Facility Location with Price-Sensitive Demands: Private, Public, and Quasi-Public

We formulate a general model for an uncapacitated facility location problem in which demands are related to the prices established at the various locations. Pricing decisions and location decisions are determined simultaneously in this model, in contrast to traditional location models that assume fixed demands and prices. We show that a transformation of the general model is equivalent to the fixed-demand location model of Efroymson and Ray, and thus may be solved by any of the exact or heuristic methods available for that model.

Specifying either a private sector objective of maximizing profits or a public sector objective of maximizing net social benefits provides a particular case of the general model. A third plausible objective is the “quasi-public” one of maximizing net social benefits subject to a constraint that ensures sufficient revenues to cover costs. A Lagrangian relaxation of this constraint, which yields another case of the general model, is used to develop a solution procedure for the quasi-public objective. Details of the solution approach are given for quadratic revenue functions, and an example illustrates the procedure.