Axle Weights in combined Vehicle Routing and Container Loading Problems

Overloaded axles not only lead to increased erosion on the road surface, but also to an increased braking distance and more serious accidents due to higher impact energy. Therefore, the load on axles should be already considered during the planning phase and thus before loading the truck in order to prevent overloading. Hereby, a detailed 2D or 3D planning of the vehicle cargo space is required. We model the Axle Weight Constraint for trucks with and without trailers based on the Science of Statics and provide flexible formulas for different axle configurations of trucks. We include the Axle Weight Constraint into the combined Vehicle Routing and Container Loading Problem ("2L-CVRP" and "3L-CVRP"). A hybrid heuristic approach is used where an outer Adaptive Large Neighbourhood Search tackles the routing problem and an inner Deepest-Bottom-Left-Fill algorithm solves the packing problem. Moreover, to ensure feasibility, we show that the Axle Weight Constraint must be checked after each placement of an item. The impact of the Axle Weight Constraint is also evaluated.