On determining the location and capacity of competitive facilities

Facilities play an important role in an organization's success in a competitive business environment. This study examines a competitive facility problem in which a firm has procured an expansion budget, to be used to increase the market capture across all of its facilities. This is to be accomplished through a combination of improvements to pre-existing facilities and new facility construction. The firm must select the locations for a set of new facilities and the capacity for each of its facilities. A new gravity-based utility model is developed, and is generalized to include elastic demand. Various constraints are introduced, including facility capacity, forbidden regions for new facility location and a budgetary limit on expenditures.;A mathematical model is presented and problem characteristics are examined, which suggest that this model be divided into two subproblems. The first subproblem examines locations for the new facilities. Two solution algorithms are devised, one based on branch-and-bound methods and the other based on a penalty function formulation using fixed-point iteration. Computational testing is presented, comparing these two algorithms along with the general-purpose nonlinear solver GAMS/MINOS. The second subproblem determines the capacity for each facility. An examination of this subproblem suggests that a successive linear programming algorithm be implemented. Computational testing for this algorithm is presented, comparing it to GAMS/MINOS. The interfacing of the two subproblem solution procedures into an iterative algorithm to solve the overall problem is discussed. Computational testing versus GAMS/MINOS shows the iterative algorithm to be superior. Potential extensions to future research are offered.