Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand
Md. Azizul Baten 1*, Anton Abdulbasah Kamil 21 Mathematics Program, School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
Received 19 June 2009; Accepted (in revised version) 19 May 2010
Available online 26 October 2010
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.AMS subject classifications: 49N05, 60H10, 90B30, 90B05
Key words: Optimal control, production models, stochastic differential equations, inventory, manufacturing systems
Email: firstname.lastname@example.org (M. A. Baten), email@example.com (A. A. Kamil)