Branch and bound algorithm for a single vehicle routing problem with toll-by-weight scheme

Abstract

Most of previous studies on vehicle routing problems assume that traversal cost of each edge is simply equivalent to a constant number. Unfortunately, the models of this kind can not be applied in China because toll per kilometer of Chinese expressways varies with vehicle's weight. Motivated by rapidly increasing market of expressway transportation in China, we address a new and special vehicle routing problem that takes a single vehicle and its weight into account. To solve this problem practically, we provide a branch-and-bound algorithm with a well-designed lower bound. This algorithm can deal with any toll scheme in which toll per unit distance monotonically increases with weight. Computational results show that test instances with up to 42 vertices can be solved in reasonable computing time. © 2010 Springer-Verlag.