AN ALTERNATE MODEL FOR LEAD-TIME DEMAND: CONTINUOUS-REVIEW INVENTORY SYSTEMS

The calculation of reorder points when the distribution of lead-time demand is normal is quite complex, primarily because of having to bound it away from negative demand values. A number of researchers have sought feasible alternative forms of lead-time demand which can be calculated without undue difficulty. It is proposed here to assume a Poisson (daily) demand and an exponential lead time (days). If they are assumed independent their convolution is geometric, which is itself asymptotically exponential. This has a number of advantages: (1) The exponential lead time is appropriate where the lead time is often short (i.e., local source), occasionally longer (when the local sources stock out), and, infrequently, quite long. (2) The geometric lead-time demand is independent of changes of time scale. (3) Reorder points and lot sizes appear in simple closed form. (4) The exponential asymptote is sufficiently close that this further simplification is usually warranted.     

A mixed inventory model with variable lead time and random supplier capacity

In this paper, we have studied analytically the implication of a controllable lead-time and a random supplier capacity on the continuous review inventory policy, in which the order quantity, reorder point and lead-time are decision variables. Two models are considered: the normal lead-time demand and lead-time demand is distributed free. For both cases, after formulating the general model, some properties of the optimal ordering policy have been developed. Particularly, we have shown that the expected annual total cost is a unimodal function and quasi-convex in the order quantity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions. Furthermore, the effects of parameters are also performed.     

The Value of Supplier Information to Improve Management of a Retailer's Inventory

The distribution of lead time demand is essential for determining reorder points in inventory systems. Usually, the distribution of lead time demand is approximated directly. However, in some cases it may be worthwhile to take the demand per unit time and lead time into account, particularly when specific information is available. This paper deals with the situation where a supplier, who produces on order in fixed production cycles, provides information on the status of the coming production run. The retailer can use this information to gain insight into the lead-time process. A fixed order (s_vQ) strategy is presented, with a set of reorder points s_v depending on the time t until the first possible delivery, which is determined by the information of the supplier. A Markov model that analyzes a given (s_vQ) strategy is used to quantify the value of the information provided by the supplier. Some numerical examples show that the approach may lead to considerable cost savings compared to the traditional approach that uses only one single reorder point, based on a two-moments approximation. Using this numerical insight, the pros and cons of a more frequent exchange of information between retailers and suppliers can be balanced.     

ON LEAD TIME DEMAND DISTRIBUTIONS

A key factor in establishing inventory policy for an item is the procurement lead time demand distribution (LTDD). Demand during lead time is a random variable if at least one of the components-length of lead time, order intensity, and order size-is a random variable. This paper discusses the problem of estimating the functional form of the LTDD for various combinations of the component random variables, using the method of generating functions. Since a normal approximation will often be used in practice, expressions are also given for the mean and variance of the LTDD for the various cases.     

REORDER-POINT MODELS WITH DISCRETE PROBABILITY DISTRIBUTIONS

This paper is concerned with the determination of reorder points and safety-stock levels for situations where both the demand and lead-time distributions are discrete and independent. Formulas are developed for computing exact probabilities for the lead-time demand distribution on the basis of empirical distributions. Practitioners can use the model to obtain exact probabilities for situations where the computational burden is justified, while academicians can use the model to evaluate heuristic approaches to the reorder-point problem.     

Inventory Rationing in a Make‐to‐Stock System with Batch Production and Lost Sales

We address an inventory rationing problem in a lost sales make‐to‐stock (MTS) production system with batch ordering and multiple demand classes. Each production order contains a single batch of a fixed lot size and the processing time of each batch is random. Assuming that there is at most one order outstanding at any point in time, we first address the case with the general production time distribution. We show that the optimal order policy is characterized by a reorder point and the optimal rationing policy is characterized by time‐dependent rationing levels. We then approximate the production time distribution with a phase‐type distribution and show that the optimal policy can be characterized by a reorder point and state‐dependent rationing levels. Using the Erlang production time distribution, we generalize the model to a tandem MTS system in which there may be multiple outstanding orders. We introduce a state‐transformation approach to perform the structural analysis and show that both the reorder point and rationing levels are state dependent. We show the monotonicity of the optimal reorder point and rationing levels for the outstanding orders, and generate new theoretical and managerial insights from the research findings.     

