The splittable pickup and delivery problem with reloads

In this paper, we consider a variant of the pickup and delivery problem where any demand may be dropped off elsewhere than at its destination, picked up later by the same or another vehicle, and so on until it has reached its destination. We discuss the complexity of this problem and present two mixed-integer linear programming formulations based on a space-time graph. We describe some valid inequalities for the problem along with separation routines. Based on these results, we develop a branch-and-cut algorithm for the problem and present some computational results.