Multi-objective capacitated location-routing problem: modelling and a simulated annealing heuristic

Location-routing problem (LRP) is established as a new research area in the context of location analysis that concerns simultaneously both the problems of location of facilities and routing of vehicles among the established facilities and the existing demand points. In this paper, we address the multi-objective capacitated LRP, which may arise in many practical contexts in logistics and supply chain management. We present a bi-objective mathematical programming formulations to model the problem. The first objective is to minimise the overall system-wide costs, while the second objective is to minimise the maximum of delivery times to the customers. To solve the developed model, a simulated annealing (SA) based heuristic is proposed and the efficiency of the proposed solution procedure is illustrated by applying it to a standard benchmark set from literature.