A Simulation Approach for Competitive Facility Location with Random Utility Maximizing Customers

Abstract

The competitive facility location problem formalizes the managerial problem faced by a firm that enters a market already occupied by competitors in which customers are assumed to choose the facility that maximizes their utility. Given a discrete choice model that expresses the probability for a customer to select each location as a function of its attributes, and given the distribution of these attributes in the population, the objective is to identify facility locations that maximize the expected market share captured by the firm.We present a simulation approach for solving this problem with any discrete choice model. Our method exploits the fact that it is possible to aggregate customers to reduce the dimension of the optimization problem without affecting its optimal solution. Our experiments indicate that solving the resulting 0-1 linear program produces high quality solutions for problems based on the mixed multinomial logit model more efficiently than existing methods.In many cases, our approach also leads to near-optimal solutions for large-scale instances based on the multinomial logit model in a fraction of the computing time required by the state-of-the-art exact method from the literature. To interpret these results, we introduce an entropy measure to characterize the properties that influence the performance of our method on different types of instances. We finally propose potential uses of this novel information-theoretic perspective in the broader context of optimization problems based on random utility maximization models.