Solving a stochastic facility location/fleet management problem with logic-based Benders' decomposition

This article addresses a stochastic facility location and vehicle assignment problem in which customers are served by full return trips. The problem consists of simultaneously locating a set of facilities, determining the vehicle fleet size at each facility, and allocating customers to facilities and vehicles in the presence of random travel times. Such travel times can arise, for example, due to daily traffic patterns or weather-related disturbances. These various travel time conditions are considered as different scenarios with known probabilities. A stochastic programming with bounded penalties model is presented for the problem. In order to solve the problem, integer programming and two-level and three-level logic-based Benders' decomposition models are proposed. Computational experiments demonstrate that the Benders' models were able to substantially outperform the integer programming model in terms of both finding and verifying the optimal solution.