Perishable Inventory Systems Research Articles

Double-ended queues with impatience

The effect of “impatient” behaviour is studied primarily in the context of “double-ended” queues where each demands service from the other, typically taxis and passengers. Related models, single queue, and double, with a variety of mechanisms are considered. “Impatience” is to be understood in a wider context than simply becoming tired of waiting: it can arise because the customer, for some reason, runs out of time (inventory and organ transplantation), or because an alternative service becomes available (communication applications). The emphasis in this paper is theoretical but a brief numerical assessment of operational consequences is given. Scope and purpose The “double-ended (or synchronization) queue” is a model for a variety of service demanding/providing systems. In an orderly taxi rank at a railway station or airport, on one side a queue is formed by the arrival of stream of passengers who wait for taxis to their destinations while on the other side a queue of taxis waiting for passengers. Obviously, the two queues can never coexist. The concept of “impatience” enters when a taxi or passenger leaves the queue before receiving service. This concept of “reneging” is widely applicable. In health care, for example, organs are stored for transplantation for needful patients. Both the organs and the demands for them have limited lifetime. A similar scenario applies to perishable inventory systems. In a similar manner, the real-time communication networks admit impatient behaviour. A typical example is a processor-shared queue in data networks with random time-out periods or deadlines. The paper sets out the basics in a variety of theoretical model settings with the common feature of exponential arrival, service and impatience mechanisms. A brief discussion based on numerical calculation is given of some operational features of the models but the thrust is on the theoretical techniques needed to make meaningful operational assessments.

Age-based vs. stock level control policies for a perishable inventory system

In this study, we investigate the impact of modified lotsize-reorder control policy for perishables which bases replenishment decisions on both the inventory level and the remaining lifetimes of items in stock. We derive the expressions for the key operating characteristics of a lost sales perishable inventory model, operating under the proposed age-based policy, and examine the sensitivity of the optimal policy parameters with respect to various system parameters. We compare the performance of the suggested policy to that of the classical ( Q, r) type policy through a numerical study over a wide range of system parameters. Our findings indicate that the age-based policy is superior to the stock level policy for slow moving perishable inventory systems with high service levels.

Continuous review perishable inventory systems: models and heuristics

We consider continuous review perishable inventory models with renewal batch demands. Assuming zero lead time, we construct an embedded Markov chain. With a probabilistic approach, we derive a closed-form long run average cost function under the (s, S) replenishment policy. Numerical analysis is then used to identify the properties of the cost function and to demonstrate the impacts of changing batch sizes and other system parameters. Based on these results, a heuristic approach to handle problems with positive lead times is proposed. The performance of the heuristics against simulation results demonstrates its effectiveness and accuracy

Continuous Review Perishable Inventory Systems: Models and Heuristics

We consider continuous review perishable inventory models with renewal batch demands. Assuming zero lead time, we construct an embedded Markov chain. With a probabilistic approach, we derive a closed-form long run average cost function under the (s,S) replenishment policy. Numerical analysis is then used to identify the properties of the cost function and to demonstrate the impacts of changing batch sizes and other system parameters. Based on these results, a heuristic approach to handle problems with positive lead times is proposed. The performance of the heuristics against simulation results demonstrates its effectiveness and accuracy.

A perishable inventory system with modified ( S−1, S) policy and arbitrary processing times

In this article we analyze a lost sales ( S−1, S) perishable system, under Poisson demands and exponential lifetimes, in which the reorders are placed at every demand epoch so as to take the inventory position back to its maximum level S. The items are replenished one at a time and the resupply time has arbitrary distribution. The various operating characteristics are obtained using Markov renewal techniques. A matrix recursive scheme is developed to determine the stationary distribution of the underlying Markov chain. The efficiency of this procedure in the determination of optimal S that minimizes the long run expected cost rate is discussed. Sensitivity analysis of various system parameters is also carried out. Scope and purpose The analysis of perishable inventory systems, which has potential applications in various sectors of industry, is far more difficult than their infinite lifetime counterparts. In the study of perishable systems under traditional ( S−1, S) policy, reorders for items are placed at demand as well as failure epochs. However, it will be more meaningful not to place orders at failure epochs, which is also practical and economical since it avoids continuous monitoring of items. This paper deals with a continuous review perishable system under a more realistic base stock policy, with variable ordering quantity and arbitrary unit resupply times. The operating characteristics of this complex model are derived using the techniques of semi-regenerative processes. A matrix recursive scheme developed to determine the stationary distribution has enabled us to code an efficient numerical program for cost optimization.

A discrete‐time model for perishable inventory systems

We study a discrete-time (s, S) perishable inventory model with geometric inter‐demand times and batch demands. With a zero lead time and allowing backlogs, we can construct a multi‐dimensional Markov chain to model the inventory‐level process and obtain a closed‐formcost function. Numerical computation for the discrete‐time models is quite manageable. Our numerical results reveal some good properties of the cost function. By comparing our results with results from the corresponding continuous‐time models, we may also conclude that discrete‐time models may be used to approximate their continuous‐time counterparts effectively.

Two-Stage Perishable Inventory Models

In this paper we consider perishable inventory systems with two types of demand. Demand may be for either fresh items or for somewhat older items. We model the system with two inventory stages. The first stage holds fresh items and the second stage holds the older items. We approximate the performance of the two-stage inventory system and compare two managerial policies.

Two-Stage Perishable Inventory Models

In this paper we consider perishable inventory systems with two types of demand. Demand may be for either fresh items or for somewhat older items. We model the system with two inventory stages. The...

Perishable inventory systems with batch demand and arrivals

In this paper we consider a perishable inventory system in which stored items have finite lifetimes. We assume that both the arrival of and demand for items are batch Poisson processes with geometrically sized batches. We find the Laplace transform and first two moments for the times between shortages and the times between outdates of inventory.

The Application of Queueing Theory to Continuous Perishable Inventory Systems

This paper develops two distinct models for studying inventory systems with continuous production and perishable items. The perishable items have a deterministic usable life after which they must be outdated. For each of the models, analytical expressions derived from queueing theory, are found for the steady-state distribution of system inventory. Knowledge of this steady-state behavior may be used for evaluation of system performance, and for consideration of alternatives for improving system performance. Both models assume that inventory is replenished by a continuous production process. The first model, assuming continuous inventory units, has Poisson demand requests with the size of each request distributed as an exponential random variable. The second model has Poisson demand requests with all demands being for a single unit. The analysis for both models exploits the similarity of the inventory system with a single-server queueing system.

A single period model for a multiproduct perishable inventory system with economic substitution

This paper develops a single period model for a specific class of multiproduct perishable inventory systems where demands are interdependent. This class of inventory systems has the property that there is economic substitution between products. It is shown that the optimal policy has the economic substitution property, and that the rate of substitution is age dependent. The model serves as a generalization of a theorem discovered by Ignall and Veinott.