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.
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