Analysis of inventory systems with (r,Q)-policies and backordering

This paper describes a Markovian approach for the evaluation of inventory systems with (r,Q) policy and backordering. Demand per unit time is assumed to be Poisson, and the order lead time is exponentially distributed. An order of size Q is placed when the inventory on-hand plus on-order minus backorder downcrosses the re-order level r. Thus, we allow multiple outstanding orders. We have developed a direct approach to solve the steady-state balance equations of the underlying Markov chain to obtain the system state probabilities and performance measures