4] Chen, B.; Guignard, M.: Polyhedral analysis and decompositions for capacitated plant location-type problems. Discrete applied mathematics 82, 79-91 (1998) · Zbl 0897.90153 [5] Deng, Q., Simchi-Levi, D., 1993. Valid inequalities, facets, and computational experience for the capacitated concentrator location problem. Research Report, Department of Industrial Engineering and Operations Research, Columbia University, New York. [6] Francis, R. L.; Lowe, T. J.: On worst-case aggregation analysis for network location problems. Annals of operations research 40, 229-246 (1992) · Zbl 0787.90046 [7] Francis, R. L.; Lowe, T. J.; Rayco, M. B.: Row-column aggregation for rectilinear distance p-median problems. Transportation science 30, 160-174 (1996) · Zbl 0865.90087 [8] Geoffrion, A.M., 1976. Customer aggregation in distribution modelling. Working paper No. 259, Western Management Science Institute, University of California, Los Angeles, CA 90024. [9] Hakimi, S. L.: Optimal locations of switching centers and the absolute centers and medians of a graph. Operations research 12, 450-459 (1964) · Zbl 0123.00305 [10] Hakimi, S. L.: Optimum distribution of switching centers in a communications network and some related graph-theoretic problems. Operations research 13, 462-475 (1965) · Zbl 0135.20501 [11] Leung, J. M. Y.; Magnanti, T. L.: Valid inequalities and facets of the capacitated plant location problem. Mathematical programming 44, 271-291 (1989) · Zbl 0686.90021 [12] Rayco, M. B.; Francis, R. L.; Lowe, T. J.: Error-bound driven demand point aggregation for the rectilinear distance p-center model. Location science 4, 213-235 (1997) · Zbl 0929.90051 [13] Sankaran, J.K., 2002. An application of integer programming for facilities planning. Working Paper, Department of Management Science and Information Systems, The University of Auckland, Private Bag 92019, Auckland, New Zealand. [14] Sankaran, J. K.; Raghavan, N. R. S.: Locating and sizing plants for bottling propane in south India. Interfaces 27, 1-15 (1997) [15] Savelsbergh, M. W. P.; Sigismondi, G. C.; Nemhauser, G. L.: Functional description of MINTO, a mixed integer optimizer. Operations research letters 15, 47-58 (1994) · Zbl 0806.90095 [16] Schrage, L. S.: Optimization modelling with LINDO. (1997) [17] Simchi-Levi, D.; Kaminsky, P.; Simchi-Levi, D.: Designing and managing the supply chain: concepts, strategies, and case studies. (2003) · Zbl 0979.90061