×

Facility location models for distribution system design. (English) Zbl 1132.90345

Summary: The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

MSC:

90B80 Discrete location and assignment
90C11 Mixed integer programming
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Aardal, K., Reformulation of capacitated facility location problems: How redundant information can help, Annals of Operations Research, 82, 289-308 (1998) · Zbl 0911.90235
[2] Aardal, K.; Labbé, M.; Leung, J. M.Y.; Queyranne, M., On the two-level uncapacitated facility location problem, INFORMS Journal on Computing, 8, 289-301 (1996) · Zbl 0863.90102
[3] Aikens, C. H., Facility location models for distribution planning, European Journal of Operational Research, 22, 3, 263-279 (1985) · Zbl 0583.90022
[4] Arora, S., Raghavan, P., Rao, S., 1998. Approximation schemes for Euclidean \(k\); Arora, S., Raghavan, P., Rao, S., 1998. Approximation schemes for Euclidean \(k\) · Zbl 1027.68979
[5] Aykin, T., Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem, European Journal of Operational Research, 79, 501-523 (1994) · Zbl 0813.90074
[6] Aykin, T., The hub location and routing problem, European Journal of Operational Research, 83, 200-219 (1995) · Zbl 0903.90110
[7] Aykin, T., Networking policies for hub-and-spoke systems with applications to the air transportation system, Transportation Science, 29, 201-221 (1995) · Zbl 0857.90028
[8] Balas, E.; Padberg, M. W., Set partitioning-A survey, SIAM Review, 18, 710-760 (1976) · Zbl 0347.90064
[9] Barcelo, J.; Casanovas, J., A heuristic Lagrangean algorithm for the capacitated plant location problem, European Journal of Operational Research, 15, 212-226 (1984) · Zbl 0544.90025
[10] Barcelo, J.; Hallefjord, Å.; Fernandez, E.; Jörnsten, K., Lagrangean relaxation and constraint generation procedures for capacitated plant location problems with single sourcing, OR-Spektrum, 12, 79-88 (1990) · Zbl 0713.90041
[11] Barros, A. I., Discrete and Fractional Programming Techniques for Location Models (1998), Kluwer Academic: Kluwer Academic London, Dordrecht, Boston · Zbl 0907.90258
[12] Barros, A.I., Labbé, M., 1992. A general model for the uncapacitated facility and depot location problem. Working Paper 92-19, European Institute for Advanced Studies in Management, Brüssel; Barros, A.I., Labbé, M., 1992. A general model for the uncapacitated facility and depot location problem. Working Paper 92-19, European Institute for Advanced Studies in Management, Brüssel
[13] Barros, A. I.; Dekker, R.; Scholten, V., A two-level network for recycling sand: A case study, European Journal of Operational Research, 110, 199-214 (1998) · Zbl 0948.90087
[14] Bauer, A.; Domschke, W.; Pesch, E., Competitive location on a network, European Journal of Operational Research, 66, 372-391 (1993) · Zbl 0779.90052
[15] Beasley, J. E., An algorithm for solving large capacitated warehouse location problems, European Journal of Operational Research, 33, 314-325 (1988) · Zbl 0637.90033
[16] Beasley, J. E., Lagrangean heuristics for location problems, European Journal of Operational Research, 65, 383-399 (1993) · Zbl 0768.90045
[17] Benati, S.; Laporte, G., Tabu search algorithms for the \((r|x_p)\)-medianoid and \((r|p)\)-centroid problems, Location Science, 2, 193-204 (1994) · Zbl 0917.90222
[18] Berman, O.; Larson, R. C., Optimal 2-facility network districting in the presence of queuing, Transportation Science, 19, 261-277 (1985) · Zbl 0606.90053
[19] Boffey, T. B., Location problems arising in computer networks, The Journal of the Operational Research Society, 40, 4, 347-354 (1989) · Zbl 0666.90030
[20] Boffey, T. B.; Karkazis, J., \(p\)-medians and multi-medians, The Journal of the Operational Research Society, 35, 1, 57-64 (1984) · Zbl 0526.90036
[21] Boffey, B.; Yates, D.; Galvão, R. D.G., An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro, Journal of the Operational Research Society, 54, 21-31 (2003) · Zbl 1088.90524
[22] Boland, N., Domı́nguez-Marı́n, P., Nickel, S., Puerto, J., 2003. Exact procedures for solving the discrete ordered median problem. Technical Report, Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany; Boland, N., Domı́nguez-Marı́n, P., Nickel, S., Puerto, J., 2003. Exact procedures for solving the discrete ordered median problem. Technical Report, Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany
[23] Bookbinder, J. H.; Reece, K. E., Vehicle routing considerations in distribution system design, European Journal of Operational Research, 37, 2, 204-213 (1988) · Zbl 0652.90036
[24] Bramel, J.; Simchi-Levi, D., A location based heuristic for general routing problems, Operations Research, 43, 4, 649-660 (1995) · Zbl 0857.90030
[25] Branco, I. M.; Coelho, J. D., The Hamiltonian \(p\)-median problem, European Journal of Operational Research, 47, 86-95 (1990) · Zbl 0706.90039
[26] Brandeau, M. L.; Chiu, S. S., An overview of representative problems in location research, Management Science, 35, 6, 645-674 (1989) · Zbl 0669.90040
