Pathwise Properties and Performance Bounds for a Perishable Inventory System

Abstract

We study a perishable inventory system under a fixed-critical number order policy. By using an appropriate transformation of the state vector, we derive several key sample-path relations. We obtain bounds on the limiting distribution of the number of outdates in a period, and we derive families of upper and lower bounds for the long-run number of outdates per unit time. Analysis of the bounds on the expected number of outdates shows that at least one of the new lower bounds is always greater than or equal to previously published lower bounds, whereas the new upper bounds are sometimes lower than and sometimes higher than the existing upper bounds. In addition, using an expected cost criterion, we compare optimal policies and different choices of critical-number policies.

Approximation Algorithms for Perishable Inventory Systems

“…demands. Cooper (2001) derived bounds on the stationary distribution of the number of outdated units in each period, under a fixed critical number order policy. Recently, following the approximation scheme of the outdating costs developed by Nahmias (1976), Chen et al (2014) proposed two heuristic policies for the joint inventory control and pricing models.…”

Simulation of different reordering policies for optimizing the inventory of perishable food: an Italian case study

“…Still for a single demand stream, Nahmias (1976Nahmias ( , 1977 and Nandakumar and Morton (1993) show that order-up-to policies perform very well compared to other methods, including optimal policies; they develop and analyze heuristics to choose the best order-up-to level. Cooper (2001) provides further analysis of the properties of the TIS policy, while Nahmias (1978) shows that when the ordering cost is high, an (s, S) type heuristic is better than order-up-to policies. Liu and Lian (1999) analyze such an (s, S) continuous review inventory system.…”

Stochastic Inventory Routing for Perishable Products

“…The most widely used periodic-review ordering policies are (R, S) (Chiu 1995, Cooper 2001, Deniz et al 2010) and (R, s, S) (Broekmeulen andVan Donselaar 2009, Lian andLiu 1999), where R refers to the number of periods between two consecutive reviews of the inventory system, s denotes the inventory level below which an order is triggered, and S is the order-up-to level value. When demands are stochastic, obtaining optimal parameters in periodic-review policies even for a single perishable product with deterministic shelf life is notoriously complicated.…”

“…The fixed shelf life perishability problem remains complex when the product lifetime is longer than two units of time in a periodic review system (Kouki and Jouini 2015). Hence, researchers have worked on approximating outdate costs (Broekmeulen andVan Donselaar 2009, Chiu 1995) or calculating upper and lower bounds on the number of outdates (Chiu 1995, Cooper 2001. Some models deal with batch demands (Lian and Liu 1999) or batch orders (Broekmeulen and Van Donselaar 2009).…”