基于二层信用支付的变质物品库存模型

基于时变需求的库存问题一直是库存管理者关注的重点之一,大多数基于二层信用支付的库存模型都是假设需求率为常数.假设需求率是时间的指数函数,建立了二层信用支付条件下的变质物品库存模型,并证明了最优解是存在且唯一的,给出了确定最优补货策略的算法步骤,最后通过数值例子对主要参数进行了灵敏度分析.     

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.     

Optimal EOQ Models for Deteriorating Items with Time-Varying Demand

In this paper, optimal inventory lot-sizing models are developed for deteriorating items with general continuous time-varying demand over a finite planning horizon and under three replenishment policies. The deterioration rate is assumed to be a constant fraction of the on-hand inventory. Shortages are permitted and are completely backordered. The proposed solution procedures are shown to generate global minimum replenishment schedules for both general increasing and decreasing demand patterns. An extensive empirical comparison using randomly generated linear and exponential demands revealed that the replenishment policy which starts with shortages in every cycle is the least cost policy and the replenishment policy which prohibits shortages in the last cycle exhibited the best service level effectiveness. An optimal procedure for the same problem with trended inventory subject to a single constraint on the minimum service level (maximum fraction of time the inventory system is out of stock during the planning horizon) is also proposed in this paper.     

A note on the inventory models for deteriorating items with ramp type demand rate

In this research we study the inventory models for deteriorating items with ramp type demand rate. We first clearly point out some questionable results that appeared in (Mandal, B., Pal, A.K., 1998. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics 1, 49–66 and Wu, K.S., Ouyang, L.Y., 2000. A replenishment policy for deteriorating items with ramp type demand rate (Short Communication). Proceedings of National Science Council ROC (A) 24, 279–286). And then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution. In addition, we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work. Moreover, we also proposed a very good inventory replenishment policy for this kind of inventory model. We believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate.     

带有两货栈及时变需求的变质性物品的最优EOQ模型(英)

本文针对一般的时变需求与两个货栈（自己货栈和租用货栈），建立了变质性物品的最优确定性EOQ模型，提供了用来寻求最优补充策略的方法，并就线性需求出示了两个数值例子．     

通货膨胀对带有时变需求的变质性物品库存补充策略的影响

本文在考虑通货膨胀的情形下，建立了带有时变需求的变质性物品在有限计划期内的库存补充模型，提供了最优补充次数、最优补充周期长度以及各次补充的最优补充量的一种简单而有效的逼近方法，并用数学例子说明了该方法的实现过程．     

Optimal policies for inventory systems with discretionary sales, random yield and lost sales

We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity （sales quantity） under random yield is more （less） than that under certain yield.     

Determining optimal selling price and lot size with a varying rate of deterioration and exponential partial backlogging

In this paper, a deterministic inventory model for deteriorating items with price-dependent demand is developed. The demand and deterioration rates are continuous and differentiable function of price and time, respectively. In addition, we allow for shortages and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. Under these assumptions, for any given selling price, we first develop the criterion for the optimal solution for the replenishment schedule, and prove that the optimal replenishment policy not only exists but also is unique. If the criterion is not satisfied, the inventory system should not be operated. Next, we show that the total profit per unit time is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use numerical examples to illustrate the algorithm.     

需求率为斜坡型的一类变质性物品最优库存策略

本文在考虑需求率服从斜坡型分布的情况下,研究了允许缺货且缺货完全回补、变质率服从威布尔分布、补货率为无穷、有限计划期内的库存模型,证明了最优补货策略的存在性,并给出了求解最优补货策略的算法.     

