Study on split delivery open vehicle routing problem within two splits

Open vehicle routing problem (OVRP) is considered as a variant of vehicle routing problem (VRP), which has two hierarchical objectives, i.e., to minimize the number of routes, and to minimize the total cost measured by travel distances. Since the split delivery vehicle routing problem (SDVRP) has been studied extensively, and demonstrated that it can reduce the cost by at most 50% by allowing to split each delivery into different vehicles. In this work, we study how delivery split can impact on the solution to OVRP. Furthermore, considering that it is not quite practical for one customer to be visited more than twice in real-life cases, especially when delivery is quite small. Thus, we focus on the performance when each delivery is allowed to split into at most two pieces. In this study, firstly we propose a priori split strategy based on the first-fit decreasing heuristic, by which each delivery is split within two pieces in advance. Then, an improved iterated local search algorithm is applied to solve the transformed problem. Computational and comparative results of 42 benchmark instances conclude that splitting delivery within two splits indeed improve OVRP solutions in terms of both two objectives.