A Perishable Inventory System with Postponed Demands and Multiple Server Vacations

A mathematical modelling of a continuous review stochastic inventorysystem with a single server is carried out in this work. We assumethat demand time points form a Poisson process. The life time of eachitem is assumed to have exponential distribution. We assume (s,S)ordering policy to replenish stock with random lead time. The servergoes for a vacation of an exponentially distributed duration at the timeof stock depletion and may take subsequent vacation depending on thestock position. The customer who arrives during the stock-out periodor during the server vacation is offered a choice of joining a pool whichis of finite capacity or leaving the system. The demands in the poolare selected one by one by the server only when the inventory levelis above s, with interval time between any two successive selectionsdistributed as exponential with parameter depending on the numberof customers in the pool. The joint probability distribution of theinventory level and the number of customers in the pool is obtainedin the steady-state case. Various system performance measures in thesteady state are derived, and the long-run total expected cost rate iscalculated