Locating service facilities whose reliability is distance dependent

We consider the problem where there is a probability, depending on the distance from the facility, that the facility may not be able to provide satisfactory service to a customer. This probability is equal to 0 at distance zero, and is a monotonically increasing function of the distance. We need to locate m facilities on a network such that the expected service level for all demand points combined, will be maximized. Alternatively, one can state the problem as minimizing the expected demand that will not get satisfactory service. The problem is formulated and properties of the solution are proved. Five metaheuristic algorithms are developed for its solution and are compared with computational results on a set of test problems.