Heuristic approaches for a vehicle routing problem with an incompatible loading constraint and splitting deliveries by order

The vehicle routing problem with an incompatible loading constraint and splitting deliveries by order is an extension of the well-known capacitated vehicle routing problem. Some orders cannot be transported alongside others due to some type of products in them or their special requirements on transportation condition. Additionally, splitting delivery by order is an effective method for enhancing vehicle efficiency since a customer might have many orders, and order is a set of compatible products. However, split delivery inevitably creates order receipt complexities and contributes to the significant complications of the problem in terms of formulating not only the model, but also the solution method. This study examines an innovative vehicle routing problem characterized by splitting deliveries by order, and addresses the inconvenience of order receipts and incompatibility among orders when fulfilling practical logistics requirements. We formulate this problem as an integer programming model, and the goal is to minimize the sum of routing cost and receipt cost. Then, two hybrid heuristic algorithms called MCWS-LS and S-ALNS are proposed to solve this problem. Furthermore, we conduct a series of experiments over existing vehicle routing problem instances, as well as analyze them under a realistic background to evaluate and demonstrate the effectiveness of the proposed model and algorithms.