Scheduling periodical deliveries from a distribution centre to minimize the fleet size

This paper studies the delivery problem in which a distribution center delivers goods to customers periodically. Each customer has a specified delivery frequency. The deliveries to the same customer must be spaced over time as evenly as possible. The objective is to minimize the fleet size. We start from the special version with customers requiring the same delivery frequency, and propose a routing-then-scheduling approach: a routing problem for making one delivery to every customer is first solved and the resulting routes are then scheduled over the period. The study mainly focuses on the scheduling of the routes. Feasibility and optimality of the solution are analyzed. Based on the analysis, we develop a general integer programming model and a two-stage method for the problem with different delivery frequencies. Numerical experiments show that both methods solve the problem quickly. However, the delivery patterns generated by the two-stage models are more stable.