The economic lot and delivery scheduling problem: The single item case

The authors have studied the problem of determining the frequency of production of a single component and the frequency of delivery of that component to a customer which uses this component at a constant rate. The objective is to minimize the average cost per unit time of production setup costs, inventory holding costs at both the supplier and the customer, and transportation costs. The model allows positive production setup times. The authors prove that the ratio between the production interval and delivery interval must be an integer in an optimal solution. This provides the basis for a very simple, optimal solution procedure. The authors use these results to characterize situations in which it is optimal to have synchronized production and delivery, and discuss the ramifications of these conditions on strategies for setup time reductions.