[27] Brimberg, J.; Mehrez, A., Multi-facility location using a maximin criterion and rectangular distances, Location Science, 2, 11-19 (1994) · Zbl 0929.90045
[28] Brimberg, J.; Hansen, P.; Mladenovic, N.; Taillard, E., Improvements and comparison of heuristics for solving the multisource Weber problem, Operations Research, 48, 3, 444-460 (2000)
[29] Bruns, A.D., 1998. Zweistufige Standortplanung unter Berücksichtigung von Tourenplanungsaspekten-Primale Heuristiken und lokale Suchverfahren. Dissertation Nr. 2152, Universität St. Gallen, Dufourstrasse 50, CH-9000 St. Gallen; Bruns, A.D., 1998. Zweistufige Standortplanung unter Berücksichtigung von Tourenplanungsaspekten-Primale Heuristiken und lokale Suchverfahren. Dissertation Nr. 2152, Universität St. Gallen, Dufourstrasse 50, CH-9000 St. Gallen
[30] Bruns, A. D.; Klose, A., A locate first-route second heuristic for a combined location-routing problem, (Operations Research Proceedings 1996 (1996), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York), 49-54, (Chapter 3) · Zbl 0915.90170
[31] Bruns, A. D.; Klose, A.; Stähly, P., Restructuring of Swiss parcel delivery services, OR-Spektrum, 22, 285-302 (2000) · Zbl 0970.90044
[32] Campbell, J. F., Location-allocation for distribution systems with transshipments and transportation economies of scale, Annals of Operations Research, 40, 77-99 (1992) · Zbl 0782.90064
[33] Campbell, J. F., Integer programming formulations of discrete hub location problems, European Journal of Operational Research, 72, 387-405 (1994) · Zbl 0790.90048
[34] Campbell, J. F., A survey of network hub location, Studies in Locational Analysis, 6, 31-47 (1994)
[35] Caprara, A., Salazar, J.J., 1995. A branch-and-cut algorithm for the index selection problem. Technical Report 95-09, DEIS, University of Bologna, Bologna; Caprara, A., Salazar, J.J., 1995. A branch-and-cut algorithm for the index selection problem. Technical Report 95-09, DEIS, University of Bologna, Bologna
[36] Caprara, A.; Salazar, J. J.G., Separating lifted odd-hole inequalities to solve the index selection problem, Discrete Applied Mathematics, 92, 111-134 (1999) · Zbl 0967.90067
[37] Caprara, A.; Fischetti, M.; Maio, D., Exact and approximate algorithms for the index selection problem in physical database design, IEEE Transactions on Knowledge and Data Engineering, 7, 6, 955-967 (1995)
[38] Chandra, P.; Fisher, M. L., Coordination of production and distribution planning, European Journal of Operational Research, 72, 503-517 (1994) · Zbl 0805.90051
[39] Chardaire, P., Hierarchical two level location problems, (Sansò, B.; Soriano, P., Telecommunications Network Planning (1999), Kluwer Academic: Kluwer Academic London, Dordrecht, Boston), 33-54, (Chapter 3)
[40] Chardaire, P.; Lutton, J.-L.; Sutter, A., Upper and lower bounds for the two-level simple plant location problem, Annals of Operations Research, 86, 117-140 (1999) · Zbl 0918.90095
[41] Chen, B.; Guignard, M., Polyhedral analysis and decompositions for capacitated plant location-type problems, Discrete Applied Mathematics, 82, 79-91 (1998) · Zbl 0897.90153
[42] Chen, P.-C.; Hansen, P.; Jaumard, B.; Tuy, H., Weber’s problem with attraction and repulsion, Journal of Regional Science, 32, 4, 467-486 (1992)
[43] Chen, P.-C.; Hansen, P.; Jaumard, B.; Tuy, H., Solution of the multisource Weber and conditional Weber problems by d.-c. programming, Operations Research, 46, 4, 548-562 (1998) · Zbl 0979.90099
[44] Cho, D. C.; Johnson, E. L.; Padberg, M. W.; Rao, M. R., On the uncapacitated plant location problem I: Valid inequalities and facets, Mathematics of Operations Research, 8, 579-589 (1983) · Zbl 0536.90029
[45] Christofides, N.; Beasley, J. E., A tree search algorithm for the \(p\)-median problem, European Journal of Operational Research, 10, 196-204 (1982) · Zbl 0481.90020
[46] Christofides, N.; Beasley, J. E., Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem, European Journal of Operational Research, 12, 19-28 (1983) · Zbl 0499.90027
[47] Chudak, F. A., Improved approximation algorithms for uncapacitated facility location, (Bixby, R. E.; Boyd, E. A.; Rı́os-Mercado, R. Z., Proceedings of the 6th International IPCO Conference. Proceedings of the 6th International IPCO Conference, Lecture Notes in Computer Science, vol. 1412 (1999), Springer-Verlag) · Zbl 0910.90201
[48] Chudak, F.A., Shmoys, D.B., 1999. Improved approximation algorithms for a capacitated facility location problem. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 875-886; Chudak, F.A., Shmoys, D.B., 1999. Improved approximation algorithms for a capacitated facility location problem. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 875-886 · Zbl 1052.90580
[49] Chudak, F.A., Williamson, D.P., 1999. Improved approximation algorithms for capacitated facility location problems. Technical Report, IBM Watson Research Center; Chudak, F.A., Williamson, D.P., 1999. Improved approximation algorithms for capacitated facility location problems. Technical Report, IBM Watson Research Center · Zbl 0955.90068
