The economic lot and delivery scheduling problem: models for nested schedules

We investigate the problem of simultaneously determining schedules for the production of several assembly components at a captive supplier and delivery of those components to the customer. We consider situations in which production economies of scale in the form of setup costs and/or setup times make it desirable for the supplier to produce in batches that are larger than the desired order quantity of the customer. The objective is to minimize the average cost per unit time of transportation, inventory at both the customer and the supplier, and, where applicable, setup costs.

We develop a heuristic solution procedure and a lower bounding approach for this problem. We also report experimental results that indicate that the heuristic provides solutions close to the lower bound in most instances. Our results provide a means to answer the often-asked question of whether just-in-time suppliers are (or should be) asked to hold inventory for their customers, and the question of how much setup costs and setup times need to be reduced so that the suppliers no longer need to hold that inventory.