On milti-dimensional facility location problems

Abstract

The purpose of this is to develop efficient computational approaches for solving the facility location problems which encompass the implications of salient aspects of distribution systems - two-level facility location, multicommodity and multiperiod. First, a branch and bound algorithm is developed to solve a two-level facility location problem which may be also viewed as a generalized formulation of a multicommodity facility location problem. The algorithm is made efficient by employing a series of devices which exploit the supermodularity of the objective function. The efficiency of the algorithm is analyzed through computational experiments with some test problems. Secondly, a new dual-based solution procedure for the static facility location problem is proposed. Based upon the existing dual-based approach, the procedure is devised with the emphasis on the solution quality at the marginal increase of computational load. Its wide applicability to other location problems is briefly discussed. Finally, this dual-based approach is generalized to a dynamic context to solve a dynamic facility location problem. This generalization is based upon the fact that the dynamic facility location problem can be viewed as a special case of the static problem. Computational experience with static as well as dynamic test problems shows that the proposed dual-based procedure appears to be an attractive heuristic, given its empirical performance and its reasonable computational requirements.