Journal of Applied Mathematics and Stochastic Analysis 
Volume 14 (2001), Issue 4, Pages 317-328
doi:10.1155/S1048953301000284

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

Abstract

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.