A dimensional analysis approach to approximate inventory policies

Abstract

A number of exact algorithms for finding optimal (s,S) inventory policies have been developed, e.g. Veinott and Wagner [5] and Federgruen Zipkin [6], but their heavy requirement for computer resources considerably reduces their practical applications. It is desirable, therefore, to find algorithms generating (s,S) policies as close as possible to the optimal ones within reasonable computer time. Ehrhardt [1], Porteus [3] and Mabin [11] have studied such approximation methods. This thesis presents the dimensional approach for finding approximate (s,S) inventory policies. The dimensional analysis approach is described in the context of Operations Research and Inventory theory. Some of the previous approaches for finding approximate (s,S) policies are studied from the dimensional viewpoint. The general form of the required models are found. Using this form a regression in powers of dimensionless parameters is fitted to D(=S-s). A refited form of Ehrhardt [2] approximation for s was used with the predicted value of D to get the complete (s,S) policies. A reasonably good fit for D and an excellent fit for s are found. Examination of residuals of the approximate dimensional model predicted from the optimal policies and a comparision of the total cost rates showed that the Dimensional model is marginally better than Ehrhardt's using his data set.