The vehicle routing problem with time windows (VRPTW) is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest time and the latest time when the customer will permit the start of service. In this paper we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch and bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be very successful on a variety of practical size benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.