1992 Volume 1992 Issue 1 Pages 39-51
The vehicle routing problem with backhauls (VRPB) can be stated as follows : Find a minimum distance route for a vehicle that services the delivery and backhaul (pick-up) customers without violating the vehicle capacity constraint. In contrast to its practical importance very limited papers have been presented for this problem. The objective of this study is to shed a theoretical light to this problem. First we derive an asymptotic formula for the VRPB assuming that all nodes (customers) are distributed on the Euclidean plane using a simple heuristic based on partition of the region. Then we analyze a probabilistic variation of the VRPB and derive a formula that gives the expected travel distance of daily vehicle routes.
