Title: Determining the location and capacity of competitive facilities

Authors: Ronald G. McGarvey, Tom M. Cavalier

Addresses: RAND, 1776 Main Street, Santa Monica, CA 90407, USA. ' The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, 310 Leonhard Building, University Park, PA 16801, USA

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.

Keywords: facilities location; competitive facilities; elastic demand; nonlinear programming; successive linear programming; facilities capacity; utility models.

DOI: 10.1504/IJMOR.2010.035495

International Journal of Mathematics in Operational Research, 2010 Vol.2 No.6, pp.694 - 723

Published online: 30 Sep 2010 *

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