Modeling and solving vehicle routing problems with many available vehicle types

Abstract

Abstract In this thesis, models have been formulated and mathematical optimization methods developed for the heterogeneous vehicle routing problem with a very large set of available vehicle types, called many-hVRP. This is an extension of the standard heterogeneous vehicle routing problem (hVRP), in which typically fairly small sets of vehicle types are considered. Two mathematical models based on standard models for the hVRP have been formulated for the many-hVRP. Column generation and dynamic programming have been applied to both these models, following a successful algorithm for the hVRP. Benders' decomposition algorithm has also been applied to one of the models. In addition to the standard cost structure, where the cost of a pair of a vehicle and a route is determined by the length of the route and the vehicle type, we have studied costs that depend also on the load of the vehicle along the route. These load dependent costs were easily incorporated into the models, and other extensions could be similarly incorporated. By using a standard set of test instances (with between three and six vehicle types in each instance) we have been able to compare our implementation with published results for hVRP. For many-hVRP, we have extended these instances to include larger sets of vehicle types (with between 91 and 381 vehicle types in each instance). The results show that the algorithms implemented for the two models nd optimal solutions in a similar amount of time, but Benders' algorithm at times takes much longer to verify optimality. However, some other properties of Benders' algorithm suggests that it may constitute a good basis for a heuristic, when instances with even larger sets of vehicle types are used.