Extended optimal stochastic production control model with application to economics

This study considers an inventory control system meeting uncertain demand in continuous time.The demand is a function of both time and price, with the price evolves as a Wiener process with no drift. 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 in which the stochastic differential equations of a type known as Ito’s equations are considered which are perturbed by a Markov diffusion process and analyzed by the optimal control of a single dimension stochastic production planning model. 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.