On an Inventory Model for Deteriorating Items With Increasing Time-varying Demand and Shortages

In this paper we present an exact solution for the inventory replenishment problem with shortages, in which items are deteriorating at a constant rate. The demand rates are increasing with time over a known and finite planning horizon. We also present a dynamic programming solution to the problem. Both these methods provide a net improvement over existing methods.     

An EOQ Model for Deteriorating Items with Shortages and Time-Varying Demand

In a recent paper, Goswami and Chaudhuri considered the inventory replenishment problem for a deteriorating item with linearly time-varying demand, finite shortage cost, and equal replenishment intervals. The analysis contained mathematical errors. The present paper proposes the correct theory for this problem. Numerical examples are included.     

An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand

We consider here the inventory replenishment policy over a fixed planning period for a deteriorating item having a deterministic demand pattern with a linear trend and shortages. The number of reorders, the interval between two successive reorders and the shortage intervals over a finite time-horizon are all determined in an optimal manner so as to keep the average system cost to a minimum. One numerical example illustrates how the procedure works. The counterpart of this example in the no-shortage case is also given. The effects of variation in the deterioration rate on the optimal policy are also indicated with numerical examples.     

线性需求合并短缺的变质性物品的生产——库存模型

本文发展了线性需求合并短缺的变质性物品的生产——库存模型，以系统平均总费用最小为目标，提供了有限计划期内的生产调整策略以便适应市场需求的变化．同时还提供了无短缺情形的相应模型，最后出示了一些数字例子     

A Heuristic for Replenishment of Deteriorating Items with a Linear Trend in Demand

Journal of the Operational Research Society - The classical no-shortage inventory policy is examined for the case of deteriorating items having a deterministic demand pattern with a linear...     

Optimal Production Policy for an Item with Shortages and Increasing Time-varying Demand

A new production-inventory model is developed for an item with increasing time-varying demand during a finite planning period. We assume that shortages are fully backordered, and the cost of adjusting the production rate depends on the magnitude of the change in the production rate. The objective is to find the optimal policy of adjusting the production rate in order to minimize the total system cost. A solution procedure is presented and a numerical example is provided for the special case of linearly increasing demand.     

Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages-An Optimal Solution

An optimal solution for inventory replenishment policy for an item having a deterministic demand pattern with linear increasing trend is developed considering shortages. Numerical examples are given to illustrate the results.     

A Comment on ‘Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages — An Optimal Solution’ by T. M. Murdeshwar

Journal of the Operational Research Society -     

An Economic order quantity model for Items with Three-parameter Weibull distribution Deterioration,Ramp-type Demand and Shortages

In this paper, we develop an economic order quantity inventory model for items with three-parameter Weibull distribution deterioration and ramp-type demand. Shortages are allowed in the inventory system and are completely backlogged. The demand rate is deterministic and varies with time up to a certain point and eventually stabilized and becomes constant. The instantaneous rate of deterioration is an increasing function of time. We provide simple analytical tractable procedures for deriving the model and give numerical examples to illustrate the solution procedure. Our adoption of ramp-type demand reflects a real market demand for newly launched product.     

An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting

An economic order quantity (EOQ) inventory model for deteriorating goods is developed with a linear, positive trend in demand allowing inventory shortages and backlogging. The effects of inflation and the time-value of money are incorporated into the model, considering two separate inflation rates: namely, the internal (company) inflation rate and the external (general economy) inflation rate. It is assumed that the goods in the inventory deteriorate over time at a constant rate θ. The inventory policy is discussed over a finite time-horizon with several reorder points. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. Several particular cases of the model are discussed in brief.     

Forecasting for Items with Intermittent Demand

In a service environment, a stockist usually has many slow moving items whose infrequency of demand can give rise to forecasting problems. Moreover, when a demand occurs, the request is sometimes for more than a single unit, which results in so-called lumpy demand. In this paper, the standard method for dealing with such intermittent demand is reassessed. Some general results are presented that enable variance estimates to be made, and these are particularly straightforward when the demand occasions can be represented as a Poisson process. Some experimental evidence is advanced to support this model in the specific situation under study. Since EWMA forecasts are central to many commercial systems, a simulation analysis was conducted to determine under what conditions intermittent demand requires its own model, rather than an unadjusted EWMA. Superior performance is demonstrated for items that have an average inter-order interval greater than 1.25 forecast review periods, and the magnitude of the improvement increases as the average interval lengthens.     

On the Variability of Demand for Families of Items

For the purposes of inventory control and production planning of multi-product lines, often consisting of hundreds or thousands of items differing only in minor ways from each other, it is often found that the variability of demand for individual items can be expressed as a simple function of the expected demand for each item. Usually this is not Poisson variability. In this paper a simple demand model is proposed which generates variability of the type often observed, and which in fact leads directly to the Quadratic Law of Burgin and Wild. It is noted how, in practice, it may be hard to distinguish between this law and the Power Law (Brown). The difference, however, is by no means unimportant, and this is discussed. The statistical problems involved in estimating either law from practical data are also shown to be non-trivial.     

Replenishment Schedule for Deteriorating Items with Time-Proportional Demand

In this paper a heuristic model is presented for determining the ordering schedule when an inventoried item is subject to deterioration and demand changes linearly over time. While the optimizing model developed by researchers fixes the ordering interval and varies the ordering size, the heuristic permits variation in both replenishment-cycle length and the size of the order. As a result, the heuristic produces a better solution than optimizing models in the study presented here.     

时值与增加量折扣并允许短缺的变质性物品的EOQ模型(英)

本文在考虑资金时值和增加量折扣的情形下，讨论了允许短缺的变质性物品在有限计划期内的经济批量问题，提供了寻求最优计货次数以及各次订货的最优批量和最优时刻的一个简单的一维方法，并出示了一个数字例子来说明本模型及其求解过程．