1 Operations Research, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Management Engineering, Technical University of Denmark
This dissertation presents a number of algorithms for solving the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW is a generalization of the well known capacity constrained Vehicle Routing Problem (VRP). In the VRP a fleet of vehicles based at a central depot must service a set of customers. In the VRPTW each customer has a time window. Service of a customer must begin within the interval given by the time window. The objective is to minimize some aspect of operating costs (e.g. total distance traveled, number of vehicles needed or a combination of parameters). Since the late 80's and the beginning of the 90's optimal methods for the VRPTW have appeared in the literature. Methods have basicly been based on three approaches: dynamic programming, Lagrange relaxation and column generation (Dantzig-Wolfe). The most successful approaches rely on column generation. Good results have also been obtained using Lagrange relaxation. This dissertation is divided into three parts. First the theoretical framework is described. Thereafter a number of techniques to improve the performance of the column-generation framework are proposed and analyzed. Finally a parallel algorithm based on the sequential algorithm developed in the previous part of the dissertation is developed and analyzed.