A simulated annealing algorithm for solving multi-depot location routing problem with backhaul

This paper presents a method for solving a multi-depot location-routing problem with backhaul (MDLRPB). In the suggested problem, there are two subsets of customers including linehaul and backhaul customers. Linehaul customers require a delivery of stock from the depot, whereas backhaul customers need to deliver stock from their location to the depot. A mathematical model and a heuristic method based on the simulated annealing (SA) algorithm have been proposed for solving the problem. Test problems from the literature have been used for generating a new test problem for the MDLRPB problem. Computational results show that the CPU time for the SA is reasonable while this value for the LINGO increase dramatically in large size problems. In the worst case, the gap between objective function value of SA algorithm and optimal solution is equal 3%. The results indicate that suggested algorithm can reach the optimal or near optimal solution in small and medium size problems in a reasonable computational time.