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 Simple Inventory Replenishment Decision Rule for a Linear Trend in Demand

We consider the situation of a deterministic demand pattern having a linear trend. The problem is to select the timing and sizes of replenishments so as to keep the total of replenishment and carrying costs as low as possible. An earlier developed heuristic for the general case of a deterministic, time-varying, demand pattern is specialized to the case of a linear trend. The simple decision rule is shown to lead to small cost penalties in two examples that have been exactly analyzed in an earlier article in this journal.     

Optimal Inventory Rule for a Linear Trend in Demand with a Constant Replenishment Period

The classical deterministic inventory model is considered for the case of constant time between each replenishment and linear trend in demand. The optimum policy is derived and shown to apply to both positive and negative trends. This policy is used in two examples considered in earlier papers on linear trend. It is shown to give only slightly higher costs than the optimal policy with varying replenishment periods, and is compared with a recent heuristic for that case.     

A Simple Inventory Replenishment Policy for Demand with Uncertainty

Research indicates that the economic order quantity is preferred to alternative techniques because it is less nervous to forecast errors. This paper attempts to establish that no statistical relationship exists between the size of forecast error and the performance of some lot-size techniques. A heuristic rule is also presented for deterministic demand. The rule does well on the examples considered and is shown to be more stable than E.O.Q.     

Inventory Replenishment Policy for Cyclic Demand

We consider optimal replenishment policy in the case of deterministic demand, with demand a known function which is periodic in time. The general formulation is a special case of Donaldson's fixed-horizon model, and two common situations are discussed: (i) demand varies sinusoidally; and (ii) there is an abrupt increase or decrease in demand, represented mathematically by a discontinuity in the demand rate.     

Inventory Replenishment Policy for Increasing Demand

The Donaldson model for inventory replenishment is investigated for a general class of increasing demands. In particular, it is shown that the system of reorder times is uniquely specified and well-behaved when the demand f(t) is log-concave, i.e. the derivative of log f(t) is a decreasing function of time. In addition, a numerical procedure is outlined which will produce the set of optimal times at which to re-order, provided the demand f(t) is of sufficiently simple form, for example a simple power law or exponential demand.     

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.     

Practical Inventory Replenishment Policies for a Linear Trend in Demand Followed by a Period of Steady Demand

Inventory policies are considered for the situation of a deterministic linear trend in demand followed by a period of constant demand: an idealised form of a common situation in spares provisioning. An analytic optimal solution is derived and its practical shortcomings discussed. The performance of practical inventory policies for this situation are compared and a policy based on the well known economic batch quantity, suitably modified for linear trend, is shown to give small cost penalties when compared to the analytic solution. The good performance of the policy based on the economic batch quantity is maintained, even when used on examples which simulate situations where the parameters of demand are not known exactly. Indeed the method is then superior to all others tried, including the "optimal" analytic method.     

A Note on an Inventory Model with Inventory-level-dependent Demand Rate

This model discusses an infinite time-horizon deterministic inventory model without shortages, where the demand rate at any instant depends on the on-hand inventory (stock level) at that instant down to a certain stock level and then it becomes constant for the remaining period of the cycle. The decision rule for finding the optimal order quantity is also given, and three numerical examples are presented to illustrate the model developed.     

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...     

The Trended Inventory Lot Sizing Problem with Shortages Under a New Replenishment Policy

In the past few years, considerable attention has been given to the inventory lot sizing problem with trended demand over a fixed horizon. The traditional replenishment policy is to avoid shortages in the last cycle. Each of the remaining cycles starts with a replenishment and inventory is held for a certain period which is followed by a period of shortages. A new replenishment policy is to start each cycle with shortages and after a period of shortages a replenishment should be made. In this paper, we show that this new type of replenishment policy is superior to the traditional one. We further propose four heuristic procedures that follow the new replenishment policy. These are the constant demand approximation method, the equal cycle length heuristic, the extended Silver approach, and the extended least cost solution procedure. We also examine the cost and computation time performances of these heuristic procedures through an empirical study. The number of test problems solved to optimality, average and maximum cost deviation from optimum were used as measures of cost performance. The results of the 10 000 test problems reveal that the extended least cost approach is most cost effective.     

An Inventory Model with Two-Component Demand Rate and Shortages

The article investigates a deterministic inventory system with two-component demand rate. The demand rate is stock-dependent down to a certain level and then constant. Shortages are allowed and are fully backlogged. The storage space is assumed to be limited. A flowchart is provided to solve a general system. To study the effects of changes in the system parameters on the average net profit a sensitivity analysis has been performed.     

A Note on Determining Order Quantities with a Linear Trend in Demand

The economic order quantity concept has received much attention. However, the model is severely restricted by the assumption of constant demand. This paper presents a procedure for adjusting the economic order quantity model for the cases of increasing or decreasing linear trend demand patterns. The primary advantage of the proposed method is its simplicity in comparison with existing procedures and, as illustrated in two examples, its near-optimal performance     

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 Alternative Procedure for Determining the Optimal Policy for an Inventory Item Having Linear Trend in Demand

In this paper we develop an iterative procedure for determining the optimal replenishment policy for an item having linear trend in demand. Shortages are permitted for the inventory item and can be backordered. Our optimal procedure is easier to apply than an earlier solution method reported in inventory literature with linearly time-varying demand and shortages. Two examples are included to illustrate the iterative procedure.