Suchergebnisse

In this paper, a variant of the vehicle routing problem with mixed backhauls (VRPMB) is presented, i.e. goods have to be delivered from a central depot to linehaul customers, and, at the same time, goods have to be picked up from backhaul customers and brought to the depot. Both types of customers can be visited in mixed sequences. The goods to be delivered or picked up are three-dimensional (cuboid) items. Hence, in addition to a routing plan, a feasible packing plan for each tour has to be provided considering a number of loading constraints. The resulting problem is the vehicle routing problem with three-dimensional loading constraints and mixed backhauls (3L-VRPMB). The simultaneous transport of linehaul and backhaul items presents a particular challenge of the problem. We consider two different loading variants in order to avoid any reloading during the tour: (i) rear loading with separate linehaul and backhaul sections and (ii) loading at a long side. In order to solve the problem, we propose a hybrid metaheuristic consisting of a reactive tabu search for the routing problem and different packing heuristics for the loading problem. Numerical experiments are reported with benchmark instances from the literature for the one-dimensional VRPMB to examine the performance of the routing algorithm and with newly generated instances for the 3L-VRPMB.

Abstract: This paper deals with a special vehicle routing problem with backhauls where each customer receives items from a depot and, at the same time, returns items back to the depot. Moreover, time windows are assumed and three-dimensional loading constraints are to be observed, i.e. the items are three-dimensional boxes and packing constraints, e.g. regarding load stability, are to be met. The resulting problem is the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), time windows, and three-dimensional loading constraints (3L-VRPSDPTW). This problem occurs, for example, if retail stores are supplied by a central warehouse and wish to return packaging material. A particular challenge of the problem is to transport delivery and pickup items simultaneously on the same vehicle. In order to avoid any reloading effort during a tour, we consider two different loading approaches of vehicles: (i) loading from the back side with separation of the loading space into a delivery section and a pickup section and (ii) loading at the long side. A hybrid algorithm is proposed for the 3L-VRPSDPTW consisting of an adaptive large neighbourhood search for the routing and different packing heuristics for the loading part of the problem. Extensive numerical experiments are conducted with VRPSDP instances from the literature and newly generated instances for the 3L- VRPSDPTW.