Affiliations: [a] Department of Statistics, School of Physical Sciences, Shahjalal University of Science and Technology, Sylhet, Bangladesh
| [b] Department of Decision Sciences, School of Quantitative Sciences, Universiti Utara Malaysia, UUM Sintok, Kedah Darul Aman, Malaysia
Correspondence:
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Corresponding author.Md. Azizul Baten, Department of Statistics, School of Physical Sciences, Shahjalal University of Science and Technology, Sylhet-3144, Bangladesh. Tel.: +880 821 713491, 714479, 713850, 717850, 716123, 715393; Fax: +880 821 715257, 725050; E-mail: [email protected].
Abstract: 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.
