Integrating axle weight restrictions in a two-dimensional vehicle routing problem with sequence based loading

Abstract

A mixed integer linear programming model for a two-dimensional capacitated vehicle routing problem (2L-CVRP) with sequence based loading and axle weight restrictions is provided. To the authors’ knowledge, it is the first time that axle weight restrictions are incorporated in a VRP. Axle weight limits impose a great challenge for transportation companies. Trucks with overloaded axles represent a significant threat for traffic safety and may cause serious damage to the road surface. Transporters face high fines when violating these limits. The problem is based on a real-world problem from a Belgian logistics service provider. The demand of the customers consists of europallets. Pallets can be placed in two horizontal rows inside the vehicle. No vertical stacking is allowed. The center of gravity of the pallets inside the vehicle is calculated to determine the axle weights. Results of the model are compared to results of a 2L-CVRP with sequence based loading without axle weight restrictions. Numerical experiments demonstrate that the model performs adequately and that the integration of axle weight constraints in vehicle routing models is necessary for a feasible route planning.