Optimum Control of a Continuous Inventory in a Stochastic Regeneration Model with Random Delay and Various Consumption Regimes

In this research work, a stochastic model of inventory management based on the regenerating process of a certain continuous product is considered. The main features of this stochastic model are the presence of random delay and different consumption regimes. The random time from the moment of replenishment of the reserve to the moment of ordering for the next replenishment will be the control parameter in the model. In this model, the stationary indicator of the effectiveness of management quality will have the meaning of the average specific profit. The solution of the stated problem of inventory control is based on the theorem of the extremum of an integral fractional-linear functional, that is, this stationary indicator of control quality will be represented in the form of an integral fractional-linear functional. Through this theorem, analytic representations for the integrands of this functional will be explicitly obtained, and the optimal control in this model is deterministic and is determined by the point at which the global extremum is reached.