||In this thesis, we study the problem in which a distribution center delivers goods to a fixed set of customers periodically. Each customer has a specified delivery frequency (the number of deliveries over a T-day period). The deliveries to the same customer are required to be spaced as evenly as possible while the actual delivery days are flexible. We propose a routing then scheduling approach to solve the problem of minimizing the fleet size. In this approach, a routing problem for making one delivery to every customer is solved first. Then these routes are scheduled over the T days based on the delivery frequency. For the problem with the same delivery frequency, a simple and effective scheduling algorithm is developed and its performance is analysed theoretically. Then a modified scheduling algorithm is proposed to generate alternative feasible solutions with the same fleet size. This modified algorithm lays the foundation for the algorithm dealing with the problem with different delivery frequencies. For the problem with different delivery frequencies, the customers with the same delivery frequency are grouped first and the optimal routes are found for each group. An Integer programming model is then given to combine the schedules of all the groups. Finally heuristics are developed to solve the problem efficiently. Delivery days for different delivery frequencies need to be well coordinated taking the flexibility in the schedule of each frequency. Our heuristic takes a dynamic pattern generation approach (sequentially determining the cluster size of delivery days for each delivery frequency) and employs a number of different coordination algorithms. Extensive computational experiments are carried out demonstrating that the average performance of the heuristics is very good. With the assumption that customers with different delivery frequencies do not appear in the same delivery route, the computational results show that the difference between the fleet size determined by the heuristics and the lower bound is one when T<60, and the difference is two when 60≤T≤360.