Murat Fadiloglu and Onder Bulut. An Embedded Markov Chain Approach to the Analysis of Inventory Systems with Backordering under Rationing

Abstract. Rationing is an inventory policy that allows prioritization of different demand classes.  The idea behind rationing is that it is possible to maintain high service levels for certain demand classes while keeping inventory costs at bay by providing lower service levels to certain other demand classes that are not critical.  In this paper, we propose a new method for the analysis of inventory systems with backorders under rationing policy.  We show that if such an inventory system is sampled at multiples of supply lead-time, the state of the system evolves according to a Markov chain.  We provide a recursive procedure to generate the transition probabilities of the embedded Markov chain.  We demonstrate that although the Markov chain has an infinite state space, it is possible to obtain the steady-state probabilities of interest with desired accuracy by considering a truncated version of the chain.  Since the probabilities obtained are also steady-state probabilities of the original continuous-time system, they permit the computation of any long-run performance measure of interest for the inventory system.