[50] Conners, M. M.; Coray, C.; Cuccaro, C. J.; Green, W. K.; Low, D. W.; Markowitz, H. M., The distribution system simulator, Management Science, 18, B425-B453 (1972)
[51] Cornuejols, G.; Thizy, J.-M., Some facets of the simple plant location polytope, Mathematical Programming, 23, 50-74 (1982) · Zbl 0485.90069
[52] Cornuejols, G.; Fisher, M. L.; Nemhauser, G. L., Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms, Management Science, 23, 789-810 (1977) · Zbl 0361.90034
[53] Cornuejols, G.; Sridharan, R.; Thizy, J.-M., A comparison of heuristics and relaxations for the capacitated plant location problem, European Journal of Operational Research, 50, 280-297 (1991) · Zbl 0734.90046
[54] (Crainic, T. G.; Laporte, G., Fleet Management and Logistics (1998), Kluwer Academic: Kluwer Academic London, Dordrecht, Boston)
[55] Current, J.; Weber, C., Application of facility location modeling constructs to vendor selection problems, European Journal of Operational Research, 76, 3, 387-392 (1994) · Zbl 0925.90246
[56] Current, J.; Min, H.; Schilling, D. A., Multiobjective analysis of facility location decisions, European Journal of Operational Research, 49, 295-307 (1990) · Zbl 0717.90042
[57] Daskin, M. S., Network and Discrete Location: Models, Algorithms, and Applications, Wiley-Interscience Series in Discrete Mathematics and Optimization (1995), John Wiley & Sons: John Wiley & Sons Chichester, New York, Brisbane, Toronto, Singapore · Zbl 0870.90076
[58] Delmaire, H.; Dı́az, J. A.; Fernández, E., Reactive GRASP and tabu search based heuristics for the single source capacitated plant location problem, INFOR, Canadian Journal of Operational Research and Information Processing, 37, 3, 194-225 (1999) · Zbl 07677590
[59] Dı́az, J.A., 2001. Algorithmic approaches for the single source capacitated facility location problem. Ph.D. Thesis, Dpt. d’Estadı́stica i Investigació Operativo, Universitat Polytecnica de Catalunya, Barcelona, Spain; Dı́az, J.A., 2001. Algorithmic approaches for the single source capacitated facility location problem. Ph.D. Thesis, Dpt. d’Estadı́stica i Investigació Operativo, Universitat Polytecnica de Catalunya, Barcelona, Spain
[60] Dı́az, J.A., Fernandez, E., 2001. A branch-and-price algorithm for the single source capacitated plant location problem. Technical Report, Dpt. d’Estadı́stica i Investigació Operativa, Universitat Politécnica de Catalunya, Barcelona, Spain; Dı́az, J.A., Fernandez, E., 2001. A branch-and-price algorithm for the single source capacitated plant location problem. Technical Report, Dpt. d’Estadı́stica i Investigació Operativa, Universitat Politécnica de Catalunya, Barcelona, Spain
[61] Dobson, G.; Karmarkar, U. S., Competitive location on a network, Operations Research, 35, 565-574 (1987) · Zbl 0636.90025
[62] Domı́nguez-Marı́n, P., Hansen, P., Mladenović, N., Nickel, S., 2003. Heuristic procedures for solving the discrete ordered median problem. Technical Report, Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany; Domı́nguez-Marı́n, P., Hansen, P., Mladenović, N., Nickel, S., 2003. Heuristic procedures for solving the discrete ordered median problem. Technical Report, Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany
[63] Domschke, W.; Drexl, A., Logistik: Standorte. Oldenbourgs Lehr- und Handbücher der Wirtschafts- und Sozialwissenschaften (1996), R. Oldenbourg Verlag: R. Oldenbourg Verlag München, Wien
[64] Drezner, Z., The planar two-center and two-median problems, Transportation Science, 18, 351-361 (1984)
[65] du Merle, O.; Villeneuve, D.; Desrosiers, J.; Hansen, P., Stabilized column generation, Discrete Mathematics, 194, 229-237 (1999) · Zbl 0949.90063
[66] Ebery, J.; Krishnamoorthy, M.; Ernst, A.; Boland, B., The capacitated multiple allocation hub location problem: Formulations and algorithms, European Journal of Operational Research, 120, 614-631 (2000) · Zbl 0985.90063
[67] Efroymson, M. A.; Ray, T. L., A branch-and-bound algorithm for plant location, Operations Research, 14, 361-368 (1966)
[68] Eiselt, H. A.; Laporte, G.; Thisse, J.-F., Competitive location models: A framework and bibliography, Transportation Science, 27, 44-54 (1993) · Zbl 0767.90006
[69] Engeler, K.; Klose, A.; Stähly, P., A depot location-allocation problem of a food producer with an outsourcing option, (Speranza, M. G.; Stähly, P., New Trends in Distribution Logistics. New Trends in Distribution Logistics, Lecture Notes in Economics and Mathematical Systems, vol. 480 (1999), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York), 95-109, (Chapter 1) · Zbl 0968.90049
[70] Erengüç, Ş. S.; Simpson, N. C.; Vakharia, A. J., Integrated production/distribution planning in supply chains: An invited review, European Journal of Operational Research, 115, 219-236 (1999) · Zbl 0949.90658
[71] Erkut, E.; Neuman, S., Analytical models for locating undesirable facilities, European Journal of Operational Research, 40, 275-291 (1989) · Zbl 0668.90025
[72] Erlenkotter, D., A dual-based procedure for uncapacitated facility location, Operations Research, 26, 992-1009 (1978) · Zbl 0422.90053
