Effects of discounting and demand rate variability on the Economic Order Quantity

The Economic Order Quantity (EOQ) formula is probably the most well-known formula in inventory theory. It determines the optimal value of the ordering quantity by minimizing the average cost in an ordering cycle. It is based on the assumptions that there is a fixed lead time and a constant demand rate. These assumptions are usually not fulfilled in practice. Especially when dealing with slow-moving items, demand seems to fluctuate. Furthermore, since the time between two successive orderings is often large for slow moving items, discounted costs instead of average costs should be minimized. In this paper we determine the optimal ordering quantity if demand is modelled by a Poisson process and the expected discounted costs are minimized. We also analyze the case where demand is uniform and/or the average cost criterion is used. We give graphical presentations of the optimal ordering quantities. Besides easily determining the optimal values, these allow us to show what the effects of changing the objective function and of changing the demand distribution are. We derive a simple (discounted cost) ordering quantity formula, denoted by EOQd, for slow moving items. We show that for items with a small demand rate and high fixed ordering costs the EOQd is much closer to the optimal (discounted cost) ordering quantity than the traditional EOQ-formula.