Modified Cramer-Lundberg models with on/off control and hyperexponential distribution of demands purchases values

The paper contains research of modified Cramer-Lundberg models of inventory management with On/Off control and hyperexponential distribution of demands purchases values. In first model we assume that input product flow has piecewise-constant rate, which depends on some threshold value, the random part of demand is modeled as Poisson process with constant intensity. Hereby system control is to switch the rate of the input product flow if the stock level in the system is more than threshold. Second model is investigated under following conditions: the rate of input product flow is a constant, the random part of demand is modeled as Poisson process with piecewise-constant intensity. In this case the idea of control the system is similar to the first model. We find explicit expressions for the stationary distribution of the inventory level for each models. The results are discussed with illustrative numerical example. © 2017, Springer International Publishing AG.