[73] Erlenkotter, D., A comparative study of approaches to dynamic facility location problems, European Journal of Operational Research, 6, 133-143 (1981) · Zbl 0451.90038
[74] Ernst, A.; Krishnamoorthy, M., Efficient algorithms for the uncapacitated single allocation \(p\)-hub median problem, Location Science, 4, 139-154 (1996) · Zbl 0927.90065
[75] Ernst, A.; Krishnamoorthy, M., An exact solution approach based on shortest-paths for the \(p\)-hub median problems, INFORMS Journal on Computing, 10, 149-162 (1998) · Zbl 1034.90505
[76] Ernst, A., Hamacher, H., Jiang, H., Krishnamoorthy, M., Woeginger, G., 2002a. Heuristic algorithms for the uncapacitated hub center single allocation problem. Technical Report, CSIRO, Australia; Ernst, A., Hamacher, H., Jiang, H., Krishnamoorthy, M., Woeginger, G., 2002a. Heuristic algorithms for the uncapacitated hub center single allocation problem. Technical Report, CSIRO, Australia
[77] Ernst, A., Hamacher, H., Jiang, H., Krishnamoorthy, M., Woeginger, G., 2002b. Uncapacitated single and multiple allocation \(p\); Ernst, A., Hamacher, H., Jiang, H., Krishnamoorthy, M., Woeginger, G., 2002b. Uncapacitated single and multiple allocation \(p\) · Zbl 1158.90372
[78] Fernández, E.; Puerto, J., Multiobjective solution of the uncapacitated plant location problem, European Journal of Operational Research, 145, 509-529 (2003) · Zbl 1011.90034
[79] Fisher, M. L., Vehicle routing, (Ball, M. O.; Magnanti, T. L.; Monma, C. L.; Nemhauser, G. L., Network Routing. Network Routing, Handbooks in Operations Research and Management Science, vol. 8 (1995), North-Holland: North-Holland Amsterdam), 1-33, (Chapter 1) · Zbl 0870.90058
[80] Fisher, M. L.; Hochbaum, D. S., Database location in computer networks, Journal of the ACM, 7, 718-735 (1980) · Zbl 0445.68071
[81] Fisher, M. L.; Jaikumar, R., A generalized assignment heuristic for vehicle routing, Networks, 11, 2, 109-124 (1981)
[82] Fleischmann, B., Designing distribution systems with transport economies of scale, European Journal of Operational Research, 70, 1, 31-42 (1993) · Zbl 0800.90398
[83] Francis, R. L.; McGinnis, L. F.; White, J. A., Facility Layout and Location: An Analytical Approach, Prentice-Hall International Series in Industrial and Systems Engineering (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[84] Frantzeskakis, M.; Watson-Gandy, C. D.T., The use of state space relaxation for the dynamic facility location problem, Annals of Operations Research, 18, 189-212 (1989) · Zbl 0707.90062
[85] Galvão, R. D., A Lagrangean heuristic for the maximal covering location problem, European Journal of Operational Research, 88, 114-123 (1996) · Zbl 0913.90200
[86] Galvão, R. D.; Espejo, L. G.A.; Boffey, T. B., A hierarchical model for the location of perinatal facilities in the municipality of Rio de Janeiro, European Journal of Operational Research, 138, 495-517 (2002) · Zbl 1008.90517
[87] Gao, L.-L.; Robinson, E. P., A dual-based optimization procedure for the two-echelon uncapacitated facility location problem, Naval Research Logistics, 39, 191-212 (1992) · Zbl 0773.90042
[88] Gao, L.-L.; Robinson, E. P., Uncapacitated facility location: General solution procedure and computational experience, European Journal of Operational Research, 76, 3, 410-427 (1994) · Zbl 0810.90085
[89] Gavish, B., Topological design of telecommunication networks-local access design methods, Annals of Operations Research, 33, 17-71 (1991) · Zbl 0736.90030
[90] Gelders, L. F.; Pintelon, L. M.; van Wassenhove, L. N., A location-allocation problem in a large Belgian brewery, European Journal of Operational Research, 28, 196-206 (1987)
[91] Geoffrion, A. M.; Graves, G. W., Multicommodity distribution system design by Benders decomposition, Management Science, 20, 822-844 (1974) · Zbl 0304.90122
[92] Geoffrion, A. M.; McBride, R., Lagrangean relaxation to capacitated facility location problems, AIIE Transactions, 10, 1, 40-47 (1978)
[93] Geoffrion, A. M.; Powers, R. F., Twenty years of strategic distribution system design: An evolutionary perspective, Interfaces, 25, 5, 105-127 (1995)
[94] Geoffrion, A. M.; Graves, G. W.; Lee, S.-J., A management support system for distribution planning, INFOR, Canadian Journal of Operational Research and Information Processing, 20, 287-314 (1982)
[95] Goetschalckx, M.; Vidal, C. J.; Dogan, K., Modeling and design of global logistics systems: A review of integrated strategic and tactical models and design algorithms, European Journal of Operational Research, 143, 1-18 (2002) · Zbl 1073.90501
[96] Goldengorin, B.; Ghosh, D.; Sierksma, G., Branch and peg algorithms for the simple plant location problem, Computers & Operations Research, 30, 967-981 (2003) · Zbl 1039.90027
[97] Gourdin, É.; Labbé, M.; Laporte, G., The uncapacitated facility location problem with client matching, Operations Research, 48, 5, 671-685 (2000) · Zbl 1106.90354
[98] Grünert, T., Lagrangean tabu search, (Ribeiro, C. C.; Hansen, P., Essays and Surveys in Metaheuristics (2002), Kluwer Academic: Kluwer Academic Boston), 379-397 · Zbl 1006.90071
