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Article Excerpt
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 expression for the operating characteristics and construct the expected cost rate function for the inventory system. Our numerical study indicates that the determinations 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 rate events, but overall appears to be a good heuristic policy.
Subject classifications: inventory: perishables; lot size-reorder point policy; lost sales; effective shelf life.
Area of review: Manufacturing, Service, and Supply Chain Operations.
History: Received May 2003; revisions received September 2004, February 2006, September 2006; accepted December 2006.
1. Introduction
Groceries, pharmaceuticals, composite materials, sheet metal, and blood and its derivatives are a few examples of perishable goods found in a wide variety of industries. Due to their common occurrence and importance, a board literature has developed over the years on management of perishable inventories. However, the existing literature is insufficient in addressing the mostly encountered setting where items have fixed shelf lives, replenishment time are constant, and ordering costs are not negligible.
In this paper, we provide the analysis of continuous-review perishable inventory system with constant shelf lives, fixed ordering costs, and constant lead times under the (Q, r) policy with the restriction r < Q, which implies at most one outstanding order at any time. With Poisson demands and lost sales, we model the system as a embedded Markov process and introduce the concept of effective shelf life, which corresponds to the remaining shelf life of items on hand at the instances when the inventory level hits Q. Based on the stationary distribution of the effective shelf life, we derive the operating characteristics of the system and construct the expected cost rate function. We provide comparisons of the (Q, r) policy with a three-parameter time-based control policy and the only existing heuristic (Chiu 1995) available for the lost-sales (Q, r) model. Our numerical results indicate that the performance of the lot size-reorder policy is good overall, but deteriorates for high service levels, and that determination of the policy parameters exactly as proposed herein results in significant cost savings. We believe that the effective shelf life concept introduced in our work may also enable analysis of other models and help in developing new control policies and heuristics.
The structure of the optimal policy for perishables with fixed lifetimes in the presence of nonnegligible lead times remains an open question. In view of the previous work on periodic-review systems (e.g., Fries 1975, Nahmias 1975), it may be conjectured that the optimal continuous-review control policy should make use of the information regarding the current inventory levels, the remaining shelf lives of the times in stock, and the remaining lead times of the outstanding orders. Even if it were found, it is unlikely that anyone interested in a real problem would be able to use such a complex optimal policy (Schmidt and Nahmias 1985). The researchers have therefore focused on lot size-recorder policies as a reasonable alternative policy class, although not necessarily optimal.
There are a few works in the literature on perishables under continuous review with fixed lifetimes. With zero lead times, Weiss (1980) shows that the (s, S) policy class is optimal for Poisson demands. For recent studies with negligible lead times, see Liu and Lian (1999), Lian and Liu (2001), and Gurler and Ozkaya (2003). With constant lead times, Schmidt and Nahmias (1985) provide the first exact analytical treatment of a system with fixed shelf lives. They consider a lost-sales system with zero ordering costs under the (S - 1, S) control policy. Perry and Posner (1998) extend the (S - 1, S) model to the case of lead-time dependent partial backordering. When ordering costs are nonnegligible, there is no exact treatment in the literature for fixed lifetimes and constant lead times. Chiu (1995) and Lian and Liu (2001) provide only approximations to the (Q, r) model.
The rest of this paper is organized as follows. Section 2 introduces the basic assumptions of our model. Section 3 defines and establishes certain properties of the effective shelf-life process, and derives its stationary distribution. The expressions for the operating characteristics of the inventory system and the expected cost rate function are developed in [section]4. In [section]5, we present our numerical study and, finally, we conclude in [section]6 with a brief summary of our work.
2. Basic Assumptions
We consider the following inventory system. Unit external demands are generated according to a Poisson process with rate [lambda]. Replenishment is done in batches, and there is a fixed, positive procurement lead time, L. All of the items in a batch have identical lifetimes. After joining stock, a batch has a constant shelf life of [tau] time units, beyond which it is no longer usable. The items are withdrawn from stock to satisfy the demand according to the FIFO policy. Each unit held in stock incurs a holding cost h per unit time, and each unit that perishes incurs a cost of p. All unmet demand is lost at a unit lost-sales cost of [phi]. There is a fixed nonzero ordering cost K. The operational objective under the...
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