Inventory management system with on/off control of output product flow

The paper contains research of the inventory management model with On/Off control. We study mathematical model of inventory management system under following conditions: the rate of input product flow is a constant, the random part of demand is modeled as Poisson process with a piecewise-constant intensity. Firstly, some property of stationary probability density function of inventory level accumulated in system is developed. Then explicit expression for a stationary distribution of the inventory level is obtained for Phase-type distributions of purchase values of demands. For case arbitrary distribution of demands purchases values Fourier transform of the stationary probability density function is determined. Finally, the obtained results are discussed with illustrative numerical examples. © 2017, Springer International Publishing AG.