Min-Coverage Competitive Facility Location Under Random Utilities

This work concerns a facility location problem in a competitive market where customer demand is modeled and predicted by a random utility maximization model. We study a variant where, instead of maximizing a capture demand objective function as in prior work, we aim to minimize the opening cost of the new facilities while ensuring that the overall demand achieved is at least a certain proportion of the competitor's captured demand. To solve the proposed problem, we leverage some important properties of the capture demand function, such as submodularity and convexity, to propose three solution methods, namely, a poly-time local search heuristic algorithm with guaran-tees, a mixed-integer linear program (MILP) reformulation that allows the problem to be solved exactly by an off-the-shelf solver, and a cutting plane method. Experiments based on generated instances of various sizes show the efficiency of our proposed solution methods, especially the cutting plane approach, in solving large-scale instances.