Constraint programming for stochastic inventory systems under shortage cost

One of the most important policies adopted in inventory control is the replenishment cycle policy. Such a policy provides an effective means of damping planning instability and coping with demand uncertainty. In this paper we develop a constraint programming approach able to compute optimal replenishment cycle policy parameters under non-stationary stochastic demand, ordering, holding and shortage costs. We show how in our model it is possible to exploit the convexity of the cost-function during the search to dynamically compute bounds and perform cost-based filtering. Our computational experience show the effectiveness of our approach. Furthermore, we use the optimal solutions to analyze the quality of the solutions provided by an existing approximate mixed integer programming approach that exploits a piecewise linear approximation for the cost function.     

An inventory model for slow moving items subject to obsolescence

In this paper, we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance. The inventory system is controlled according to a one-for-one replenishment policy with a fixed lead time. Adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks. We show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs. We propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period. We find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs.     

Optimal time varying lot-sizing models under inflationary conditions

This paper deals with the inventory replenishment problem over a fixed planning horizon for items with linearly time-varying demand and under inflationary conditions. We develop models and optimal solution procedures with and without shortages. We do not put any restriction on the length of the replenishment cycles making the proposed methods the first optimal solution procedure for this problem. Using four examples, we illustrate the proposed solution procedures and study the effect of changing the inflation and discount rates on the optimal replenishment schedules.     

Integrating inventory control and a price change in the presence of reference price effects: a two-period model

Demand and procurement planning for consumer electronics products must cope with short life cycles, limited replenishment opportunities and a willingness to pay that is influenced by past prices and decreases over time. We therefore propose the use of an integrated pricing and inventory control model with a two-period linear demand model, in which demand also depends on the difference between a price-history-based reference price and the current price. For this model we prove that the optimal joint pricing/inventory policy for the replenishment opportunity after the first period is a base-stock list-price policy. That is, stock is either replenished up to a base-stock level and a list-price is charged, or it is not replenished and a discount is given that increases with the stock-level. Furthermore, we use real-world cell phone data to study the differences between an integrated policy and traditional sequential optimization, where prices are initially optimized based on the expected demand and ordering cost, and the resulting demand distribution is used to determine an optimal inventory policy. Finally, we discuss possible extensions of the model.     

Inventory models with ramp type demand rate,partial backlogging and Weibull deterioration rate

In this paper, an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand is considered. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The model is fairly general as the demand rate, up to the time point of its stabilization, is a general function of time. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy for the model is derived for both the above mentioned policies.     

Inventory models with variable lead time and present value

The figures for inventory make up a huge proportion of a company's working capital. Because of this, we formulated the optimal replenishment policy considering the time value of money to represent opportunity cost. In this article, we provide a mixed inventory model, in which the distribution of lead time demand is normal, to consider the time value. First, the study tries to find the optimal reorder point and order quantity at all lengths of lead time with components crashed to their minimum duration. Secondly, we develop a method to insure the uniqueness of the reorder point to locate the optimal solution. Finally, some numerical examples are given to illustrate our findings.     

Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging

Inventory model for time-dependent deteriorating items with trapezoidal type demand rate and partial backlogging is considered in this paper. The demand rate is defined as a continuous trapezoidal function of time, and the backlogging rate is a non-increasing exponential function of the waiting time up to the next replenishment. We proposed an optimal replenishment policy for such inventory model, numerical examples to illustrate the solution procedure.     

Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.     

The Inventory Lot-Sizing Problem with Continuous Time-Varying Demand and Shortages

In this study, we develop and analyse an optimal solution procedure for the inventory lot-sizing problem with a general class of time-varying demand functions. The objective of the procedure is to determine the optimal replenishment schedule over a finite planning horizon during which shortages are allowed and are completely backordered. We show that the procedure yields a unique optimal replenishment schedule for both increasing and decreasing demand patterns. We also discuss two particular cases of linear and non-linear demand trend models, and we illustrate the optimal solution procedure with four numerical examples.     

允许租用货栈的库存系统的最优进货策略

本文从实际背景出发，提出了允许租用货栈的库存系统的库存模型，在一般时变需求并允许短缺的假定下，得到了寻求该系统最优进货策略的一种交替逼近方法。并给出了数字例子。