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。     

MODELING DEMAND DURING LEAD TIME*

This paper treats some of the important considerations in constructing an analytical model for the distribution of demand during lead time. It presents a formal model that can be developed along one of two lines. The first has order size and order intensity leading to a compound distribution of period demand, then period demand and lead time giving rise to a compound distribution of demand during lead time. The second has order intensity and lead time giving rise to a compound distribution of lead-time order intensity, then lead-time order intensity and order size leading to a compound distribution of demand during lead time. The paper also condenses the state of the art in a table and proposes some simple classification schemes that could help researchers extend that state of the art.     

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.     

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.     

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.     

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.     

The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts

We quantify the bullwhip effect (which measures how the variance of replenishment orders is amplified as the orders move up the supply chain) when both random demands and random lead times are estimated using the industrially popular moving average forecasting method. We assume that the lead times constitute a sequence of independent identically distributed random variables and the correlated demands are described by a first-order autoregressive process. We obtain an expression that reveals the impact of demand and lead time forecasting on the bullwhip effect. We draw a number of conclusions on the bullwhip behaviour with respect to the demand auto-correlation and the number of past lead times and demands used in the forecasts. We find maxima and minima in the bullwhip measure as a function of the demand auto-correlation.     

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.     

On variance amplification in a three-echelon supply chain with minimum mean square error forecasting

We analyse a three echelon supply chain model. First-order autoregressive end consumer demand is assumed. We obtain exact analytical expressions for bullwhip and net inventory variance at each echelon in the supply chain. All of the three supply chain participants employ the order-up-to policy with the minimum mean square error forecasting scheme. After demonstrating that the character of the stochastic ordering process observed at each level of the supply chain is mathematically tractable, we show that the upper stream participants have complete information of the market demand process. Then we quantify the bullwhip produced by the system, together with the amplification ratios of the variance of the net inventory levels. Our analysis reveals that the level of the supply chain has no impact upon the bullwhip effect, rather bullwhip is determined by the accumulated lead-time from the customer and the local replenishment lead-time. We also find that the conditional variance of the forecast error over the lead-time is identical to the variance of the net inventory levels and that the net inventory variance is dominated by the local replenishment lead-time.     

双渠道模式下定价与提前期联合优化研究

在双渠道模式下，本文对零售商的价格和提前期决策进行研究。根据零售商线上服务范围的不同，双渠道服务模式可以划分为近端服务模式、中端服务模式和远端服务模式。本文分析了零售商在三种服务模式下最优的价格和提前期决策，并对三种服务模式进行对比。结果表明，如果零售商的配送速度较低，零售商应该选择近端服务模式。如果零售商的配送速度较高，则在中端和远端服务模式中进行选择，且随着成本的增加，提前期均会缩短，这是因为零售商的服务范围会随着配送成本增加而缩小，此外，配送速度的增大也会导致提前期缩短；而价格在两种模式中变化趋势不同，中端服务模式下价格呈现非递增趋势，而远端服务模式下价格呈现非递减趋势。因为在中端服务模式下，零售商更加愿意提供降价来吸引更多的线下需求，而远端服务模式则是提升价格来保证产品的边际收益。研究结论可为零售企业提供有效的科学的参考和理论指导。     

Anticipatory shipment for pickup point supply

Many retailers allow customers to shop online and collect their orders at a pickup point nearby. In this paper, we study the anticipatory shipment of items to such pickup points in order to improve service and operational efficiency. We formulate a stochastic programming model to support the selection of products and associated quantities to ship to the pickup points in anticipation of customers’ demand. The results of our numerical experiments suggest that anticipatory shipments can have substantial benefits both in terms of cost and lead-time. The benefits increase with the storage space at the pickup point. The anticipatory shipment strategy is especially beneficial in a setting which requires short delivery lead-times and when the e-fulfilment warehouse is further away.     

The Effect of Lead Time Uncertainty on Safety Stocks

The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service‐level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.     

