Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables

Abstract

In this note, we consider a variation of the economic order quantity (EOQ) model where cumulative holding cost is a nonlinear function of time. This problem has been studied by Weiss [Weiss, H., 1982. Economic order quantity models with nonlinear holding costs. European Journal of Operational Research 9, 56–60], and we here show how it is an approximation of the optimal order quantity for perishable goods, such as milk, and produce, sold in small to medium size grocery stores where there are delivery surcharges due to infrequent ordering, and managers frequently utilize markdowns to stabilize demand as the product’s expiration date nears. We show how the holding cost curve parameters can be estimated via a regression approach from the product’s usual holding cost (storage plus capital costs), lifetime, and markdown policy. We show in a numerical study that the model provides significant improvement in cost vis-à-vis the classic EOQ model, with a median improvement of 40%. This improvement is more significant for higher daily demand rate, lower holding cost, shorter lifetime, and a markdown policy with steeper discounts.