Balancing capacity and lot sizes

In many companies there is an on-going discussion about capacity, capacity utilization and capital tied up in inventories. However, traditional models such as the EOQ model only include capacity considerations in the set-up cost, or in the cost of a replenishment order. This implies e.g. that they do not consider the set-up time as a capacity constraint. Furthermore, in these models the set-up cost is usually treated as a constant, even though the opportunity cost for capacity in general is dependent upon the capacity utilization.The purpose of this paper is to derive an analytical model for the balancing of capacity and lot sizes. The model includes costs for capacity, work-in-process (queueing, set-up, and processing time), and finished goods inventory. The total costs are minimized with respect to capacity. Then, the corresponding, recommended lot sizes are determined. The model was tested with data from a Swedish manufacturing company. The results turned out to coincide with experiences of the company in many important respects. The model offers production management an opportunity to discuss the relationship between capacity, work-in-process, and lot sizes.