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We study a joint facility location and cost planning problem in a competitivemarket under random utility maximization (RUM) models. The objective is tolocate new facilities and make decisions on the costs (or budgets) to spend onthe new facilities, aiming to maximize an expected captured customer demand,assuming that customers choose a facility among all available facilitiesaccording to a RUM model. We examine two RUM frameworks in the discrete choiceliterature, namely, the additive and multiplicative RUM. While the former hasbeen widely used in facility location problems, we are the first to explore thelatter in the context. We numerically show that the two RUM frameworks can wellapproximate each other in the context of the cost optimization problem. Inaddition, we show that, under the additive RUM framework, the resultant costoptimization problem becomes highly non-convex and may have several localoptima. In contrast, the use of the multiplicative RUM brings severaladvantages to the competitive facility location problem. For instance, the costoptimization problem under the multiplicative RUM can be solved efficiently bya general convex optimization solver or can be reformulated as a conicquadratic program and handled by a conic solver available in some off-the-shelfsolvers such as CPLEX or GUROBI. Furthermore, we consider a joint location andcost optimization problem under the multiplicative RUM and propose threeapproaches to solve the problem, namely, an equivalent conic reformulation, amulti-cut outer-approximation algorithm, and a local search heuristic. Weprovide numerical experiments based on synthetic instances of various sizes toevaluate the performances of the proposed algorithms in solving the costoptimization, and the joint location and cost optimization problems.

Joint Location and Cost Planning in Maximum Capture Facility Location under Multiplicative Random Utility Maximization