An optimal control approach to inventory-production systems with Weibull distributed deterioration

Baten M. A., KAMIL A. A.

Journal of Mathematics and Statistics, vol.5, no.3, pp.206-214, 2009 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 3
  • Publication Date: 2009
  • Doi Number: 10.3844/jmssp.2009.206.214
  • Journal Name: Journal of Mathematics and Statistics
  • Journal Indexes: Scopus
  • Page Numbers: pp.206-214
  • Keywords: Inventory-production system, Linear quadratic regulator, Optimal control, Principle of optimality, Weibull distributed deterioration
  • Istanbul Gelisim University Affiliated: No

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. © 2009 Science Publications.