Extended optimal stochastic production control model
What is it about?
This study considers an inventory control system meeting uncertain demand in continuous time. The goal is to use the stochastic optimal control principle to completely solve a production planning model for the demand rate. A stochastic optimal control problem is formulated and analyzed in which the stochastic differential equations of a type known as Ito’s equations are considered which are perturbed by a Markov diffusion process. The existence of a complete solution to the associated HJB equation is established and the optimal policy is characterized. Numerical examples and solutions of this optimal control model are then presented.
Why is it important?
This study focuses on stochastic optimal control problems related to demand management and production control decisions for a single product under capacity limitations and demand uncertainties. Other studies have the drawback of considering a pre-determined policy that is not guaranteed to be optimal.