不确定环境下的Supply-hub协同补货决策

个性化需求与零部件创新使得产品需求和补货提前期不确定,对供应链补货决策和运行成本产生重要影响。将提前期不确定因素引入Supply-hub协同补货研究中,探讨提前期随机和需求不确定情况下,考虑零部件配套性的三供应商单制造商生产两定制产品的Supply-hub协同补货决策问题;提出了三种补货策略,以供应链运行成本最小化为目标,建立不同策略下的供应链补货模型并求解最优补货批量和供应链最小运行成本;发现三种补货策略均存在唯一最优补货批量,基于Supply-hub的两种协同补货策略和基于分散决策的供应商独立补货策略各有优势,但基于Supply-hub的批量及时间协同的补货策略恒优于基于Supply-hub的集中补货策略。最后,通过MATLAB进行算例分析验证结论,发现基于Supply-hub的批量及时间协同的补货策略能有效降低需求不确定性带来的成本增加风险;通用件的提前期波动对于供应链期望运行成本的影响要高于定制件提前期波动的影响,因此在进行供应链补货策略选择时更加关注通用件提前期。     

Inventory control with seasonality of lead times

The practical challenges posed by the seasonality of lead times have largely been ignored within the inventory control literature. The length of the seasons, as well as the length of the lead times during a season, may demonstrate cyclical patterns over time. This study examines whether inventory control policies that anticipate seasonal lead-time patterns can reduce costs. We design a framework for characterizing different seasonal lead-time inventory problems. Subsequently, we examine the effect of deterministic and stochastic seasonal lead times within periodic review inventory control systems. We conduct a base case analysis of a deterministic system, enabling two established and alternating lead-time lengths that remain valid through known intervals. We identify essential building blocks for developing solutions to seasonal lead-time problems. Lastly, we perform numerical experiments to evaluate the cost benefits of implementing an inventory control policy that incorporates seasonal lead-time lengths. The findings of the study indicate the potential for cost improvements. By incorporating seasonality in length of seasons and length of lead times within the season into the control models, inventory controllers can make more informed decisions when ordering their raw materials. They need smaller buffers against lead-time variations due to the cyclical nature of seasonality. Reductions in costs in our experiments range on average between 18.9 and 26.4% (depending on safety time and the probability of the occurrence of stock out). Therefore, inventory control methods that incorporate seasonality instead of applying large safety stock or safety time buffers can lead to substantial cost reductions.     

Impact of investing in quality improvement on (Q,r, L) model involving the imperfect production process

This paper investigates the impact of quality improvement on the modified lot size reorder point models involving variable lead time and partial backorders. The formulated models include the imperfect production process and an investing option of improving the process quality. The objective is simultaneously optimizing the lot size, reorder point, process quality level and lead time. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution-free case where only the mean and standard deviation of lead time demand are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.     

提前期、构建成本和短缺量拖后率均可控的EOQ模型

传统库存模型通常将提前期和构建成本视为不可控制。事实上可以通过追加投资缩短提前期和降低构建成本。缺货期间,为减少订单丢失量和补偿顾客的损失,供应商会给予一定的价格折扣。现实库存系统中,容易得到需求的期望值和标准差,但较难得到其分布规律。基于此,考虑短缺量拖后率与价格折扣和缺货期间库存水平相关,提出了一种需求为任意分布且提前期和构建成本均可控的EOQ模型,证明了模型存在唯一最优解,给出了一种寻优算法。数值仿真分析表明,一般情况下,压缩提前期和降低构建成本能降低订购批量和安全库存,降低库存总成本;短缺量拖后系数和缺货概率对库存总成本影响较大,企业应尽量降低缺货概率,尤其在短缺量拖后系数较小时。     

Sizing Inventory When Lead Time and Demand are Correlated

Determining appropriate inventory levels has been a subject of interest for both researchers and practitioners. Standard practice is to treat lead time demand as a random sum of random numbers and rely on established probability theory to calculate both reorder point and safety stock levels. A key assumption in these calculations, however, is that lead time and demand are not correlated. In this paper, we first explore situations where this assumption is untrue and then develop equations to determine the reorder point and the safety stock when lead time and demand are correlated. More specifically, we (1) derive formulas for the average and variance of the demand in a lead time, which can then be used to calculate the reorder point and the safety stock, (2) apply these formulas to two distributions for which there is a closed‐form solution: normal and Poisson, and (3) examine the effect of correlation on safety stock requirements under the normal distribution.     

RFID技术压缩提前期对供应链收益的影响与协调

RFID技术能够压缩供应链的提前期,提高零售商的服务水平,同时也会增加供应链的成本,如何协调采用RFID技术后供应链成员的收益是迫切需要解决的问题。本文针对单供应商和单零售商的两级供应链,考虑提前期变化对供应链及其成员收益的影响,在假定RFID单位标签成本为一定值的情况下,研究了采用RFID技术前后分散式供应链和集中式供应链的收益,并探讨了契约参数的变化对供应链协调的影响。结果表明,收益共享契约能有效地协调采用RFID技术后的供应链,实现供应链成员的共赢,但是采用RFID技术后,能够协调供应链的契约参数的区间缩小,零售商的最优订货量减少,供应商的批发价格上升。最后得出供应链采用RFID技术后提前期压缩量的阈值,通过数值分析对结论进行了验证,该研究为供应链企业采用RFID技术提供了相应的管理启示。     

延迟支付下短生命周期产品批发价契约研究

在需求随机且允许延迟支付的情况下,如果零售商的销售款不足以清偿应支付给制造商的货款,制造商将承担一定的回款风险。对此,以报童模型为基础,针对短生命周期产品建立了延迟支付下的批发价契约模型。分析表明,如果需求分布是IGFR,那么对于一定的批发价,零售商有确定的最优订货批量。制造商的预期利润是批发价的递增函数。制造商根据零售商至少应获得的预期利润来确定批发价。当满足一定条件时供应链能够实现协调,但这是一种系统利润分配缺乏柔性的协调。     

