A comparison of different methods for estimating the average inventory level in a (Q,R) system with backorders

Abstract In a continuous-review order-quantity-reorder-point inventory system with backordering, the most common approximation to the average inventory level is Hadley–Whitin's expression ( 1 2 Q +safety stock), where Q is the order quantity. In the literature it has been indicated that this approximation depends on the assumption of negligible stockout probability; for situations in which this assumption is violated, various alternative approximation expressions have been developed. This study shows that: (i) Hadley–Whitin's expression is more robust than the literature appears to imply; (ii) the currently available alternatives are not sufficiently accurate to take over when the Hadley–Whitin approximation's accuracy begins to deteriorate due to increasing stockout probability. A simpler and more accurate alternative approximate expression is then presented, and its applications are illustrated.