TY - JOUR
T1 - Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand
AU - Md. Azizul Baten & Anton Abdulbasah Kamil
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 - <p style="text-align: justify;">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.</p>