Perishable Inventory Model Research Articles

A single cycle perishable inventory model with time dependent quadratic ramp-type demand and partial backlogging

In order to analyse the behaviour of inventory level of a product level after it's introduction to the market a single item perishable inventory model is developed in this paper, where it is assumed that the demand is time dependent accelerated growth-effect of accelerated growth-steady type. The deterioration of inventory starts after a certain time. Shortages are allowed and are partially backlogged. The profit function is derived and unique existence of the solution is established. A numerical example is presented and sensitivity of the model is examined. The rationale of time dependent quadratic ramp-type demand is discussed.

Consideration of the Undershoot in an (r,Q) Inventory Model for Perishables

Abstract In this paper, we consider a perishable inventory control model under an ( r,Q ) review policy, i.e. at every unit time, the inventory position is monitored and a replenishment of size Q is made if the inventory position hits r. The lifetime of products and the lead time are an integral number of the unit time. We derive approximate expressions of the key operating characteristics of the inventory system (such as the expected quantity of perished products, the expected shortage and the expected inventory level) and obtain a closed form expression of the average total cost per unit time. The effectiveness of approximations is tested by a simulation experiment implemented in Arena software. A numerical analysis is developed to illustrate the advantages of using the proposed policy compared to the classical ( r,Q ) policy which ignores the perishability of products.

A note on an economic lot size model for a perishable age-dependent inventory system with backorders

This paper discusses the production, inventory and backorder costs of an agedependent perishable inventory system. We develop a finite–horizon Economic Lot Size (ELS) system and use an example to illustrate the problem. Whenever inventory is insufficient to satisfy demand, stock–out occurs. Stock–out results in a loss of profit and unspecified loss of goodwill. In general, stock–out results in backorders at the manufacturing side and lost sale in the retail side. This paper considers an age–dependent production cost function where age–dependent inventory backordering increases stock–out cost as a result of emergency orders. In this research, we show that the production cost has the most significant influence on the age–dependent perishable inventory model with backorders.

A controlled M / G / 1 workload process with an application to perishable inventory systems

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload \(a\in (0,1)\). The result is used to obtain the overflow distribution of this controlled workload process; we derive \(\mathbb{E}e^{-\alpha} W(T)\) and \(\mathbb{E}[e^{{-\alpha}^{W(T)}} | W(T) \geq 1]\), where T is the duration of the first cycle. W(t) can be linked to a certain perishable inventory model, and we use our results to determine the distribution of the duration of an empty period.

Analysis of the effect of various unit costs on the optimal incoming quantity in a perishable inventory model

In a previous paper, we presented a periodic review perishable inventory model and showed how to compute the optimal incoming order quantity for a single period model with useful shelf lifetime of two periods and no backlogging on demand. The incoming order quantities were computed as a function of the inventory on-hand and on-order for different demand distributions with different levels of demands, and for lead times up to four periods. This paper utilizes the same model and examines the effect of four unit costs: ordering, holding, shortage and outdating costs, on the optimal incoming quantity for the case of one period lead time.

A note on "Continuous review perishable inventory systems: models and heuristics"

In a recent paper, Lian and Liu (2001) consider a continuous review perishable inventory model with renewal arrivals, batch demands and zero lead times. However, the main analytical result they provide holds only for some special cases such as Poisson arrivals with exponential interarrival times. In this note we generalize Theorem 1 of Lian and Liu (2001) for the case where the arrivals follow an arbitrary renewal process.

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.

A single-period perishable inventory model where deterioration begins at a random point in time

This paper develops a single-period inventory model where the stock begins to deteriorate at a random point in time within the period. Once this deterioration begins, the selling price can be adjusted once at that point. Optimum order size and pricing policies are determined for such an inventory model through a numerical illustration.

A perishable inventory model with positive order lead times

In this paper we will derive the necessary equations to determine the single period, periodic review, optimal incoming quantity for a single product with a useful lifetime of two periods, subject to a known positive order lead time and a lost sales policy. Generalization to the multiperiod, finite horizon or the constrained optimization problem can be easily accomplished. Optimal order quantities for lead times up to four periods are computed for different levels of demands and for different demand distributions. The experimental results indicate that the order quantity is a function of the order lead time and the quantity of goods on-hand and on order.

Optimal inventory control policy subject to different selling prices of perishable commodities

In this paper, we propose a perishable inventory model with consideration of different selling prices of perishable commodities under stochastic demand. In this model, different lifetimes of perishable commodities are provided, and we consider the discriminating selling prices by different lifetimes. We formulate the model into a Markov decision process model to determine an optimal inventory policy that maximizes the expected average profit per period.

