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The Uncapacitated Facility Location Problem with Client Matching

Author

Listed:
  • Éric Gourdin

    (SMG and ISRO, Université Libre de Bruxelles, Boulevard du Triomphe, CP210/01, B-1050 Brussels, Belgium)

  • Martine Labbé

    (SMG and ISRO, Université Libre de Bruxelles, Boulevard du Triomphe, CP210/01, B-1050 Brussels, Belgium)

  • Gilbert Laporte

    (Centre de Recherche sur les Transports, Université de Montréal, Case Postale 6128, Succursale “Centre-ville,” Montreal, Canada H3C 3J7)

Abstract

The Uncapacitated Facility Location Problem with Client Matching (LCM) is an extension of the Uncapacitated Facility Location Problem (UFLP), where two clients allocated to a facility can be matched. As in the UFLP, facilities can be opened at any of m predefined locations with given fixed costs, and n clients have to be allocated to the open facilities. In classical location models, the allocation cost is the distance between a client and an open facility. In the LCM, the allocation cost is either the cost of a return trip between the facility and the client, or the length of a tour containing the facility and two clients. The similarities of the LCM with the classical UFLP and the matching problem are exploited to derive valid inequalities, optimality cuts, and polyhedral results. A greedy heuristic and a branch-and-cut algorithm are developed, and several separation procedures are described. Computational experiments confirm the efficiency of the proposed approach.

Suggested Citation

  • Éric Gourdin & Martine Labbé & Gilbert Laporte, 2000. "The Uncapacitated Facility Location Problem with Client Matching," Operations Research, INFORMS, vol. 48(5), pages 671-685, October.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:5:p:671-685
    DOI: 10.1287/opre.48.5.671.12410
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    References listed on IDEAS

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    1. labbe, M. & Peeters, D. & Thisse, J.F., 1992. "Location on Networks," Papers 9216, Universite Libre de Bruxelles - C.E.M.E..
    2. Current, John & Weber, Charles, 1994. "Application of facility location modeling constructs to vendor selection problems," European Journal of Operational Research, Elsevier, vol. 76(3), pages 387-392, August.
    3. Labbé, M. & Peeters, D. & Thisse, J.-F., 1995. "Location on Network. Network Routing," LIDAM Reprints CORE 1182, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Lai, Xiaofan & Xu, Zhou, 2016. "Improved algorithms for joint optimization of facility locations and network connections," European Journal of Operational Research, Elsevier, vol. 250(3), pages 745-753.
    2. Huang, Sen & Liu, Kanglin & Zhang, Zhi-Hai, 2023. "Column-and-constraint-generation-based approach to a robust reverse logistic network design for bike sharing," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 90-118.
    3. Amiri, Ali, 2006. "Designing a distribution network in a supply chain system: Formulation and efficient solution procedure," European Journal of Operational Research, Elsevier, vol. 171(2), pages 567-576, June.
    4. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. Bahman Naderi & Kannan Govindan & Hamed Soleimani, 2020. "A Benders decomposition approach for a real case supply chain network design with capacity acquisition and transporter planning: wheat distribution network," Annals of Operations Research, Springer, vol. 291(1), pages 685-705, August.
    6. C. Archetti & R. Mansini & M. G. Speranza, 2005. "Complexity and Reducibility of the Skip Delivery Problem," Transportation Science, INFORMS, vol. 39(2), pages 182-187, May.
    7. F J Vasko & D D Newhart & K L Stott & F E Wolf, 2003. "A large-scale application of the partial coverage uncapacitated facility location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 11-20, January.
    8. Sheu, Jiuh Biing & Kundu, Tanmoy, 2018. "Forecasting time-varying logistics distribution flows in the One Belt-One Road strategic context," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 117(C), pages 5-22.
    9. Wasner, Michael & Zapfel, Gunther, 2004. "An integrated multi-depot hub-location vehicle routing model for network planning of parcel service," International Journal of Production Economics, Elsevier, vol. 90(3), pages 403-419, August.
    10. 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.

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