Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 4, Pages 317-328

A stochastic inventory model with stock dependent demand items

Lakdere Benkherouf, Amin Boumenir, and Lakhdar Aggoun

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

Received 1 April 2000; Revised 1 December 2000

Copyright © 2001 Lakdere Benkherouf et al. 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.


In this paper, we propose a new continuous time stochastic inventory model for stock dependent demand items. We then formulate the problem of finding the optimal replenishment schedule that minimizes the total expected discounted costs over an infinite horizon as a Quasi-Variational Inequality (QVI) problem. The QVI is shown to have a unique solution under some conditions.