A Shortest Path Approach to the Multiple-Vehicle Routing Problem with Split Pick-Ups

We examine a multiple-vehicle routing problem that permits split pick-ups (mVRPSP). This problem involves a fleet of trucks having identical capacity, multiple suppliers, and a single assembly plant. The fleet is responsible for moving parts from the suppliers to the assembly plant. The problem is to determine, for each truck, how many parts to pick up at each supplier to then transport to the assembly plant. The objective is to minimize the total transportation cost for the fleet. The cost depends on the number of trucks used and their routes but not the number of parts transported. The mVRPSP differs from the typical multiple vehicle routing problem in that any supplier may have its parts picked up by more than one truck. We formulate the mVRPSP as a dynamic program (DP) having uncountably infinite state and action spaces. We then show that this DP is equivalent to a finite action DP that has a finite state space for any given initial condition. A best-first shortest path search procedure is used to solve the equivalent DP. We show that this approach requires significantly less computational time than two mixed integer programs (MIPs) and that this approach can solve significantly larger mVRPSP’s than can be solved using the MIPs.