Randomized local search for the discrete competitive facility location problem

Consider a finite set of consumers that two competing companies are willing to service. The companies open facilities one by one. The set of locations available to open facilities is finite. The problem is to find a facility location for the first company that maximizes its profit given that the second company also makes its decision by maximizing the profit. We propose a randomized local search scheme that employs an internal local search procedure to estimate the solutions being enumerated. Numerical experiments with random input data show that the scheme is able to find high quality approximate solutions for examples with dimension that has not been amenable to previously known algorithms.