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Multi-level facility location problems

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  • Ortiz-Astorquiza, Camilo
  • Contreras, Ivan
  • Laporte, Gilbert

Abstract

We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field.

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  • Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:3:p:791-805
    DOI: 10.1016/j.ejor.2017.10.019
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    1. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2015. "Multi-level facility location as the maximization of a submodular set function," European Journal of Operational Research, Elsevier, vol. 247(3), pages 1013-1016.
    2. Lucas P. Melo & Flávio K. Miyazawa & Lehilton L. C. Pedrosa & Rafael C. S. Schouery, 2017. "Approximation algorithms for k-level stochastic facility location problems," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 266-278, July.
    3. Anantaram Balakrishnan & Thomas L. Magnanti & Prakash Mirchandani, 1994. "A Dual-Based Algorithm for Multi-Level Network Design," Management Science, INFORMS, vol. 40(5), pages 567-581, May.
    4. A. J. Goldman, 1969. "Optimal Locations for Centers in a Network," Transportation Science, INFORMS, vol. 3(4), pages 352-360, November.
    5. Barros, A. I. & Dekker, R. & Scholten, V., 1998. "A two-level network for recycling sand: A case study," European Journal of Operational Research, Elsevier, vol. 110(2), pages 199-214, October.
    6. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Addis, Bernardetta & Carello, Giuliana & Ceselli, Alberto, 2013. "Combining very large scale and ILP based neighborhoods for a two-level location problem," European Journal of Operational Research, Elsevier, vol. 231(3), pages 535-546.
    8. Alfred A. Kuehn & Michael J. Hamburger, 1963. "A Heuristic Program for Locating Warehouses," Management Science, INFORMS, vol. 9(4), pages 643-666, July.
    9. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    10. Tcha, Dong-wan & Lee, Bum-il, 1984. "A branch-and-bound algorithm for the multi-level uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 18(1), pages 35-43, October.
    11. Bernard Fortz, 2015. "Location Problems in Telecommunications," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 537-554, Springer.
    12. Gollowitzer, Stefan & Gouveia, Luis & Ljubić, Ivana, 2013. "Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities," European Journal of Operational Research, Elsevier, vol. 225(2), pages 211-222.
    13. Alumur, Sibel A. & Yaman, Hande & Kara, Bahar Y., 2012. "Hierarchical multimodal hub location problem with time-definite deliveries," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(6), pages 1107-1120.
    14. Roberto Roberti & Enrico Bartolini & Aristide Mingozzi, 2015. "The Fixed Charge Transportation Problem: An Exact Algorithm Based on a New Integer Programming Formulation," Management Science, INFORMS, vol. 61(6), pages 1275-1291, June.
    15. A Klose, 1999. "An LP-based heuristic for two-stage capacitated facility location problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(2), pages 157-166, February.
    16. Pitu B. Mirchandani, 1987. "Generalized Hierarchical Facility Locations," Transportation Science, INFORMS, vol. 21(2), pages 123-125, May.
    17. Mark S. Daskin & Lawrence V. Snyder & Rosemary T. Berger, 2005. "Facility Location in Supply Chain Design," Springer Books, in: André Langevin & Diane Riopel (ed.), Logistics Systems: Design and Optimization, chapter 0, pages 39-65, Springer.
    18. Klose, Andreas, 2000. "A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 126(2), pages 408-421, October.
    19. Vahidreza Ghezavati & Faezeh Soltanzadeh & Ashkan Hafezalkotob, 2015. "Optimization of reliability for a hierarchical facility location problem under disaster relief situations by a chance-constrained programming and robust optimization," Journal of Risk and Reliability, , vol. 229(6), pages 542-555, December.
    20. Simona Mancini, 2013. "Multi-echelon distribution systems in city logistics," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 54, pages 1-2.
    21. Contreras, Ivan & Fernández, Elena, 2012. "General network design: A unified view of combined location and network design problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 680-697.
    22. Ro, Hyung-bong & Tcha, Dong-wan, 1984. "A branch and bound algorithm for the two-level uncapacitated facility location problem with some side constraints," European Journal of Operational Research, Elsevier, vol. 18(3), pages 349-358, December.
    23. T. L. Magnanti & R. T. Wong, 1984. "Network Design and Transportation Planning: Models and Algorithms," Transportation Science, INFORMS, vol. 18(1), pages 1-55, February.
    24. S. L. Hakimi & S. N. Maheshwari, 1972. "Optimum Locations of Centers in Networks," Operations Research, INFORMS, vol. 20(5), pages 967-973, October.
    25. Yaman, Hande, 2009. "The hierarchical hub median problem with single assignment," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 643-658, July.
    26. Donald Erlenkotter, 1978. "A Dual-Based Procedure for Uncapacitated Facility Location," Operations Research, INFORMS, vol. 26(6), pages 992-1009, December.
    27. Narula, Subhash C., 1984. "Hierarchical location-allocation problems: A classification scheme," European Journal of Operational Research, Elsevier, vol. 15(1), pages 93-99, January.
    28. Igor Litvinchev & Edith L. Ozuna, 2012. "Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem," International Journal of Energy Optimization and Engineering (IJEOE), IGI Global, vol. 1(1), pages 59-71, January.
