Two perishable inventory systems with one-way substitution

Motivated by the ABO issue of the blood bank system, in which the portions stored have constant shelf life, we consider two subsystems of perishable inventory. The two Perishable Inventory Subsystems-PIS A and PIS B, are correlated to each other through a one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsystem are four Poisson processes, which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items, an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items, an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. This one-way substitution of the issuing policy generates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis of PIS B is known from previous work. Thus, in this study we focus on the marginal performance analysis of PIS A. Based on a fluid formulation and a Markovian approximation for the one-way substitution demand process, we develop a unified approach to efficiently and accurately approximate the performance of the PIS A. The effectiveness of the approach is investigated by extensive numerical experiments.