The ship routing problem with backhaul and time windows: Formulation and a heuristic approach

The ship routing problem with backhauls and time windows (SRPBTW) is an extension of the classical vehicle routing problem with backhauls and time windows (VRPBTW). The VRPBTW includes both a set of customers to whom products are to be delivered from a depot, and a set of suppliers whose products need to be picked up and transported back to the depot, in which it is traditionally assumed that on each route all deliveries have to be made before any goods can be picked up to avoid rearranging the loads on the vehicle. Such a limitation can be relaxed for the SRPBTW. This paper formulates SRPBTW as MIP and proposes a variable neighbor search (VNS) algorithm for it. Numerical experiments indicate the proposed method is effective in reducing the total shipping cost.