INVESTMENT IN SETUP COST,LEAD TIME,AND DEMAND PREDICTABILITY IMPROVEMENT IN THE EOQ MODEL

We study an economic order quantity/reorder point (EOQ/ROP) model with stochastic demand and backorders where options of investing in reducing setup cost, lead time, and variance of demand forecast errors are available. The model is quite comprehensive relative to previous models since it simultaneously addresses the strategic decisions associated with these three investment opportunities as well as the tactical decisions of determining both the lot size and the safety stock. We develop a simple search procedure to obtain the optimal values of setup cost, lead time, variance of demand forecast errors, order quantity, and safety stock multiplier. Computational studies are performed to determine the sensitivity of the optimal solution of the model to changes in the model's parameters.     

THE HERMITE DISTRIBUTION AS A MODEL OF DEMAND DURING LEAD TIME FOR SLOW-MOVING ITEMS

Heretofore, the Poisson and the Laplace distributions have been used to model demand during lead time for slow-moving items. In this paper, we present a Poisson-like distribution called the Hermite. The advantage of the Hermite is that it is as simple to use as the Poisson and the Laplace are. Moreover, the Hermite is the exact distribution of demand during lead time when unit demand is Poisson, P(Λ), and lead time is normally distributed, N(μ, σ²), so long as (μ/σ²)≥Λ. Thus, the Hermite can enhance the accuracy of analysis as well as add to the tools available to the analyst.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

On Optimal Expediting Policy for Supply Systems with Uncertain Lead‐Times

We examine the role of expediting in dealing with lead‐time uncertainties associated with global supply chains of “functional products” (high volume, low demand uncertainty goods). In our developed stylized model, a retailer sources from a supplier with uncertain lead‐time to meet his stable and known demand, and the supply lead‐time is composed of two random duration stages. At the completion time of the first stage, the retailer has the option to expedite a portion of the replenishment order via an alternative faster supply mode. We characterize the optimal expediting policy in terms of if and how much of the order to expedite and explore comparative statics on the optimal policy to better understand the effects of changes in the cost parameters and lead‐time properties. We also study how the expediting option affects the retailer's decisions on the replenishment order (time and size of order placement). We observe that with the expediting option the retailer places larger orders closer to the start of the selling season, thus having this option serve as a substitute for the safety lead‐time and allowing him to take increased advantages of economies of scale. Finally we extend the basic model by looking at correlated lead‐time stages and more than two random lead‐time stages.     

含交付时间不确定性的供应链协调策略研究

分析含有交付时间不确定性的季节性供应链管理问题.如果在供应链中共享供应商的交付时间不确定性信息,零售商可以调整订货量,减少销售损失,就有可能提高供应链的整体利润.分析指出,当交付时间不确定性程度大时,信息共享能提高改进供应链绩效的可能性,但不一定能提高供应链的整体绩效,因而,仅仅采用信息共享有应用价值,但有一定的局限性.进一步分析发现,存在能协调这种含有交付时间不确定性供应链策略,能使供应链达到整体绩效最大化,并且对供应链的利润进行分配,协调策略能有效地弥补信息共享的局限性.     

二阶段供应链中提前期压缩的影响与协调

提前期是衡量业务过程绩效一个重要的因素,基于时间竞争的供应链管理战略核心就在于提前期的压缩,提前期压缩是形成供应链战略优势的有力来源.在市场需求预测精度随提前期变化的假设下,采用逻辑证明和数值分析的方法,研究由供应商-零售商构成的两阶段供应链中提前期压缩对供应链及其成员收益的影响以及如何实现供应链的渠道协调.研究结果表明:当供应链的服务水平小于0.5时,提前期的压缩可以获得供应链成员收益的Pareto改进;当供应链的服务水平大于等于0.5,引入线性转移支付补偿机制,可以实现供应链的渠道协调,获得供应链成员收益的Pareto改进.     

CIVIL SOCIETY AND THE STATE: THE INTERPLAY BETWEEN COOPERATION AND MINIMUM WAGE REGULATION

In a cross‐section of countries, state regulation of labor markets is negatively correlated with the quality of labor relations. In this paper, we argue that these facts reflect different ways of regulating labor markets, either through the state or through the civil society, depending on the degree of cooperation in the economy. We rationalize these facts with a model of learning of the quality of labor relations. Distrustful labor relations lead to low unionization and high demand for direct state regulation of wages. In turn, state regulation crowds out the possibility for workers to experiment negotiation and learn about the potential cooperative nature of labor relations. This crowding out effect can give rise to multiple equilibria: a “good” equilibrium characterized by cooperative labor relations and high union density, leading to low state regulation; and a “bad” equilibrium, characterized by distrustful labor relations, low union density, and strong state regulation of the minimum wage.