Abstract:
The work is devoted to the study of the problem of managing the stock of a certain continuous product, the evolution of the volume of which is described by a regenerating stochastic process. The main feature of the considered mathematical model is that the cost characteristics that determine the price of supplying the product to the consumer and the costs associated with ensuring the functioning of the system depend on random external factors. The random control parameter is the time from the moment of the next replenishment of the stock to the moment of the next order for replenishment. It is proved that the stationary cost indicator of control efficiency in the optimization problem under consideration in its analytical structure is a fractional-linear integral functional depending on the distribution function of the control parameter. The theoretical solution of the optimization problem is based on the use of the extremum theorem for linear-fractional integral functionals.
Keywords:continuous product inventory control problem, random cost characteristics of the system, controlled regenerative stochastic processes, linear-fractional integral functionals in problems of stochastic optimal control.
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