Optimal production control in stochastic manufacturing systems with degenerate demand


Baten M. A., KAMIL A. A.

East Asian Journal on Applied Mathematics, vol.1, no.1, pp.89-96, 2011 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 1
  • Publication Date: 2011
  • Doi Number: 10.4208/eajam.190609.190510a
  • Journal Name: East Asian Journal on Applied Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.89-96
  • Keywords: Inventory, Manufacturing systems, Optimal control, Production models, Stochastic differential equations
  • Istanbul Gelisim University Affiliated: No

Abstract

The paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in manufacturing systems with degenerate stochastic demand. We have developed the optimal inventory production control problem by deriving the dynamics of the inventory-demand ratio that evolves according to a stochastic neoclassical differential equation through Ito's Lemma. We have also established the Riccati based solution of the reduced (one-dimensional) HJB equation corresponding to production inventory control problem through the technique of dynamic programming principle. Finally, the optimal control is shown to exist from the optimality conditions in the HJB equation. © 2011 Global-Science Press.