Simple Economic Order Quantity heuristics for stochastic inventory control

Abstract Accepted by: Phil Scarf Derived for deterministic demand, the Economic Order Quantity (EOQ) formula remains a popular method for stochastic demand, typically in combination with an order level. Textbooks split the inventory cost into the ‘cycle inventory’ cost (the cost of holding half the order quantity) and the cost of safety stock (order level minus expected lead time demand), showing that the EOQ minimizes the total cost of ordering and the cycle-inventory cost. However, under stochastic demand, the EOQ is smaller than the optimal order quantity and often much smaller. A number of authors have suggested exact procedures for determining the optimal order quantity (and order level), but the derivations (and resulting procedures) are complicated, in contrast with the intuitively appealing nature of EOQ and its simplicity. This paper presents an alternative approximation, leading to closed-form order quantity formulas under both a cost and service objective for normally distributed lead-time demand. It splits inventory costs, but (i) uses that the average cycle stock is less than half of the order quantity due to backorders, and (ii) considers inventory left-over at the end of a cycle instead of safety stock. A numerical investigation shows that the approximation is very accurate, with a cost error of 0.02% on average. For the traditional EOQ formula, the cost error is considerable, going up to 6% in some cases, and so it is worthwhile in many real-life situations to use our newly proposed formulas. Moreover, for teaching and training purposes, the adaptations help understand why the EOQ is suboptimal.