New exact solution approaches for the split delivery vehicle routing problem

In this study, we propose exact solution methods for the split delivery vehicle routing problem (SDVRP). We first give a new vehicle-indexed flow formulation for the problem and then a relaxation obtained by aggregating the vehicle-indexed variables over all vehicles. This relaxation may have optimal solutions where several vehicles exchange loads at some customers. We cut off such solutions, in a nontraditional way, either by extending the formulation locally with vehicle-indexed variables or by node splitting. We compare these approaches using instances from the literature and new randomly generated instances. Additionally, we introduce two new extensions of the SDVRP by restricting the number of splits and by relaxing the depot return requirement and modify our algorithms to handle these extensions.