Single-supplier/multiple-buyer supply chain coordination: Incorporating buyers’ expectations under vertical information sharing

We address the coordination problem in a single-supplier/multiple-buyer supply chain. The supplier wishes to coordinate the supply chain by offering quantity discounts. To obtain their complete cost information, the supplier exchanges his own cost parameters with buyers leading to vertical information sharing. The supplier thinks that the buyers, as they have access to supplier’s setup and holding cost information, may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain. We model each buyer’s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only. These expectations are then incorporated into the modeling of the supply chain, which results in a generalization of the traditional Stackelberg type models. We discuss alternative efficiency sharing mechanisms, and propose methods to design the associated discount schemes that take buyers’ expectations into account. In designing the discount schemes, we consider both price discriminatory and non-price discriminatory approaches. The study adds to the existing body of work by incorporating buyers’ expectations into a constrained Stackelberg structure, and by achieving coordination without forcing buyers to explicitly comply with the supplier’s replenishment period in choosing their order quantities. The numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels, and retain a significant portion of the net savings.     

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。     

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。     

突发事件下需求信息不对称时的供应链协调应对

协调供应链系统使其具有抗突发事件性的研究是供应链管理的核心议题之一。为了分析突发事件下需求信息不对称时的供应链协调问题,考虑由一个制造商和一个零售商组成的供应链,在随机市场需求下,首先分析了数量折扣契约对供应链的协调作用;然后探讨了突发事件导致市场需求发生变化且变化后的需求信息是不对称信息时数量折扣契约对供应链的协调作用,研究表明:基准的数量折扣契约对突发事件下的供应链不再发挥协调作用,为此,给出了供应链应对突发事件的最优应对策略,并调整了原来的数量折扣契约使其具有抗突发事件性。最后,应用一个算例对比加以说明。     

Demand disruption and coordination of the supply chain with a dominant retailer

This paper develops two coordination models of a supply chain consisting of one manufacturer, one dominant retailer and multiple fringe retailers to investigate how to coordinate the supply chain after demand disruption. We consider two coordination schedules, linear quantity discount schedule and Groves wholesale price schedule. We find that, under the linear quantity discount schedule, the manufacturer only needs to adjust the maximum variable wholesale price after demand disruption. For each case of the disrupted amount of demand, the higher the market share of the dominant retailer, the lower its average wholesale price and the subsidy will be under the linear quantity discount schedule, while the higher its fraction of the supply chain’s profit will be under Groves wholesale price schedule. When the increased amount of demand is very large and production cost is sufficiently low, linear quantity discount schedule is better for the manufacturer. However, when the production cost is sufficiently large, Groves wholesale price schedule is always better. We also find that the disrupted amount of demand largely affects the allocation of the supply chain’s profit.     

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.     

The optimal quantity discount that a supplier should offer

Quantity discounts are a useful mechanism for coordination. Here we investigate such discounts from the supplier's perspective, both from a non-cooperative game-theoretical approach and a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and Pareto optimal solution set are derived for the non-cooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than non-cooperatively. Moreover, we extend our model in three directions: (1) the product is transported by a private fleet; (2) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (3) the case of heterogeneous buyers. Numerical case studies are employed throughout the paper to illustrate the practical applications of the models presented and the sensitivity to model parameters.     

Ordering and pricing decisions in a two-echelon supply chain with asymmetric demand information

This article examines coordinated decisions in a decentralized supply chain that consists of one supplier and one retailer, and faces random demand of a single product with a short life cycle. We consider a setting where the retailer has accurate demand information while the supplier does not. Such a problem with asymmetric demand information can be viewed as an extension of the newsboy problem in which both the supplier and the retailer possess the same demand information. Combining the mechanism of sharing demand information and that of quantity discount and return policy enables us to develop three coordinated models in contrast with the basic and uncoordinated model. We are able to show the ordinal relationship among the retailer’s optimal order quantities in these four models under a general form of random demand, and compare the supply chain profits and conduct sensitivity analysis analytically in four models under uniform random demand. We also provide numerical results under normal random demand that bear a resemblance to those under uniform random demand.     

