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The Uncapacitated Facility Location Problem with Client Matching

SMG and ISRO, Université Libre de Bruxelles, Boulevard du Triomphe, CP210/01, B-1050 Brussels, Belgium
SMG and ISRO, Université Libre de Bruxelles, Boulevard du Triomphe, CP210/01, B-1050 Brussels, Belgium
Centre de Recherche sur les Transports, Université de Montréal, Case Postale 6128, Succursale "Centre-ville," Montreal, Canada H3C 3J7
eric.gourdin{at}francetelecom.fr
mlabbe{at}crt.umontreal.ca
gilbert{at}crt.umontreal.ca

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.

Subject classifications: Facilities, location, discrete: client matching; Transportation, vehicle routing: depot location; Programming, integer, branch and cut; Algorithms, cutting plane, facet generation.
History: Received November 1997; revision received November 1998; revision received January 1999; accepted February 1999.

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