Managing Perishables with Substitution: Inventory Issuance and Replenishment Heuristics

Abstract

We consider a discrete-time supply chain for perishable goods having separate demand streams for items of different ages. For a good that has two periods of lifetime, we build a model that generalizes and/or subsumes many of the models in the literature and study the effectiveness of two intuitive heuristic (base-stock) replenishment policies combined with different substitution rules. For each replenishment policy, we identify sufficient conditions on cost parameters for a substitution rule to be economically superior to others under our base-stock replenishment policies. Our analysis shows that the replenishment policy almost universally advocated in the perishable inventory literature may lead to pathological behavior when used with issuance rules that pool inventory (via substitution) to satisfy multiple, age-differentiated demand streams. Furthermore, we find that system behavior is typically more predictable, and potentially less costly, under a policy long-discarded in the literature that ignores the inventory of aged items, ordering a constant amount each period. Thus the benefit of pooling inventory for substitutable, perishable products depends critically on the replenishment policy used.inventory management, perishable goods, substitution, heuristics

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.…”

A Stochastic Approach to Blood Supply, Demand and Screening in Central Blood Banks - A Review

“…(Cohen, 1977;Doshi, 1992), under the assumption that the item and demand arrival processes are Poisson processes and that the shelf life time of items is constant (deterministic). Several extensions and ramifications have been studied; see for example (Bar-Lev and Perry, 1989;Berk and Gürler, 2008;Deniz et al, 2010;Doshi, 1992;Kaspi and Perry, 1983;1984;Nahmias, 2011;Nahmias et al, 2004;Parlar et al, 2010;Perry, 1985;1997;Perry 1999;Perry and Posner, 1990;Perry and Stadje, 1999;2000a;2000b;Perry et al, 2000;Perry and Stadje, 2001;Perry, 2003;Boxma et al, 2001;Zhang, 2013). The main mathematical tools employed in those studies are level crossing theory for Markov processes, martingales and stopping times.…”

“…Their engagement has resulted in several papers, (c.f., (Bar-Lev et al, 2009;2017;2017a;2017b;Bar-Lev and Perry, 1989;Bar-Lev et al, 2005;2007;2013;. Other works can be found in (Abolnikov and Dukhovny, 2003;Kopach et al, 2008;Beliën and Forcé, 2012;Civelek et al, 2015;Ghandforoush and Sen, 2010;Karaesmen et al, 2011;Marshall et al, 2004;Sebastian et al, 2012;Shi and Zhao, 2010;Deniz et al, 2010;Blake and Hardy, 2014;Xie et al, 2012). The aim in those paper was to develop comprehensive inventory control and group testing models that incorporate the key features of a CBS and a hospital blood bank.…”

A compound Poisson EOQ model for perishable items with intermittent high and low demand periods

“…The second category goes back to Pal [15], who investigated the performance of an (S − 1, S) control policy. The third category, originated by Weiss [18], is of relevance to our model; [5], [10], [11], [12] and [16] made significant contributions to models in this category. In particular, Lian, Liu and Neuts [11] consider discrete demand for items and perishability times that are either fixed (and known) or follow a phase-type distribution.…”