Production and inventory control at ABB Motors and Volvo Wheel Loaders,two examples of MRP in practical use

The paper presents the main routines of production and inventory control at ABB Motors, Västerås and Volvo Wheel Loaders, Eskilstuna. The primary interest is to present how Material Requirements Planning (MRP) is used in these two companies. If the number of end items is large, the company assembles-to-order or makes-to-order then additions to pure MRP seem to be necessary. ABB Motors and Volvo Wheel Loader use: planning bills, a normal bill of materials with 'adding bills of materials', a master production schedule planning system with an available-to-promise function and a home-made 'system' for modules available-to-promise. One important measure for the both companies is the accumulative lead-time. An increase of the Master Production Schedule in a shorter time than the accumulative lead-time is avoided, because it will lead to suggestions of purchase in past time periods and therefore most probably to future material shortages.     

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.     

Decision support for lead time and demand variability reduction

Companies undertaking operations improvement in supply chains face many alternatives. This work seeks to assist practitioners to prioritize improvement actions by developing analytical expressions for the marginal values of three parameters – (i) lead time mean, (ii) lead time variance, and (iii) demand variance – which measure the marginal cost of an incremental change in a parameter. The relative effectiveness of reducing lead time mean versus lead time variance is captured by the ratio of the marginal value of lead time mean to that of lead time variance. We find that this ratio strongly depends on whether the lead time mean and variance are independent or correlated. We illustrate the application of the results with a numerical example from an industrial setting. The insights can help managers determine the optimal investment decision to modify demand and supply characteristics in their supply chain, e.g., by switching suppliers, factory layout, or investing in information systems.     

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.     

Trade-off between quoted lead time and price

In a make-to-order environment, lead time and price can play a crucial role in determining the financial success of a firm. Their importance increases when demand is sensitive to the quoted lead time and price. A model is presented which uses the quoted lead time and price as a mechanism to determine the optimal demand level. The relationships between the model parameters and their impacts on the firm's profit is also analysed. In addition, the effect of the number of job requests, and the mean processing time are examined. Based on the results presented in this paper, there is clear indication that the firm's profit is sensitive to the inventory holding rate, and that the inventory holding cost component is redundant in the presence of a tardiness cost component.     

基于分层MTO订单的准入策略研究

研究按订单生产(make to order,MTO)模式下随机订单的准入策略.本文提出的准入决策方法分为两步,首先在考虑随机订单的不同属性基础上,采用TOPSIS(technique for order preference by similarity to an ideal solution)方法计算新到订单与理想订单的接近程度,以此作为订单的综合收益,从而对新订单进行分层排序;其次采用MDP(Markov decision process)模型分别计算接受和拒绝订单的期望收益,从而决定是否接受该订单.研究发现,当市场需求接近或大于产能时,企业可从订单分层中获益;反之,市场需求显著小于产能时,分层不会带来额外收益.企业分层收益随需求增加或产能减少而递增,且与生产前置期呈倒U型关系.数值模拟发现,订单分层越精细,收益越大,且分层数约为需求与企业产能的比值时,订单分层收益接近最大值.     

A BRANCH-AND-BOUND APPROACH FOR SEQUENCING EXPANSION PROJECTS

The paper examines the problem of finding a sequence of a finite set of expansion projects to meet a deterministic demand projection at minimum discounted cost. As the general problem is NP-complete, we focus on the case when the demand growth is in the exponential form, which is quite often found in applications of electric power generation, transportation, water resources and communication. We find that projects' annual costs are an effective ranking criteria for determining an optimal expansion sequence. As the annual cost for a project is a function of time or capacity level, an optimal expansion sequence can be obtained easily if dominance orders of the annual costs exist for all pairwise projects, which is likely to be the case for most practical problems. When the annual costs for the projects are in conditional order, a branch-and-bound algorithm has been developed to effectively reduce the searching range. Our extensive computational results show that the approach is very efficient compared with the other approaches and always solves the problem to optimum although the optimality of the approach still remains to be proven.     

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.