An embedded Markov chain approach to stock rationing

Rationing is an inventory policy that allows prioritization of demand classes. It enables the inventory system to provide higher service levels for critical demand classes. In this paper, we propose a new method for the analysis of the backordering inventory systems under rationing with batch orders. 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 this embedded chain. Although the embedded 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. The obtained probabilities are also the steady-state probabilities of the original continuous-time system and permit the computation of any long-run performance measure of interest.

• Type: Journal
• Year: 2010
• Where: ORL
• Authors: Mehmet Murat Fadiloglu, Önder Bulut
• Keywords: Demand Classes, Inventory, Markov Chain, Operations Research, ORL 2010