Reactive Tabu Search and Variable Neighbourhood Descent Applied to the Vehicle Routing Problem with Backhauls

We are in the presence of the VRP with backhauls, also known as the linehaul-backhaul problem, when the vehicles are not only required to deliver goods to customers, but also to pick up goods at customers locations. An example of this partition of the set of customers could be the grocery industry. The supermarkets and shops are the linehaul customers and the grocery suppliers are the backhaul customers. The VRPB has the same constraints of the VRP, with the additional constraint that, on each route, the backhaul customers, if any, are visited after all linehaul customers. The reason for this precedence constraint is that it may be difficult to re-arrange the load on the vehicle, when goods for delivery and pick up exist. Furthermore, accepting pick ups before finishing all deliveries results in a fluctuating load and this may overload the vehicle, breaking the legal rules. This type of procedure is also motivated by the fact that, in practical applications, linehaul customers have higher priority.