Economical reorder quantities and reorder points with uncertain demand

Abstract The problem of determining reorder quantities and reorder points that minimize the total costs of carrying inventory, placing orders, and penalties for back orders, in the face of uncertain demand, is considered in this paper. By making approximations to the total cost function and the safety factor versus service function relationship, an economic order quantity is derived that depends on the uncertainty in the foiecast of demand during the lead time, but is independent of the back order cost. Reorder points are then determined for the case in which the back order cost is explicitly stated, and for the case in which the back order cost is unknown and the desired customer service is used as the controlling parameter. Simulations indicate that, when compared with use of the Wilson economic order quantity, the use of the formulae derived in this paper will lead to approximately a 5‐7‐percent reduction in the total cost.