A Multi Service Capacitated Facility Location Problem with Stochastic Demand

This paper considers the problem of identifying optimal locations for wireless service installations in smart cities. The problem is modelled as a facility location problem with multiple service types, known as the Multi Service Facility Location Problem (MSCFLP). Given a set of potential facility locations and demand point data, the goal is to identify at which locations the facilities should be opened, and which demand points should be serviced by each open facility in order to minimise costs. In this study, the demand quantities at each demand point are assumed to follow a probability distribution. An adaptive neighbourhood search heuristic is proposed in order to find a good solution to the problem, where the stochastic demand was translated to a deterministic capacity constraint. The heuristic iteratively improves the service allocations in sub-regions of the problem instances, starting from an initial feasible solution. The results show that the heuristic is able to find good solutions within very short time. Furthermore, we assessed the handling of the stochasticity by the model. Its performance is assessed by means of simulation, and results show that this approach works well in various scenarios of traffic models.