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 such as retail, 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 retailers to seek replenishment policies with a fixed order quantity. We derive estimators of the first two moments of the (periodic) demand by means of renewal theoretical concepts. We then propose a regressionbased approximation to improve the quality of the estimators. These estimators are used 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 mean total cost per period, to the (s, S) policy obtained via the PA method when the demand process is fully observable.