[99] Guha, S., Khuller, S., 1998. Greedy strikes back: Improved facility location algorithms. In: Proceedings of the 9th Annual ACM-SIAM Symposioum on Discrete Algorithms, pp. 649-657; Guha, S., Khuller, S., 1998. Greedy strikes back: Improved facility location algorithms. In: Proceedings of the 9th Annual ACM-SIAM Symposioum on Discrete Algorithms, pp. 649-657 · Zbl 0936.68114
[100] Guignard, M., Fractional vertices, cuts and facets of the simple plant location problem, Mathematical Programming Study, 12, 150-162 (1980) · Zbl 0439.90061
[101] Guignard, M., A Lagrangean dual ascent algorithm for simple plant location problems, European Journal of Operational Research, 35, 193-200 (1988) · Zbl 0696.90025
[102] Guignard, M., Kim, S., 1983. A strong Lagrangean relaxation for capacitated plant location problems. Working Paper 56, Decision Sciences Department, University of Pennsylvania, The Wharton School; Guignard, M., Kim, S., 1983. A strong Lagrangean relaxation for capacitated plant location problems. Working Paper 56, Decision Sciences Department, University of Pennsylvania, The Wharton School
[103] Hakimi, S. L., Optimum locations of switching centers and the absolute centers and medians of a graph, Operations Research, 12, 450-459 (1964) · Zbl 0123.00305
[104] Hakimi, S. L., Optimum distribution of switching centers in a communication network and some related graph theoretic problems, Operations Research, 13, 462-475 (1965) · Zbl 0135.20501
[105] Hakimi, S. L., On locating new facilities in a competitive environment, European Journal of Operational Research, 12, 29-35 (1983) · Zbl 0499.90026
[106] Hamacher, H. W.; Nickel, S., Combinatorial algorithms for some 1-facility median problems in the plane, European Journal of Operational Research, 79, 340-351 (1994) · Zbl 0822.90095
[107] Hamacher, H. W.; Nickel, S., Classification of location models, Location Science, 6, 229-242 (1998)
[108] Hamacher, H.W., Labbé, M., Nickel, S., Sonneborn, T., 2000. Polyhedral properties of the uncapacitated multiple allocation hub location problem. Working Paper, Fraunhofer Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany; Hamacher, H.W., Labbé, M., Nickel, S., Sonneborn, T., 2000. Polyhedral properties of the uncapacitated multiple allocation hub location problem. Working Paper, Fraunhofer Institut für Techno- und Wirtschaftsmathematik, Kaiserslautern, Germany
[109] Handler, G. Y., Complexity and efficiency in minimax network location, (Christofides, N.; Mingozzi, A.; Toth, P.; Sandi, C., Combinatorial Optimization (1979), John Wiley & Sons: John Wiley & Sons Chichester, New York, Brisbane, Toronto, Singapore), 281-314, (Chapter 10) · Zbl 0427.90082
[110] Hanjoul, P.; Peeters, D., A comparison of two dual-based procedures for solving the \(p\)-median problem, European Journal of Operational Research, 20, 387-396 (1985) · Zbl 0565.90011
[111] Hansen, P.; de Luna Pedrosa Filho, E.; Ribeiro, C. C., Location and sizing of offshore platforms for oil exploration, European Journal of Operational Research, 58, 202-214 (1992) · Zbl 0775.90273
[112] Hansen, P.; de Luna Pedrosa Filho, E.; Ribeiro, C. C., Modelling location and sizing of offshore platforms, European Journal of Operational Research, 72, 602-606 (1994) · Zbl 0806.90078
[113] Hansen, P.; Mladenovic, N.; Taillard, E., Heuristic solution of the multisource Weber problem as a \(p\)-median problem, Operations Research Letters, 22, 55-62 (1998) · Zbl 0911.90240
[114] Harkness, J.; ReVelle, C., Facility location with increasing production costs, European Journal of Operational Research, 145, 1-13 (2003) · Zbl 1012.90024
[115] Heller, M.; Cohon, J. L.; ReVelle, C. S., The use of simulation in validating multiobjective EMS location model, Annals of Operations Research, 18, 303-322 (1989)
[116] Hindi, K. S.; Basta, T., Computationally efficient solution of a multiproduct, two-stage distribution-location problem, The Journal of the Operational Research Society, 45, 11, 1316-1323 (1994) · Zbl 0812.90092
[117] Hindi, K. S.; Basta, T.; Pieńkosz, K., Efficient solution of a multi-commodity, two-stage distribution problem with constraints on assignment of customers to distribution centers, International Transactions in Operations Research, 5, 6, 519-528 (1998)
[118] Holmberg, K.; Rönnqvist, M.; Yuan, D., An exact algorithm for the capacitated facility location problems with single sourcing, European Journal of Operational Research, 113, 544-559 (1999) · Zbl 0947.90059
[119] Hotelling, H., Stability in competition, Economic Journal, 39, 41-57 (1929)
[120] Jacobsen, S. K.; Madsen, O. B.G., A comparative study of heuristics for a two-level routing-location problem, European Journal of Operational Research, 5, 378-387 (1980) · Zbl 0441.90028
[121] Käfer, B.; Nickel, S., Error bounds for the approximate solution of restricted planar location problems, European Journal of Operational Research, 135, 67-85 (2001) · Zbl 1077.90549
[122] Karkazis, J.; Boffey, T. B., The multi-commodity facilities location problem, The Journal of the Operational Research Society, 32, 803-814 (1981) · Zbl 0461.90025
