A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints

This paper deals with a special vehicle routing problem with backhauls where customers may want to receive items from a depot and, at the same time, return 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 consists of transporting delivery and pickup items simultaneously on the same vehicle. In order to avoid any reloading effort during a tour, we consider two different approaches for loading the vehicles: (i) loading from the back with separation of the loading space into a delivery section and a pickup section and (ii) loading from 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.