Analysis of the (Q, r) Inventory Model for Perishables with Positive Lead Times and Lost Sales

Abstract

We consider a perishable inventory system with Poisson demands, fixed shelf lives, constant lead times, and lost sales in the presence of nonnegligible fixed ordering costs. The inventory control policy employed is the continuous-review (Q r) policy, where r < Q. The system is modeled using an embedded Markov process approach by introducing the concept of the effective shelf life of a batch in use. Using the stationary distribution of the effective shelf life, we obtain the expressions for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determination of the policy parameters exactly as modeled herein results in significant improvements in cost rates with respect to a previously proposed heuristic. We also compare the (Q r) policy with respect to a time-based benchmark policy and find that the (Q r) policy might be impractical for rare events, but overall appears to be a good heuristic policy.

A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time

“…In the particular case of Poisson demand, Berk and Gürler (2008) analyzed the optimal total cost of the (r, Q) policy. They observed that the distribution of the remaining shelf life at epochs when the inventory level is equal to Q has Markovian properties and showed that the remaining shelf life constitutes an embedded Markov process.…”

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

“…These tools embrace and incorporate various areas in probability and OR such as inventory management, chain supply, queueing theory, level crossing theory, perishable commodities and optimization of cost functions which take into account all related costs (c.f. (Bar-Lev and Perry, 1993;Bassok et al, 1999;Berk and Gürler, 2008;Claeys et al, 2010;Cohen, 1977;Doshi, 1992;Kaspi and Perry, 1983;1984;Nahmias, 2011;Nahmias et al, 2004a;Parlar et al, 2010;Perry, 1985;1997;Perry and Posner, 1990;Perry and Stadje, 1999;2000a;2000b;Perry et al, 2000;Perry and Stadje, 2001;Zhang, 2013). The next subsections describe some features and ingredients of the stochastic approach.…”

“…(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.…”

A Fluid EOQ Model of Perishable Items with Intermittent High and Low Demand Rates

“…The second family is of models with obsolescences ( [19]). Here, the items might perish at each period with some probability which is typically increasing over time ( [15], [3]). …”