A note on supply chain coordination for joint determination of order quantity and reorder point using a credit option

Credit options and side payments are two methods suggested for achieving coordination in a two-echelon supply chain. We examine the credit option coordination mechanism introduced by Chaharsooghi and Heydari [Chaharsooghi, S., & Heydari, J. (2010). Supply chain coordination for the joint determination of order quantity and reorder point using credit option. European Journal of Operational Research, 204(1), 86–95]. This method assumes that the supplier’s opportunity costs are equal to the reduction in the buyer’s financial holding costs during the credit period. In this note, we show that Chaharsooghi and Heydari’s method is not applicable when buyer and supplier opportunity costs are not equal. We introduce an alternate per order rebate method that reduces supply chain costs to centralized management levels.     

提前期需求为模糊随机条件下的连续库存补货策略

考虑提前期内需求为模糊随机变量且提前期为可缩短情形下,建立由购买商和供应商所组成的简单供应链连续库存补货策略优化模型,其中订单量、再订货点和提前期为决策变量.首先推导出模糊随机需求条件下购买商和供应链的成本函数,然后,进一步考虑总需求为三角模糊数,推导出供应商、购买商和供应链的模糊成本函数.在此基础上分别从购买商成本最小和供应链成本最小角度对模型进行求解,结合具体算例对模型进行应用分析和比较分析,结果表明模型具有有效性和实用性,并得出如下结论:从购买商本身角度考虑订购策略所产生的供应链成本总是大于从供应链整体角度考虑订货策略所产生的供应链成本,同时从购买商本身角度考虑订货策略所产生的最优订购量、购买商成本低于从供应链整体角度考虑订货策略所产生的最优订购量、购买商成本.     

A quantity discount approach to supply chain coordination

Quantity discounts provide a practical foundation for inventory coordination in supply chains. However, typical supply chain participants may encounter difficulties in implementing the coordination policy simply because (1) specified lot size adjustments may deviate from the economic lot sizes and (2) the buying firm may face amplified overstocking risks related to increased order quantities. The main objective of this study is to develop a quantity discount model that resolves the practical challenges associated with implementing quantity discount policies for supply chain coordination between a supplier and a buyer. The proposed Buyer’s Risk Adjustment (B-RA) model allows the supplier to offer discounts that capitalize on the original economic lot sizes and share the buyer’s risk of temporary overstocking under uncertain demand. The analytical results suggest that the proposed B-RA discount approach is a feasible alternative for supply chain coordination under uncertain demand conditions.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

基于M-CVaR和生产资金约束的供应链协调研究

本文针对供应商面临生产资金约束的情况,在需求随机条件下研究了由一个风险中性零售商和一个具有风险偏好的供应商组成的二级供应链的协调问题。文章在零售商享有批发价折扣的提前支付和供应商银行信贷两种融资方式下,分别建立了零售商的最优决策模型以及基于M-CVaR测度工具的供应链整体订购决策模型,并给出了采用两种不同融资模式时零售商和供应链整体的最优订购量以及供应链的协调条件,分析了供应商的风险偏好对供应链整体最优决策及协调条件的影响。最后通过算例验证了文章的主要结论。研究表明,当提前支付价格折扣大于临界值时,零售商会选择提前支付货款;提前支付模式下供应链整体的最优订购量大于银行信贷模式;随着供应商的风险偏好由风险规避向风险喜好转变,供应链整体的最优订购量逐渐增大。     

供应链买卖双方协调订货模型

供需关系贯穿供应链的整个过程;然而,如何促使非一体化供应链协调问题在实践中是非常重要的.因此,供需双方订货批量的研究是供应链管理的一个重要内容之一.本文以订单方式为背景,针对供应链环境下单个供应商和多个订货商在非合作情况下的订货模型进行讨论,并在此基础上给出了一个改进后的线性价格折扣策略,该策略同时考虑了增量折扣和减量折扣两种情况,同时给出了供需上双方订货的S tackelberg博弈模型.数字实验结果表明该折扣模型对于改善供应链运作协调是相当有效的.     

