Journal of Applied Mathematics and Stochastic Analysis
Volume 15 (2002), Issue 3, Pages 235-245

Filtering and predicting the cost of hidden perished items in an inventory model

Lakhdar Aggoun and Lakdere Benkherouf

Sultan Qaboos University, Department of Mathematics and Statistics, P.O. Box 36, Al-Khod 123, Oman

Received 1 August 2001; Revised 1 June 2002

Copyright © 2002 Lakhdar Aggoun and 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 is concerned with a discrete time, discrete state inventory model for items of changing quality. Items are assumed to be in one of a finite number, M, of quality classes that are ordered in such a way that Class 1 contains the best quality and the last class contains the pre-perishable quality. The changes of items' quality are dependent on the state of the ambient environment. Furthermore, at each epoch time, items of different classes may be sold or moved to a lower quality class or stay in the same class. These items are priced according to their quality, and costs are incurred as items lose quality. Based on observing the history of the inventory level and prices, we propose recursive estimators as well as predictors for the joint distribution of the accumulated losses and the state of the environment.