Research Article Open Access

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

Md. Azizul Baten and Anton Abdulbasah Kamil

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.

Journal of Mathematics and Statistics
Volume 5 No. 3, 2009, 206-214

DOI: https://doi.org/10.3844/jmssp.2009.206.214

Submitted On: 15 April 2009 Published On: 30 September 2009

How to Cite: Baten, M. A. & Kamil, A. A. (2009). An Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration . Journal of Mathematics and Statistics, 5(3), 206-214. https://doi.org/10.3844/jmssp.2009.206.214

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Keywords

  • Inventory-production system
  • Weibull distributed deterioration
  • linear quadratic regulator
  • principle of optimality
  • optimal control