Optimization based models and algorithms for routing and scheduling with time window constraints: Koskosidis, Ioannis Alkiviadis, Ph.D. Princeton University, 1988, 282pp.

Abstract

In this dissertation we deal with the development of models and algorithms for the Vehicle Routing Problem with Time Window Constraints based on a new class of algorithms, named global optimization based heuristics. The intrinsic difficulty of routing problems has prevented exact optimization algorithms from solving realistic size problems and thereby, heuristic algorithms have been the only alternative. Optimization based heuristics stand between the two extremes providing good quality solutions within reasonable computational requirements. This research has been the first effort to develop and apply global optimization heuristic algorithms to the time window constrained VRP. First we develop a new relaxation based formulation for the VRP with time windows, which treats the time windows as soft constraints allowing their violation at a cost. The result is a more flexible model (compared to hard constraints models) which is less likely to get caught into local optima. Next we decompose the problem into a clustering component and a routing and scheduling component. In the clustering phase customers are partitioned into groups and a vehicle is assigned to service each group. In the routing and scheduling phase we seek for the optimal routing of vehicles. Due to the complexity of the objective function of the problem the partitioning of customers is based on approximate clustering cost coefficients. An iterative scheme between the clustering phase and the routing and scheduling phase is employed to sharpen the approximation. Computational tests using randomly generated problems and benchmark problems have shown the superiority of the optimization based heuristic compared to local improvement heuristics. Furthermore, we have studied and developed algorithms for the Capacitated Clustering Problem and the Traveling Salesman Problem with Soft Time Windows, which are the two prevailing components of the routing and scheduling problem. As a final step, we used the global optimization heuristic to solve routing and scheduling problems phased by a major manufacturer. Compared to the routing schedules implemented in the field, the model has been found capable to provide significant support to the company's distribution management in a tactical, strategic and even operational level.