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Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand

Published online by Cambridge University Press:  28 May 2015

Azizul Baten  and
Anton Abdulbasah Kamil
Azizul Baten*
Affiliation:
Mathematics Program, School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
Anton Abdulbasah Kamil*
Affiliation:
Mathematics Program, School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
*
Corresponding author. Email: baten_math@yahoo.com
Corresponding author. Email: anton@usm.my
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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.

Keywords

49N0560H1090B3090B05Optimal controlproduction modelsstochastic differential equationsinventorymanufacturing systems
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 1 , Issue 1 , February 2011 , pp. 89 - 96
Copyright
Copyright © Global-Science Press 2011

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