The Vehicle Routing Problem with Backhauls

The Vehicle Routing Problem with Backhauls is a pickup/delivery problem where on each route all deliveries must be made before any pickups. A two-phase solution methodology is proposed. In the first phase, a high quality initial feasible solution is generated based on spacefilling curves. In the second phase, this solution is improved based on optimization of the subproblems identified in a mathematical model of the problem. An extensive computational analysis of several initial solution algorithms is presented, which identifies the tradeoffs between solution quality and computational requirements. The class of greedy algorithms is capacity oriented, while K-media algorithms focus on distance. It is concluded that the greedy and K-median algorithms generate equivalent tour lengths, but that the greedy procedure reduces the required number of trucks and increases the truck utilization. The effect of exchange improvement procedures as well as optimal procedures on solution quality and run time is demonstrated. Comparisons with the Clark-Wright method adapted to backhauls are also given.