A Dual-Based Algorithm for Multiproduct Uncapacitated Facility Location

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.