Investigation of the problem of continuous product stock control in a stochastic model of regeneration with two optimization parameters

The paper proposes and analyzes a new stochastic model of regeneration of continuous product stock control. The volume of stock at an arbitrary moment of time is the status of the system. The control parameters are a maximum deterministic allowable stock volume and a random time from replenishment until the next order. For a stationary value indicator of the efficiency of control — medium specific profit, an explicit analytical representation was obtained. By its structure, this indicator is a fractional linear integral functional from the distribution of a random control parameter. The integrands in the numerator and the denominator of the specified functional depend on the second deterministic control parameter. A special form of the theorem on the extremum of a fractional linear integral functional is used to solve the optimization problem. An analytical study of the main function of this functional on the global extremum was conducted. Based on this study, analytical properties of the original characteristics of the model, under which there is an optimal solution of the management task, are established and a description of this solution is obtained.