风险规避供应商参与下基于实物期权的供应链协调

研究不确定性需求下,由风险规避的供应商和占主导地位的零售商组成的二级供应链的协调问题。构建了基于实物期权的协调机制,给出了实现协调的最优期权价格和期权执行价格的求解算法,分析了供应商风险规避特性对各方订货量和利润的影响。结果表明,在供应商风险规避条件下,基于实物期权的契约可以实现不确定需求下的供应链协调。     

随机需求下供应链商业信用契约协调

研究一个供应商和一个零售商构成的两级供应链面对随机需求时的商业信用契约协调问题。通过分析商业信用对供应商与零售商各自目标利润及供应链的总利润的影响,建立了商业信用契约协调模型,推导了最优信用期和最优订货量,指出通过信用策略可以使双方实现对利润的合理分配与协调。最后通过数值算例说明了所得结论。     

资金约束下基于CVaR的供应链协调性研究与融资策略选择

在零售商的资金约束下,供应商愿意提供贸易信用融资或者信用担保下的银行贷款。在考虑双方均为风险规避型的情况下采用CVaR风险度量方法建立了双方以及供应链的风险收益值模型,给出了两种融资模式下的供应链协调条件,最优订货量以及批发价格,并且研究了银行贷款利率对供应链协调以及供应商融资方式选择的影响。结果表明实现供应链协调的条件取决于生产成本、银行利率以及双方的风险规避程度,不同的银行利率会导致实现供应链协调的条件不同,供应商将根据双方风险规避程度选择提供给零售商的融资方式。     

信用支付下基于收益共享契约的网购供应链协调策略研究

信用支付在网购交易中成为了日益重要的支付方式,考虑网络零售商能否在规定的免息期内支付货款两种情形,针对实际延迟支付时间影响网络零售商订货量问题,建立当网络零售商面临不确定的市场需求时的网购供应链决策模型,运用逆向归纳法分析供应商、网络零售商对相关参数的决策并设计收益共享契约实现网购供应链的协调。结果表明:网络零售商的订购量不会随着网络零售商实际支付时间的无限延长而持续增加,只有在供应商规定的免息期内,信用支付策略才会对订购量具有激励作用;两种情形下只要收益共享系数满足一定条件都能够实现网购供应链的协调。最后利用数值算例对上述结论进行了验证。     

随机需求下基于商业信用的回购与收入共享联合契约协调研究

在由单个供应商和单个零售商组成的供应链中,零售商由于资金短缺或风险规避不能达到系统的最优订货量,因此需要采取一些措施使得供应链节点企业间相互合作来实现供应链的协调。本文针对需求随机且供应链节点企业存在缺货惩罚的情况,通过设计基于商业信用(即供应商允许零售商延期支付货款)的完全回购契约来促进零售商提高订购量,以实现供应链系统达到最优利润,分析给出了该契约下的最优订货量和批发价格;在此基础上,为了合理分配供应链系统的总利润,建立了回购与收入共享联合契约模型,发现通过共享系数的变动能够实现供应链系统协调和渠道成员双赢。     

Coordination and profit sharing between a manufacturer and a buyer with target profit under credit option

Several studies have focused on buyer vendor coordination through quantity discount/credit option mechanism but few quantitative models and investigations are available that have explored the mechanism for transfer of surplus generated due to coordination. In this paper, we develop a coordination mechanism through credit option such that both the parties can divide the surplus equitably after satisfying their own profit targets. Two situations are explored here; in the first situation; both the parties have no individual profit target from the business whereas in the second situation, there are individual profit target for both the parties. The proposed mechanism for division of surplus is studied through a numerical study and the impact of different parameter values on the results are examined.     

