Advances in Operations Research
Volume 2012 (2012), Article ID 490983, 11 pages
Research Article

Adaptive Control of a Reverse Logistic Inventory Model with Uncertain Deteriorations and Disposal Rates

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 31 October 2011; Revised 6 March 2012; Accepted 25 March 2012

Academic Editor: Chandal Nahak

Copyright © 2012 Ahmad Alshamrani. 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.


An adaptive control of a reverse logistic inventory system with unknown deterioration and disposal rates is considered. An adaptive control approach with a feedback is applied to track the inventory levels toward their goal levels. Also, the updating rules of both deterioration and disposal rates are derived from the conditions of asymptotic stability of the reference model. Important characteristics of the adaptive inventory system are discussed. The adaptive controlled system is modeled by a nonlinear system of differential equations. Finally, the numerical solution of the controlled system is discussed and displayed graphically.