    29. Mercedes Landete & Alfredo Marín, 2009. "New facets for the two-stage uncapacitated facility location polytope," Computational Optimization and Applications, Springer, vol. 44(3), pages 487-519, December.
    30. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    31. Tragantalerngsak, Suda & Holt, John & Ronnqvist, Mikael, 1997. "Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 102(3), pages 611-625, November.
    32. Karen Aardal, 1998. "Reformulation of capacitated facility location problems:How redundant information can help," Annals of Operations Research, Springer, vol. 82(0), pages 289-308, August.
    33. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    34. Jesus Gonzalez-Feliu & Jean-Louis Routhier & Frédéric Semet, 2014. "Sustainable urban logistics: Concepts, methods and information systems," Post-Print halshs-01056156, HAL.
    35. Bloemhof-Ruwaard, Jacqueline M. & Salomon, Marc & Van Wassenhove, Luk N., 1996. "The capacitated distribution and waste disposal problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 490-503, February.
    36. Hasan Pirkul & Vaidyanathan Jayaraman, 1996. "Production, Transportation, and Distribution Planning in a Multi-Commodity Tri-Echelon System," Transportation Science, INFORMS, vol. 30(4), pages 291-302, November.
    37. Maria Albareda-Sambola, 2015. "Location-Routing and Location-Arc Routing," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 399-418, Springer.
    38. Hinojosa, Y. & Puerto, J. & Fernandez, F. R., 2000. "A multiperiod two-echelon multicommodity capacitated plant location problem," European Journal of Operational Research, Elsevier, vol. 123(2), pages 271-291, June.
    39. Li, Jinfeng & Chu, Feng & Prins, Christian & Zhu, Zhanguo, 2014. "Lower and upper bounds for a two-stage capacitated facility location problem with handling costs," European Journal of Operational Research, Elsevier, vol. 236(3), pages 957-967.
    40. Bernard Gendron & Paul-Virak Khuong & Frédéric Semet, 2016. "A Lagrangian-Based Branch-and-Bound Algorithm for the Two-Level Uncapacitated Facility Location Problem with Single-Assignment Constraints," Transportation Science, INFORMS, vol. 50(4), pages 1286-1299, November.
    41. Gerard Cornuejols & Marshall L. Fisher & George L. Nemhauser, 1977. "Exceptional Paper--Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms," Management Science, INFORMS, vol. 23(8), pages 789-810, April.
    42. P. Chardaire & J.‐L. Lutton & A. Sutter, 1999. "Upper and lower bounds for the two‐level simple plant location problem," Annals of Operations Research, Springer, vol. 86(0), pages 117-140, January.
    43. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    44. CORNUEJOLS, Gérard & FISHER, Marshall L. & NEMHAUSER, George L., 1977. "Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms," LIDAM Reprints CORE 292, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    45. Donglei Du & Xing Wang & Dachuan Xu, 2010. "An approximation algorithm for the k-level capacitated facility location problem," Journal of Combinatorial Optimization, Springer, vol. 20(4), pages 361-368, November.
    46. Stefan Gollowitzer & Bernard Gendron & Ivana Ljubić, 2013. "A cutting plane algorithm for the Capacitated Connected Facility Location Problem," Computational Optimization and Applications, Springer, vol. 55(3), pages 647-674, July.
    47. Melo, M.T. & Nickel, S. & Saldanha-da-Gama, F., 2009. "Facility location and supply chain management - A review," European Journal of Operational Research, Elsevier, vol. 196(2), pages 401-412, July.
    48. Ivana Ljubić & Stefan Gollowitzer, 2013. "Layered Graph Approaches to the Hop Constrained Connected Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 256-270, May.
    49. Bloemhof-Ruwaard, Jacqueline M. & Salomon, Marc & Van Wassenhove, Luk N., 1994. "On the coordination of product and by-product flows in two-level distribution networks: Model formulations and solution procedures," European Journal of Operational Research, Elsevier, vol. 79(2), pages 325-339, December.
    50. Barros, A. I. & Labbe, M., 1994. "The multi-level uncapacitated facility location problem is not submodular," European Journal of Operational Research, Elsevier, vol. 72(3), pages 607-609, February.
    51. Karen Aardal & Martine Labbé & Janny Leung & Maurice Queyranne, 1996. "On the Two-Level Uncapacitated Facility Location Problem," INFORMS Journal on Computing, INFORMS, vol. 8(3), pages 289-301, August.
    52. Richard E. Wendell & Arthur P. Hurter, 1973. "Optimal Locations on a Network," Transportation Science, INFORMS, vol. 7(1), pages 18-33, February.
    53. Gouveia, Luis & Leitner, Markus & Ljubić, Ivana, 2014. "Hop constrained Steiner trees with multiple root nodes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 100-112.
    54. Manzini, Riccardo & Bindi, Filippo, 2009. "Strategic design and operational management optimization of a multi stage physical distribution system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(6), pages 915-936, November.
    55. Tragantalerngsak, Suda & Holt, John & Ronnqvist, Mikael, 2000. "An exact method for the two-echelon, single-source, capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 123(3), pages 473-489, June.
    56. Fischetti, Matteo & Ljubić, Ivana & Sinnl, Markus, 2016. "Benders decomposition without separability: A computational study for capacitated facility location problems," European Journal of Operational Research, Elsevier, vol. 253(3), pages 557-569.
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