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

The subject of this paper is investigation of the inventory management systems mathematical model with following assumptions: Compound Poisson demand process with hyperexponential, Phase-type and arbitrary batch sizes distributions,On/Off control of piecewise-constant rate of input product flow. Stationary distribution explicit expressions of inventory level accumulated in the system are obtained in this paper with hyperexponential and Phase-type distributions of demands purchases values. Fourier transform of the stationary probability density function is also determinated here in case of arbitrary distribution of demands purchases values. The results obtained in this paper are shown with illustrative numerical examples. © Springer International Publishing AG 2017.