Journal of Mathematics and Statistics

An Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration

Md. Azizul Baten and Anton Abdulbasah Kamil

DOI : 10.3844/jmssp.2009.206.214

Journal of Mathematics and Statistics

Volume 5, Issue 3

Pages 206-214

Abstract

Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items. Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem. Results: It was then illustrated with the help of an example. By the principle of optimality we also established the Riccati based solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with this control problem. Conclusion: As an application to quadratic control theory we showed an optimal control policy to exist from the optimality conditions in the HJB equation.

Copyright

© 2009 Md. Azizul Baten and Anton Abdulbasah Kamil. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.