Heuristic Solutions to the Facility Location Problem with General Bernoulli Demands

In this paper, a heuristic procedure is proposed for the facility location problem with general Bernoulli demands. This is a discrete facility location problem with stochastic demands that can be formulated as a two-stage stochastic program with recourse. In particular, facility locations and customer assignments must be decided here and now, i.e., before knowing the customers who will actually require to be served. In a second stage, service decisions are made according to the actual requests. The heuristic proposed consists of a greedy randomized adaptive search procedure followed by a path relinking. The heterogeneous Bernoulli demands make prohibitive the computational effort for evaluating feasible solutions. Thus the expected cost of a feasible solution is simulated when necessary. The results of extensive computational tests performed for evaluating the quality of the heuristic are reported, showing that high-quality feasible solutions can be obtained for the problem in fairly small computational times.