Integrated inventory and inspection policies for stochastic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier when his inventory level drops to a certain point, due to demand which is stochastic in nature. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. The order quantity, reorder point and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks is set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

需求与库存水平相关的供应链量折扣协调模型

考虑由一个供应商和一个零售商构成的供应链系统,零售商的市场需求依赖于该产品的库存水平,研究了利用批量折扣实现供应链完美协调的问题.首先,我们得出了在分散式系统下供应链无法实现完美协调,讨论了供需双方的最优决策.其次,作为stackelberg的主导方,供应商提供批量折扣计划,得出了此折扣计划实现系统完美协调的条件,分别给出了实现完美协调和不能实现完美协调时的批量折扣计划.最后分析了需求函数中的参数和产品的成本对实现供应链系统完美协调的影响.     

基于期权契约的供应链协调研究

供应链协调与优化一直都是供应链管理的核心议题之一.为分析供应链竞合背景下的供应链协调问题,验证期权契约对供应链的协调效果,文章在分析供应链基本运作的基础上,利用优化理论和方法构建了无契约协调时供应链的基准模型和期权契约下的供应链模型,通过有无契约时供应链及供应链成员利润的对比,分析说明期权契约的协调效果,通过不同决策模式下供应链及供应链成员利润分析,给出期权契约完全协调供应链的条件.在此基础上,进一步引入供应商间和零售商间的跨链补货,验证跨链补货策略对于提高供应链成员利润的有效性.     

Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing

In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of S periods, and the retailer in turn provides a trade credit of R periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, and (c) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights.     

需求依赖努力水平的农产品供应链期权契约优化

针对供应商和零售商组成的农产品供应链,研究市场需求受到努力水平影响的农产品供应链协调问题.由于双重边际效应,分散式供应链中的最优生产数量低于集中式供应链的情况,零售商努力水平也相对较低.引入期权契约时,在零售商主导期权契约的供应链中,研究得到零售商的最优初始订货量和最优期权价格,以及供应商的最优生产数量,实现供应链协调.数值分析证实了期权契约有助于提高零售商的努力水平以及整个供应链的利润.     

A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

This paper deals with the operational issues of a two-echelon single vendor–multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.     

Trade credit for supply chain coordination

Trade-credit is a seller’s short-term loan to the buyer, allowing the buyer to delay payment of an invoice. It has been the largest source of working capital for a majority of business-to-business firms in the United States. Numerous theories have been proposed to explain trade-credit, mainly from finance perspectives. It has also been an important issue in supply chain management. Surprisingly, most literature in supply chain management has examined the retailer’s stocking policies given a supplier’s trade-credit. This paper attempts to shed light on trade-credit from a supplier’s perspective, and presents it as a tool for supply chain coordination. Specifically, we explicitly assume firms’ financial needs for inventory. Following a Newsvendor framework, we assume that the supplier grants trade-credit and markdown allowance. Given the supplier’s offer, the retailer determines order quantity and the financing option for the inventory, either trade-credit or direct financing from a financial institution. Our result shows that the supplier’s markdown allowance alone cannot fully coordinate the supply chain if the retailer employs direct financing. Positive financing costs call for trade-credit in order to subsidize the retailer’s costs of inventory financing. Using trade-credit in addition to markdown allowance, the supplier fully coordinates the retailer’s decisions for the largest joint profit, and extracts a greater portion of the maximized joint profit.     

销售商出售看跌期权的供应链优化研究

在由一个供应商和一个销售商组成的单期两级供应链中,处于主导地位的销售商以其卖场所具有的销售能力参与供应链合作,并从销售的每一个产品中获取既定收益。同时,销售商还向供应商出售建立在产品销售量保障基础上的看跌期权,以激励供应商参与供应链合作。论文对上述情形的销售商出售看跌期权的供应链合作问题进行了研究,通过建模与优化分析,证明了在销售商提供看跌期权的供应链合作中,供应商存在唯一的最优生产批量和看跌期权采购量,以及销售商存在最优的从每一单位产品销售中获取的既定收益。论文还揭示了销售商提供看跌期权,虽然无法实现供应链协调,但可以实现供应链参与企业所获得的收益与其所承担的风险相匹配。最后,论文论证了在销售商出售看跌期权机制下,供应链存在收益损失较小的理想合作区域。