Scheduling and routing of vehicles: Fleet size Optimization

This work addresses the problem of finding the minimum number of vehicles required to service weekly a set of customers subject to time windows. The specific structure of the problem requires that a full loaded vehicle serve only one customer each time it leaves the depot. As a consequence, all feasible schedules involve the same total distance traveled. The fleet is homogeneous and is located in a common depot. Vehicle capacity is finite, weekly mileage is limited, and split service is not permitted. Four heuristics are developed to obtain feasible solutions. Results are reported for 1000 randomly generated problems with up to 150 deliveries. It is shown that the new heuristics outperform the actual algorithm used by the Transportation Company in terms of computation time and the quality of solution. To gauge the quality of the solutions, three lower bounding procedures are developed. The first considers the ?bin packing aspect of the problem? with regard to the maximum weekly mileage. The second exploits the time windows constraints while the third lowerbounding method uses a network flow formulation.