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
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.
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.