Two perishable inventory systems with one-way substitution

Motivated by the ABO issue of the blood banks 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 so-called 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. Such a 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. Hence, 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 demands process, we develop a unified approach to efficiently and accurately approximate the performance of PIS A. The effectiveness of the approach is investigated by extensive numerical experiments

Perishable inventories with random input:a unifying survey with extensions

This paper is devoted to the theory of perishable inventory systems. In such systems items arrive and stay ‘on the shelf’ until they are either taken by a demand or become outdated. Our aim is to survey, extend and enrich the probabilistic analysis of a large class of such systems. A unifying principle is to consider the so-called virtual outdating process V , where V(t) is the time that would pass from t until the next outdating if no new demands arrived after t. The steady-state density of V is determined for a wide range of perishable inventory systems. Key performance measures like the rate of outdatings, the rate of unsatisfied demands and the distribution of the number of items on the shelf are subsequently expressed in that density. Some of the main ingredients of our analysis are level crossing theory and the observation that the V process can be interpreted as the workload process of a specific single server queueing system.</p

Product Selection Policies for Perishable Inventory Systems

A comparison is made of the performance characteristics of perishable inventory systems with LIFO and FIFO selection policies. For each system one has Poisson arrivals to inventory and Poisson demand epochs with known rates and deterministic shelf life. The comparison requires development of a new analytical framework for the LIFO systems and extension of earlier results on the FIFO systems via Green's function methods. The performance characteristics derived for both policies are spoilage rate, loss sales rate, mean time between stockouts, inventory level on hand and the distribution of age of items delivered. In particular, the dependance of these characteristics on the replenishment rate, demand rate and shelf life are evaluated both theoretically and numerically. Several important management implications are explored and discussed

Stochastic Perishable Inventory Systems: Dual-Balancing and Look-Ahead Approaches

We study a single-item, multi-period, stochastic perishable inventory problem under both backlogging and lost-sales circumstances, with and without an order capacity constraint in each period. We first model the problem as a dynamic program and then develop two heuristics namely, Dual-Balancing (DB) and Look-Ahead (LA) policies, to approximate the optimal inventory level at the beginning of each period. To characterize the holding and backlog cost functions under the proposed polices, we introduce a truncated marginal holding cost for the marginal cost accounting scheme. Our numerical examples demonstrate that both DB and LA policies have a possible worst-case performance guarantee of two in perishable inventory systems under different assumptions, and the LA policy significantly outperforms the DB policy in most situations. We also analyze the target inventory level in each period (the inventory level at the beginning of each period) under different policies. We observe that the target inventory level under the LA policy is not larger than the optimal one in each period in systems without an order capacity constraint

A note on "continuous review perishable inventory systems: Models and heuristics"

In a recent paper, Lian and Liu (2001) consider a continuous review perishable inventory model with renewal arrivals, batch demands and zero lead times. However, the main analytical result they provide holds only for some special cases such as Poisson arrivals with exponential interarrival times. In this note we generalize Theorem 1 of Lian and Liu (2001) for the case where the arrivals follow an arbitrary renewal process