A Dual-Based Algorithm for Multiproduct Uncapacitated Facility Location

• Published in: Transportation science Vol. 21; no. 3; pp. 198 - 206
• Main Authors: Klincewicz, John G, Luss, Hanan
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.08.1987; Transportation Science Section of the Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Capital costs; Cost allocation; Exact sciences and technology; Fixed costs; Ground, air and sea transportation, marine construction; Heuristics; Linear programming; Marketing strategies; Minimization of cost; Optimal solutions; Warehouses; Costs; User; Transportation; Heuristic method; Facility; Localization; Algorithm
• ISSN: 0041-1655; 1526-5447
• DOI: 10.1287/trsc.21.3.198

The multiproduct uncapacitated facility location problem (MUFLP) is a generalization of the classic uncapacitated facility location problem (UFLP). In MUFLP, different products are required by the customers. In addition to the fixed cost for opening a facility, there is an added fixed cost for handling a particular product. Assignment costs are incurred for satisfying a customer's requirement for each of the separate products. The objective is to minimize the total fixed costs plus assignment costs subject to satisfying all customer requirements. We propose a new dual-based algorithm for MUFLP that extends previous work for UFLP that has proved so successful. Dual ascent and dual adjustment procedures generate a good feasible solution to the dual of the linear programming relaxation of MUFLP. A feasible primal solution to MUFLP can then be constructed based on this dual solution. Like the analogous procedures for UFLP, these procedures can be used either as a stand-alone heuristic or, else, they can be incorporated into a branch-and-bound algorithm. Computational experience is given for both randomly generated and nonrandom problems with quite favorable results.