[123] Khumawala, B. M., An efficient branch and bound algorithm for the warehouse location problem, Management Science, 18, 12, B718-B731 (1972) · Zbl 0238.90048
[124] Klamroth, K., Planar Weber location problems with line barriers, Optimization, 49, 517-527 (2001) · Zbl 0995.90065
[125] Klincewicz, J. G., A dual algorithm for the uncapacitated hub location problem, Location Science, 4, 173-184 (1996) · Zbl 0929.90049
[126] Klincewicz, J. G.; Luss, H., A Lagrangian relaxation heuristic for capacitated facility location with single source constraints, The Journal of the Operational Research Society, 37, 495-500 (1986) · Zbl 0588.90025
[127] Klincewicz, J. G.; Luss, H.; Rosenberg, E., Optimal and heuristic algorithms for multiproduct uncapacitated facility location, European Journal of Operational Research, 26, 251-258 (1986) · Zbl 0593.90028
[128] Klose, A., 1993. Das kombinatorische \(p\); Klose, A., 1993. Das kombinatorische \(p\)
[129] Klose, A., Using clustering methods in problems of combined location and routing, (Kleinschmidt, P.; Bachem, A.; Derigs, U.; Fischer, D.; Leopold-Wildburger, U.; Möhring, R., Operations Research Proceedings 1995 (1996), Deutsche Gesellschaft für Operations Research e.V. (DGOR), Springer-Verlag: Deutsche Gesellschaft für Operations Research e.V. (DGOR), Springer-Verlag Berlin, Heidelberg, New York), 411-416
[130] Klose, A., A branch and bound algorithm for an uncapacitated facility location problem with a side constraint, International Transactions in Operational Research, 5, 155-168 (1998)
[131] Klose, A., An LP-based heuristic for two-stage capacitated facility location problems, The Journal of the Operational Research Society, 50, 2, 157-166 (1999) · Zbl 1054.90590
[132] Klose, A., A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem, European Journal of Operational Research, 126, 2, 185-198 (2000)
[133] Klose, A., Standortplanung in distributiven Systemen (2001), Physica: Physica Heidelberg
[134] Klose, A., Drexl, A., 2001. Lower bounds for the capacitated facility location problem based on column generation. Technical Report, Universität St. Gallen; Klose, A., Drexl, A., 2001. Lower bounds for the capacitated facility location problem based on column generation. Technical Report, Universität St. Gallen · Zbl 1232.90255
[135] Klose, A., Wittmann, S., 1995. Facility location based on clustering. In: Proceedings of the Second International Workshop on Distribution Logistics (IWDL-2); Klose, A., Wittmann, S., 1995. Facility location based on clustering. In: Proceedings of the Second International Workshop on Distribution Logistics (IWDL-2)
[136] Köksalan, M.; Süral, H.; Kırca, Ö., A location-distribution application for a beer company, European Journal of Operational Research, 80, 16-24 (1995) · Zbl 0929.90054
[137] Körkel, M., On the exact solution of large-scale simple plant location problems, European Journal of Operational Research, 39, 157-173 (1989) · Zbl 0673.90032
[138] Korupolu, M.R., Plaxton, C.G., Rajaraman, R., 1998. Analysis of a local search heuristic for facility location problems. Technical Report 98-30, DIMACS, Rutgers University; Korupolu, M.R., Plaxton, C.G., Rajaraman, R., 1998. Analysis of a local search heuristic for facility location problems. Technical Report 98-30, DIMACS, Rutgers University · Zbl 0922.90100
[139] Krarup, J.; Pruzan, P. M., Selected families of location problems, Annals of Discrete Mathematics, 5, 327-387 (1979) · Zbl 0415.90063
[140] Krarup, J.; Pruzan, P. M., The simple plant location problem: Survey and synthesis, European Journal of Operational Research, 12, 1, 36-81 (1983) · Zbl 0506.90018
[141] Laporte, G.; Norbert, Y.; Pelletier, P., Hamiltonian location problems, European Journal of Operational Research, 12, 82-89 (1983) · Zbl 0502.90021
[142] Laporte, G.; Norbert, Y.; Taillefer, S., Solving a family of multi-depot vehicle routing and location-routing problems, Transportation Science, 22, 3, 161-172 (1988) · Zbl 0662.90039
[143] Laporte, G.; Louveaux, F.; van Hamme, L., Exact solution to a location problem with stochastic demands, Transportation Science, 28, 95-103 (1994) · Zbl 0821.90077
[144] Lee, C. Y., An algorithm for a two-staged distribution system with various types of distribution centers, INFOR, Canadian Journal of Operational Research and Information Processing, 34, 2, 105-117 (1996) · Zbl 0868.90073
[145] Lin, J.-H.; Vitter, J. S., Approximation algorithms for geometric median problems, Information Processing Letters, 44, 245-249 (1992) · Zbl 0764.68079
[146] Listes, O., Dekker, R., 2001. Stochastic approaches for product recovery network design: A case study. Econometric Institute Report EI 2001-08, Erasmus University Rotterdam; Listes, O., Dekker, R., 2001. Stochastic approaches for product recovery network design: A case study. Econometric Institute Report EI 2001-08, Erasmus University Rotterdam · Zbl 1134.90433
[147] Love, R. F.; Morris, J. G.; Wesolowsky, G. O., Facilities Location: Models & Methods, Publications in Operations Research Series, vol. 7 (1988), North-Holland: North-Holland Amsterdam · Zbl 0685.90036
