Open AccessAn Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration
Author(s) -
Md. Azizul Baten,
Anton Abdulbasah Kamil
Publication year - 2009
Publication title -
journal of mathematics and statistics
Language(s) - English
Resource type - Journals
eISSN - 1558-6359
pISSN - 1549-3644
DOI - 10.3844/jmssp.2009.206.214
Subject(s) - weibull distribution , mathematics , production (economics) , mathematical optimization , statistics , macroeconomics , economics
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