Heuristics for vehicle routing problems with backhauls, time windows, and 3D loading constraints

In this paper, we consider vehicle routing problems with backhauls and time windows (VRPBTW). Different backhaul variants are studied, namely clustered backhauls (CB), mixed linehauls and backhauls, and variants with simultaneous delivery and pickup and with divisible delivery and pickup. Three dimensional loading constraints are assumed. A two-phase approach following the principle packing first, routing second is proposed. In the first phase, the packing of goods is carried out by solving a 3D strip packing problem for each customer using tabu search. The resulting VRPTW instance is solved in the second phase using first a multi-start evolutionary strategy to minimize the number of vehicles while again tabu search is applied to minimize the total travel distance. We show that the various backhaul types can be incorporated into this framework. For the backhaul variants different from CB, unloading and reloading efforts are taken into account. Moreover, side loading and a separation of the loading space into separate compartments for goods of linehaul and backhaul customers are proposed. Computational results for benchmark instances and new randomly generated problem instances are presented that demonstrate that the heuristics determine high-quality solutions in a short amount of computing time. The unloading and reloading strategies outperform the strategies based on two separate compartments.