[148] Marı́n, A.; Pelegrı́n, B., Applying Lagrangian relaxation to the resolution of two-stage location problems, Annals of Operations Research, 86, 179-198 (1999) · Zbl 0921.90104
[149] (Martello, S.; Toth, P., Knapsack Problems: Algorithms and Computer Implementations (1990), John Wiley & Sons: John Wiley & Sons Chichester, New York, Brisbane, Toronto, Singapore) · Zbl 0708.68002
[150] Mayer, G.; Wagner, B., Hublocater: An exact solution method for the multiple allocation hub location problem, Computers & Operations Research, 29, 715-739 (2002) · Zbl 1001.90044
[151] Mazzola, J. B.; Neebe, A. W., Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type, European Journal of Operational Research, 115, 285-299 (1999) · Zbl 0938.90049
[152] Melachrinoudis, E., An efficient computational procedure for the rectilinear maximin location problem, Transportation Science, 22, 217-223 (1988) · Zbl 0656.90031
[153] Miehle, W., Link-length minimization in networks, Operations Research, 6, 232-243 (1958) · Zbl 1414.90068
[154] Mirchandani, P. B.; Oudjit, A.; Wong, R. T., Multidimensional extensions and a nested dual approach for the \(m\)-median problem, European Journal of Operational Research, 21, 121-137 (1985) · Zbl 0587.90037
[155] Mirzaian, A., Lagrangian relaxation for the star-star concentrator location problem: Approximation algorithm and bounds, Networks, 15, 1-20 (1985) · Zbl 0579.94031
[156] Mulvey, J. M.; Crowder, H. P., Cluster analysis: An application of Lagrangean relaxation, Management Science, 25, 4, 329-340 (1979) · Zbl 0415.90085
[157] Nagy, G.; Salhi, S., Nested heuristic methods for the location-routing problem, The Journal of the Operational Research Society, 47, 9, 1166-1174 (1996) · Zbl 0869.90019
[158] Nauss, R. M., An improved algorithm for the capacitated facility location problem, The Journal of the Operational Research Society, 29, 1195-1201 (1978) · Zbl 0402.90063
[159] Nauss, R. M.; Markland, R. E., Theory and application of an optimizing procedure for lock box location analysis, Management Science, 27, 855-865 (1981) · Zbl 0461.90044
[160] O’Kelly, M. E., The location of interacting hub facilities, Transportation Science, 20, 92-106 (1986)
[161] O’Kelly, M. E., A quadratic integer program for the location of interacting hub facilities, European Journal of Operational Research, 32, 393-404 (1987) · Zbl 0627.90030
[162] Ostresh, L. M., TWAIN-exact solutions to the two-source location-allocation problem, (Rushton, G.; Goodchild, M. F.; Ostresh, L. M., Computer Programs for Location-Allocation Problems (1973), Department of Geography, University of Iowa), pp. 15-28
[163] Owen, S. H.; Daskin, M. S., Strategic facility location: A review, European Journal of Operational Research, 111, 423-447 (1998) · Zbl 0938.90048
[164] Perl, J.; Daskin, M. S., A warehouse location-routing problem, Transportation Research, 19, 381-396 (1985)
[165] Pirkul, H., Efficient algorithms for the capacitated concentrator location problem, Computers & Operations Research, 14, 197-208 (1987) · Zbl 0617.90019
[166] Pirkul, H.; Jayaraman, V., Production, transportation, and distribution planning in a multi-commodity tri-echelon system, Transportation Science, 30, 291-302 (1996) · Zbl 0879.90129
[167] Pirkul, H.; Jayaraman, V., A multi-commodity, multi-plant, capacitated facility location problem: Formulation and efficient heuristic solution, Computers & Operations Research, 25, 10, 869-878 (1998) · Zbl 1042.90580
[168] Pooley, J., Integrated production and distribution facility planning at Ault foods, Interfaces, 24, 113-121 (1994)
[169] ReVelle, C., The maximum capture or “spere of influence” location problem: Hotelling revisited on a network, Journal of Regional Science, 26, 343-358 (1986)
[170] ReVelle, C. S., Facility siting and integer-friendly programming, European Journal of Operational Research, 65, 147-158 (1993) · Zbl 0776.90047
[171] ReVelle, C. S.; Laporte, G., The plant location problem: New models and research prospects, Operations Research, 44, 6, 864-874 (1996) · Zbl 0879.90130
[172] Robinson, E. P.; Gao, L.-L.; Muggenborg, S. D., Designing an integrated distribution system at DowBrands, Inc, Interfaces, 23, 3, 107-117 (1993)
[173] Rosing, K. E., The optimal location of steam generators in large heavy oil fields, American Journal of Mathematical and Management Sciences, 12, 1, 19-42 (1992)
[174] Rosing, K. E., An optimal method for solving the (generalized) multi-Weber problem, European Journal of Operational Research, 58, 3, 414-426 (1992) · Zbl 0760.90064
[175] Ryu, C., Guignard, M., 1992a. An efficient algorithm for the capacitated plant location problem. Working Paper 92-11-02, Decision Sciences Department, University of Pennsylvania, The Wharton School; Ryu, C., Guignard, M., 1992a. An efficient algorithm for the capacitated plant location problem. Working Paper 92-11-02, Decision Sciences Department, University of Pennsylvania, The Wharton School
