A modification to the holding cost expression in the case of constant lead times and stochastic demands

In this note the authors examine a reorder point inventory system with constant lead times and stochastic demands. In the standard approach, the holding cost expression used is an overestimate because when shortages occur, holding costs are computed even though there is no safety stock on hand in such situations. The authors derive the expression for this overestimation and the size of this overestimation is numerically investigated for various demand distributions and different probabilities of stockout.