Modeling and solving the bi-objective capacitated location-routing problem with probabilistic travel times

The location-routing problem (LRP) is a relatively new research area within location analysis that concerns simultaneously both the problems of location of facilities and routing of vehicles among the established facilities and the demand points. In this work, we address the capacitated LRP with probabilistic travel times, which may arise in many practical contexts in logistics and supply chain management, and present some bi-objective mathematical programming formulations to model the problem using different stochastic programming approaches. The first objective is to minimize the overall system-wide costs, while the second objective concerns minimization of the maximum delivery time to the customers. In all the cases, the deterministic equivalents of the stochastic models have been extracted. To solve the resulted models, a variable neighborhood descent-based heuristic is proposed and finally computational study is performed and numerical results are reported.