Retrial inventory model with negative customers and multiple working vacations

Abstract

This paper analyses a continuous review (s, S) inventory system at a service facility, wherein an item demanded by a customer is issued after performing service on the item. Primary arrivals follow a Poisson distribution and they may turn out to be positive or negative and then enter into the orbit. The orbiting demands compete for service according to an exponential distribution. The server takes multiple working vacations at zero inventory. Replenishment times, vacation times, service times during regular busy periods and vacation periods are exponentially distributed. A matrix analytic method is used for the steady-state distribution of the model. Various performance measures and cost analyses are shown with numerical results.