arrow
Volume 1, Issue 1
Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand

Md. Azizul Baten & Anton Abdulbasah Kamil

East Asian J. Appl. Math., 1 (2011), pp. 89-96.

Published online: 2018-02

Export citation
  • 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.

  • AMS Subject Headings

49N05, 60H10, 90B30, 90B05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-1-89, author = {}, title = {Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {1}, number = {1}, pages = {89--96}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.190609.190510a}, url = {http://global-sci.org/intro/article_detail/eajam/10898.html} }
TY - JOUR T1 - Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand JO - East Asian Journal on Applied Mathematics VL - 1 SP - 89 EP - 96 PY - 2018 DA - 2018/02 SN - 1 DO - http://doi.org/10.4208/eajam.190609.190510a UR - https://global-sci.org/intro/article_detail/eajam/10898.html KW - Optimal control, production models, stochastic differential equations, inventory, manufacturing systems. AB -

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.

Md. Azizul Baten & Anton Abdulbasah Kamil. (1970). Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand. East Asian Journal on Applied Mathematics. 1 (1). 89-96. doi:10.4208/eajam.190609.190510a
Copy to clipboard
The citation has been copied to your clipboard