Vertical Stability Constraints in Combined Vehicle Routing and 3D Container Loading Problems

The vertical stability of the cargo is one of the most important loading constraints, since it ensures parcels from falling on the ground. However, frequently considered constraints either lead to unstable positions, are too restrictive or have high complexity. This paper focuses on the evaluation of different vertical stability constraints, analyses corner cases and introduces a new improved constraint. For the first time, constraints based on the science of statics are considered in the context of combined Capacitated Vehicle Routing Problem with Time Windows and 3D Loading (3L-VRPTW). All constraints are embedded in an established hybrid heuristic approach, where an outer Adaptive Large Neighbourhood Search tackles the routing problem and an inner Deepest-Bottom-Left-Fill algorithm solves the packing problem. For the computational tests, we use a well-known instance set enabling a comparison w.r.t. the number of customers, the number of items and the number of item types. Based on the impact on the objective values and on the performance, we give recommendations for future work.