[176] Ryu, C., Guignard, M., 1992b. An exact algorithm for the simple plant location problem with an aggregate capacity constraint. Working Paper 92-04-09, Decision Sciences Department, University of Pennsylvania, The Wharton School; Ryu, C., Guignard, M., 1992b. An exact algorithm for the simple plant location problem with an aggregate capacity constraint. Working Paper 92-04-09, Decision Sciences Department, University of Pennsylvania, The Wharton School
[177] Salhi, S.; Fraser, M., An integrated heuristic approach for the combined location-vehicle fleet mix problem, Studies in Locational Analysis, 8, 3-22 (1996) · Zbl 1176.90362
[178] Scaparra, M.P., 2002. Multi-exchange algorithms for some capacitated facility location problems. Ph.D. Thesis, Department of Computer Science, University of Pisa, Pisa; Scaparra, M.P., 2002. Multi-exchange algorithms for some capacitated facility location problems. Ph.D. Thesis, Department of Computer Science, University of Pisa, Pisa
[179] Schilling, D. A., Dynamic location modeling for public-sector facilities: A multicriteria approach, Decision Sciences, 11, 714-724 (1980)
[180] Schilling, D. A.; Jayaraman, V.; Barkhi, R., A review of covering problems in facility location, Location Science, 1, 1, 25-55 (1993) · Zbl 0923.90108
[181] Shetty, B., Approximate solutions to large scale capacitated facility location problems, Applied Mathematics and Computation, 39, 159-175 (1990) · Zbl 0707.65042
[182] Shmoys, D.B., Tardos, E., Aardal, K., 1997. Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265-274; Shmoys, D.B., Tardos, E., Aardal, K., 1997. Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265-274 · Zbl 0962.68008
[183] Shulman, A., An algorithm for solving dynamic capacitated plant location problems with discrete expansion sizes, Operations Research, 39, 3, 423-436 (1991) · Zbl 0742.90049
[184] Simchi-Levi, D.; Berman, O., A heuristic algorithm for the traveling salesman location problem on networks, Operations Research, 36, 478-484 (1988) · Zbl 0647.90097
[185] 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
[186] Sridharan, R., The capacitated plant location problem, European Journal of Operational Research, 87, 2, 203-213 (1995) · Zbl 0914.90180
[187] Taillard, E., 1996. Heuristic methods for large multi-source Weber problems. Technical Report IDSIA96-96, IDSIA, Lugano; Taillard, E., 1996. Heuristic methods for large multi-source Weber problems. Technical Report IDSIA96-96, IDSIA, Lugano
[188] Tcha, D.; Lee, B., A branch and bound algorithm for the multi-level uncapacitated facility location problem, European Journal of Operational Research, 18, 35-43 (1984) · Zbl 0542.90034
[189] Thizy, J.-M., A facility location problem with aggregate capacity, INFOR, Canadian Journal of Operational Research and Information Processing, 32, 1, 1-18 (1994) · Zbl 0802.90065
[190] Tragantalerngsak, S.; Holt, J.; Rönnqvist, 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
[191] Tüshaus, U.; Wittmann, S., Strategic logistic planning by means of simple plant location: A case study, (Fleischmann, B.; van Nunen, J. A.E. E.; Speranza, M. G.; Stähly, P., Advances in Distribution Logistics. Advances in Distribution Logistics, Lecture Notes in Economics and Mathematical Systems, vol. 460 (1998), Springer-Verlag: Springer-Verlag Berlin, Heidelberg, New York), 241-263, (Chapter 2) · Zbl 0907.90195
[192] Van Roy, T. J., A cross decomposition algorithm for capacitated facility location, Operations Research, 34, 145-163 (1986) · Zbl 0594.90022
[193] Van Roy, T. J.; Erlenkotter, D., A dual-based procedure for dynamic facility location, Management Science, 28, 10, 1091-1105 (1982) · Zbl 0495.90033
[194] Vasko, F. J.; Newhart, D. D.; Stott, K. L.; Wolf, F. E., A large-scale application of the partial coverage uncapacitated facility location problem, Journal of the Operational Research Society, 54, 11-20 (2003) · Zbl 1088.90038
[195] Vidal, C. J.; Goetschalckx, M., Strategic production-distribution models: A critical review with emphasis on global supply chain models, European Journal of Operational Research, 98, 1, 1-18 (1997) · Zbl 0922.90062
[196] Weber, A., Über den Standort der Industrien. 1. Teil: Reine Theorie des Standorts (1909), Verlag J.C. B. Mohr: Verlag J.C. B. Mohr Tübingen
[197] Weiszfeld, E., Sur le point pour lequel la somme des distances de \(n\) points donnés est minimum, Tôhoku Mathematical Journal, 43, 355-386 (1937) · Zbl 0017.18007
[198] Wentges, P., 1994. Standortprobleme mit Berücksichtigung von Kapazitätsrestriktionen: Modellierung und Lösungsverfahren. Dissertation Nr. 1620, Hochschule St. Gallen, Dufourstrasse 50, CH-9000 St. Gallen; Wentges, P., 1994. Standortprobleme mit Berücksichtigung von Kapazitätsrestriktionen: Modellierung und Lösungsverfahren. Dissertation Nr. 1620, Hochschule St. Gallen, Dufourstrasse 50, CH-9000 St. Gallen
[199] Wentges, P., Accelerating Benders’ decomposition for the capacitated facility location problem, Mathematical Methods of Operations Research, 44, 267-290 (1996) · Zbl 0862.90089
[200] Wesolowsky, G. O., The Weber problem: History and perspectives, Location Science, 1, 1, 5-23 (1993) · Zbl 0923.90110
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.