Perishable inventory model with Markovian arrival process, retrial demands and multiple working vacations

In this paper, we consider a continuous review perishable inventory system in which two types of customers, positive and negative, arrive according to a Markovian arrival process. The life time of an item and the lead time of reorder are exponentially distributed. Demands that occur during stock out period or busy period either enter an orbit of size N or are lost. The orbital demands compete their service with an exponential rate depending on the number of demands in the orbit. The waiting demands in the orbit may renege the system after an exponentially distributed amount of time. The server takes multiple working vacations at zero inventory. The steady state joint probability distribution of the number of customers in the orbit and the inventory level is obtained. Various performance measures and cost analysis are shown with numerical results.