Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 158193, 9 pages
Research Article

On the Optimality of (s,S) Inventory Policies: A Quasivariational Approach

Lakdere Benkherouf

Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 22 February 2008; Revised 9 June 2008; Accepted 17 July 2008

Academic Editor: Ho Lee

Copyright © 2008 Lakdere Benkherouf. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper revisits the classical discrete-time stationary inventory model. A new proof, based on the theory of quasivariational inequality (QVI), of the optimality of (s,S) policy is presented. This proof reveals a number of interesting properties of the optimal cost function. Further, the proof could be used as a tutorial for applications of QVI to inventory control.