Using Geo-statistical Methods to Decide an Additional Facility Location

In this paper, we propose an approach for locating an additional facility—to add to a chain of existing facilities—based on geo-statistical methods. This approach does not make assumptions on customer demand behavior with respect to distance from the nearest facility (as is commonly made in location models) but rather implicitly takes into account intrinsic factors. The goal is to maximize the probability of a randomly chosen customer visiting the chain. Our model is derived from the adaptive spatial sampling problem in geo-statistics. We present a case study for a cellular application to illustrate the behavior of the non-linear objective function. Two versions, based respectively on discrete and continuous optimization techniques, are presented. A Simulated Annealing heuristic is developed to solve the discrete version whereas a special heuristic called Geometric Search is proposed to solve the continuous version. Results show that both of these heuristics perform remarkably well considering the fact that the objective function is highly non-linear and complex (non-differentiable; discontinuous). Geometric Search reports optimal solutions in all the instances tested. Our empirical investigation reveals that the continuous version cannot be solved efficiently by using a discrete modeling approximation. Subject Classifications: Location Models, Correlation, Estimation, Sampling.