An exact algorithm for the vehicle routing problem with backhauls

Abstract

We consider the Vehicle Routing Problem with Backhauls, in which a eet of vehicles located at a central depot is to be used to serve a set of customers partitioned into two subsets of linehaul and backhaul customers. The ob jective of the problem is to minimize the total distance traveled by the entire eet. The problem is known to be N P-hard in the strongest sense and nds many practical applications in distribution planning. We present an exact algorithm for the Asymmetric Vehicle Routing Problem with Backhauls based on solving a relaxation of the problem. In a cutting plane fashion, the algorithm iteratively solves the relaxation while at each iteration, infeasible solutions are identi ed and seperated from the feasible set of the relaxation. The procedures to identify infeasible solutions are presented, and a set of cuts to eliminate these solutions is proposed. Local search procedures are incorporated to improve the algorithm. Computational tests on randomly generated instances, involving up to 90 customers, are given. The results show the e ectiveness of the proposed approach.