A simple and robust batch-ordering inventory policy under incomplete demand knowledge

Generally, the derivation of an inventory policy requires the knowledge of the underlying demand distribution. Unfortunately, in many settings demand is not completely observable in a direct way or inventory records may be inaccurate. A variety of factors, including the potential inaccuracy of inventory records, motivate managers to seek replenishment policies where the inventory is reviewed periodically and a fixed quantity Q is ordered once the inventory level is found to be under a certain point r. To apply such a policy, however, firms must derive the values r and Q without a clear understanding of the demand distribution. We develop estimators of the first two moments of the (periodic) demand by means of renewal theoretical concepts and a regression-based method, and use these estimators in conjunction with the Power Approximation (PA) method of Ehrhardt and Mosier (1984) to obtain an (r, Q) replenishment policy. The proposed methodology is robust and easy to code into a spreadsheet application. A series of numerical studies are carried out to evaluate the accuracy and precision of the estimators, and to investigate the impact of the estimation on the optimality of the inventory policies. Our experiments indicate that the proposed (r, Q) policy is very close, with regard to the expected total cost per period, to the (s, S) policy obtained via the PA method when the demand process is fully observable and inventory records are accurate.