Journal of Probability and Statistics
Volume 2009 (2009), Article ID 370217, 23 pages
doi:10.1155/2009/370217
Research Article

Some Results on Bellman Equations of Optimal Production Control in a Stochastic Manufacturing System

Azizul Baten and Anton Abdulbasah Kamil

School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 19 September 2008; Revised 27 March 2009; Accepted 12 May 2009

Academic Editor: Nikolaos E. Limnios

Copyright © 2009 Azizul Baten and Anton Abdulbasah Kamil. 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

The paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in a manufacturing system with degenerate stochastic demand. We establish the existence of a unique solution of the Hamilton-Jacobi-Bellman (HJB) equations associated with this problem. The optimal control is given by a solution to the corresponding HJB equation.