Determining the location and capacity of competitive facilities

Abstract

This paper examines a competitive facility location problem in which the objective is to increase market capture subject to an expansion budget. This is accomplished by determining both the locations for a set of new facilities and the capacities of new and existing facilities. A gravity-based elastic-demand utility model is presented, in which the capacity of a facility serves as its measure of attractiveness. An examination of problem characteristics suggests that the model be divided into two subproblems. The first subproblem identifies locations for new facilities, and is solved using a penalty function formulation with fixed-point iteration. The second subproblem determines facility capacities and it is solved using a Successive Linear Programming algorithm. The interfacing of the two subproblem procedures into an iterative algorithm for solution of the overall problem is discussed. Computational testing shows the iterative algorithm to be superior to a general-purpose non-linear solver.