The Economic Lot and Delivery Scheduling Problem: Powers of Two Policies

We investigate the problem of simultaneously scheduling the final production line of a captive supplier and the delivery of components produced on that line to an assembly facility that uses these components at a constant rate. The supplier incurs a sequence-independent setup cost and/or setup time each time the production line is changed over from one component to another. On the other hand, setup costs and times for the assembly facility are negligible. We consider two types of delivery costs: a fixed charge for each delivery, and a fixed-charge-per-truck cost. We develop a heuristic procedure to find a cyclic production and delivery schedule with the power-of-two property. That is, in each cycle, each component is produced 2 (mu) times for some small integer (mu), where the value of (mu) may differ across components. In addition, several equally-spaced deliveries occur in each cycle, where the number of deliveries is equal to the least common multiple of the component production frequencies. The objective is to find the schedule that minimizes the average cost per unit time of transportation, inventory at both the supplier and the assembly facility, and setup costs at the supplier. Computational results suggest that the heuristic performs well in an absolute sense, and that significant savings can be achieved by using coordinated production and delivery schedules rather than approaches in which they are decided sequentially. The results also indicate that in many situations, pure just-in-time policies (in which production and delivery frequencies are equal) are far from optimal. Our model provides a basis for determining the type and extent of improvements needed in the quest for just-in-time.