A unified heuristic for a large class of Vehicle Routing Problems with Backhauls

The Vehicle Routing Problem with Backhauls is a generalization of the ordinary capacitated vehicle routing problem where goods are delivered from the depot to the linehaul customers, and additional goods are brought back to the depot from the backhaul customers. Numerous ways of modeling the backhaul constraints have been proposed in the literature, each imposing different restrictions on the handling of backhaul customers. A survey of these models is presented, and a unified model is developed that is capable of handling most variants of the problem from the literature. The unified model can be seen as a Rich Pickup and Delivery Problem with Time Windows, which can be solved through an improved version of the large neighborhood search heuristic proposed by Ropke and Pisinger. The results obtained in this way are comparable to or improve on similar results found by state of the art heuristics for the various variants of the problem. The heuristic has been tested on 338 problems from the literature and it has improved the best known solution for 227 of these. An additional benefit of the unified modeling and solution method is that it allows the dispatcher to mix various variants of the Vehicle Routing Problem with Backhauls for the individual customers or vehicles.