Optimizing pricing and location decisions for competitive service facilities charging uniform price

Abstract

In this paper, we present the problem of optimizing the location and pricing for a set of new service facilities entering a competitive marketplace. We assume that the new facilities must charge the same (uniform) price and the objective is to optimize the overall profit for the new facilities. Demand for service is assumed to be concentrated at discrete demand points (customer markets); customers in each market patronize the facility providing the highest utility. Customer demand function is assumed to be elastic; the demand is affected by the price, facility attractiveness, and the travel cost for the highest-utility facility. We provide both structural and algorithmic results, as well as some managerial insights for this problem. We show that the optimal price can be selected from a certain finite set of values that can be computed in advance; this fact is used to develop an efficient mathematical programming formulation for our model.

Keywords:

• competitive location models
• capacity planning
• pricing
• non-linear integer programming
• approximation

Acknowledgements

The authors would like to thank two anonymous referees for valuable suggestions that have resulted in many improvements in the paper. The research of the second and third authors was supported by their NSERC grants.