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.

A lost sales (S — 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.

A lost sales (S ? 1, S) perishable inventory system with renewal demand

This article analyzes a one-to-one ordering perishable inventory model with renewal demands and exponential lifetimes. The leadtimes are independently and exponentially distributed and the demands that occur during stock out periods are lost. Although the items are assumed to decay at a constant rate, the output process is not renewal and the Markov renewal techniques are successfully employed to obtain the operating characteristics. The problem of minimizing the long run expected cost rate is discussed and numerical values of optimal stock level are also provided. © 1996 John Wiley & Sons, Inc.

An approximation to the continuous review inventory model with perishable items and lead times

A continuous review perishable inventory model based on approximations to the expected outdating, the expected shortage quantity, and the expected inventory level is developed to determine a best ( Q, r) ordering policy under a positive order leadtime when the total expected average cost per unit time is minimized. The approximation method is simple and verified by a comparison with the Weiss model. The results reveal that the mean absolute deviation from the optimal total expected average cost per unit time is only 0.58%. This paper also compares the proposed model to the conventional model with no perishability. A value is given to the item lifetime indicating when an approximate answer approaches closely to the conventional ordering policy. Finally, a simulation model written in SIMSCRIPT II.5 is used to validate the approximate results.

A heuristic ( R, T) periodic review perishable inventory model with lead times

This paper deals with the problem of determining a best order-up-to-level and review interval policy for a fixed-life perishable product under the assumption that the lead time is positive. After the analysis of the behavioral pattern of the perishability process, a simple yet good approximation to the expected outdating is developed. Two extended bounds on the expected outdating and the total expected costs of holding inventory, ordering, backlogging unsatisfied demand, and disposing of perished inventory are derived to construct a heuristic ( R, T) model. Validation tests for both unrestricted and restricted cases are performed to assess the effectiveness of the approximate outdating. The performance of the heuristic model is tested empirically by comparing it with results from a simulation. Computational studies reveal that the approximate outdating and the heuristic model are accurate. The general results of a comparison between the heuristic model and no outdating model are also provided in this paper.

Storing Crossmatched Blood: A Perishable Inventory Model with Prior Allocation

The process of testing a sample of a patient's blood against units of blood from inventory to ensure compatibility is called crossmatching. When a physician orders blood, it is crossmatched and then held for a patient. As a precautionary measure, physicians tend to order blood in excess of the amount that is transfused (used by the patient). Consequently, a large proportion of blood held for a patient (often higher than 50 percent) is eventually not transfused. This leads to increased outdates. The effects of crossmatching on outdates are widely acknowledged, but have seldom been included in blood inventory control models. In this paper, we develop a model for determining outdates and shortages for crossmatched blood using generally accepted parameters, such as proportion of crossmatched blood that is actually transfused, and the number of days after which crossmatched blood is released if not transfused. This model can be used as a decision support system that allows the blood bank administrator to do sensitivity analyses related to controllable blood inventory parameters.

A continuous review perishable inventory model

A continuous review (8, S) inventory system in which items are removed from stock one at a time either due to random demand or random failure of item is considered. It is assumed that demands for items occur in Poisson manner and life time of any item is negative exponential. Assuming instantaneous delivery of orders, the steady state proba¬bility distributions of the stock level and mean time between successive reorders are de¬rived: The optimum decision rules in the long run are also given, The results are illustrated numerically

Bounds on the Solution of the Lagged Optimal Inventory Equation with No Demand Backlogging and Proportional Costs

These equations depict the following inventory situation. A nonnegative order for a single product is to be placed at the beginning of each of an infinite sequence of equally spaced periods into the future, labeled 0, 1, 2, .. Demands depleting the inventory form a nonnegative sequence of independent identically distributed random variables 40, 1, '2, * . For analytic convenience the distribution is assumed to possess a continuous positive density function 0(4) on [0, oo). An order zi placed at the beginning of period i arrives after a fixed Aperiod lag at the beginning of period i + A, and is relabeled Y(i + ), which explains (4). The pipeline vector qi at the beginning of period i consists of the inventory on hand at that point xi together with the sequence of outstanding orders to arrive in succeeding periods Y(i+ 1), Y(i+ 2)' ... , Y(i+ -1) If demand in a given period exceeds inventory on hand, two extreme cases are considered. In model I, also called the no backlogging or the lost sales case, no customer will wait, so the inventory level is conveniently thought of as being nonnegative; it is recursively generated by (5a). In model II, also called the backlogging case, all customers