TY  - JOUR
AU  - Baten, Md. Azizul 
AU  - Kamil, Anton Abdulbasah 
PY  - 2009
TI  - An Optimal Control Approach to Inventory-Production Systems with Weibull Distributed Deterioration 
JF  - Journal of Mathematics and Statistics
VL  - 5
IS  - 3
DO  - 10.3844/jmssp.2009.206.214
UR  - https://thescipub.com/abstract/jmssp.2009.206.214
AB  - Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items. Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem. Results: It was then illustrated with the help of an example. By the principle of optimality we also established the Riccati based solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with this control problem. Conclusion: As an application to quadratic control theory we showed an optimal control policy to exist from the optimality conditions in the HJB equation.