A two-stage supply chain coordination mechanism considering price sensitive demand and quantity discounts

This paper explores the coordination between a supplier and a buyer within a decentralized supply chain, through the use of quantity discounts in a game theoretic model. Within this model, the players face inventory and pricing decisions. We propose both cooperative and non-cooperative approaches considering that the product traded experiences a price sensitive demand. In the first case, we study the dynamics of the game from the supplier's side as the leader in the negotiation obtaining a Stackelberg equilibrium, and then show how the payoff of this player could still improve from this point. In the second case, a cooperative model is formulated, where decisions are taken simultaneously, emulating a centralized firm, showing the benefits of the cooperation between the players. We further formulate a pricing game, where the buyer is allowed to set different prices to the final customer as a reaction to the supplier's discount decisions. For the latter we investigate the difference between feasibility of implementing a retail discount given a current coordination mechanism and without it. Finally the implications of transportation costs are analyzed in the quantity discount schedule. Our findings are illustrated with a numerical example showing the difference in the players’ payoff in each case and the optimal strategies, comparing in each case our results with existing work.     

A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain

We consider a real-world automobile supply chain in which a first-tier supplier serves an assembler and determines its procurement transport planning for a second-tier supplier by using the automobile assembler’s demand information, the available capacity of trucks and inventory levels. The proposed fuzzy multi-objective integer linear programming model (FMOILP) improves the transport planning process for material procurement at the first-tier supplier level, which is subject to product groups composed of items that must be ordered together, order lot sizes, fuzzy aspiration levels for inventory and used trucks and uncertain truck maximum available capacities and minimum percentages of demand in stock. Regarding the defuzzification process, we apply two existing methods based on the weighted average method to convert the FMOILP into a crisp MOILP to then apply two different aggregation functions, which we compare, to transform this crisp MOILP into a single objective MILP model. A sensitivity analysis is included to show the impact of the objectives weight vector on the final solutions. The model, based on the full truck load material pick method, provides the quantity of products and number of containers to be loaded per truck and period. An industrial automobile supply chain case study demonstrates the feasibility of applying the proposed model and the solution methodology to a realistic procurement transport planning problem. The results provide lower stock levels and higher occupation of the trucks used to fulfill both demand and minimum inventory requirements than those obtained by the manual spreadsheet-based method.     

Supply chain coordination for the joint determination of order quantity and reorder point using credit option

Decisions regarding order quantity and reorder point are two major challenges in supply chain inventory management. In this paper, a coordination model of the joint determination of these two decision variables is proposed. A decentralized supply chain consisting of one buyer and one supplier in a multi-period setting is investigated. Demand and lead times are uncertain in our model. An incentive scheme based on credit option has been developed to encourage the buyer to participate in the coordination model. In this model, the downstream member has the option of using credit to purchase goods during the credit time, subject to its commitment to a jointly agreed order quantity and reorder point. The credit time is determined in such a way that the two parties have incentives to participate. The proposed incentive scheme can share the benefits of coordination between the two members based on their bargaining power. The proposed model shows that the coordination of the reorder point, together with order quantity, can increase the overall chain profitability as well as each member’s profitability.     

Optimal order lot sizing and pricing with free shipping

Companies, especially those in e-business, are increasingly offering free shipping to buyers whose order sizes exceed the free shipping quantity. In this paper, given that the supplier offers free shipping, we determine the retailer’s optimal order lot size and the optimal retail price. We explicitly incorporate the supplier’s quantity discount, and transportation cost into the model. We analytically and numerically examine the impacts of free shipping, quantity discount and transportation cost on the retailer’s optimal lot sizing and pricing decisions. We find that free shipping can benefit the supplier, the retailer, and the end customers, and can effectively encourage the retailer to order more of the good, to the extent of ordering a few times of the optimal order lot size without free shipping. The order lot size will increase and the retail price will decrease if the supplier offers proper free shipping.     

A scenario-based stochastic model for supplier selection in global context with multiple buyers,currency fluctuation uncertainties,and price discounts

Suppliers network in the global context under price discounts and uncertain fluctuations of currency exchange rates have become critical in today’s world economy. We study the problem of suppliers’ selection in the presence of uncertain fluctuations of currency exchange rates and price discounts. We specifically consider a buyer with multiple sites sourcing a product from heterogeneous suppliers and address both the supplier selection and purchased quantity decision. Suppliers are located worldwide and pricing is offered in suppliers’ local currencies. Exchange rates from the local currencies of suppliers to the standard currency of the buyer are subject to uncertain fluctuations overtime. In addition, suppliers offer discounts as a function of the total quantity bought by the different customer’ sites over the time horizon irrespective of the quantity purchased by each site.     

需求预测更新条件下两阶段电子商务供应链契约协调

研究了一类在贝叶斯需求预测更新情形下,生命周期中采用B2C与C2B两阶段进行产品销售的供应链模型,研究发现无法使用单一契约来协调供应链。在此基础上,设计了具有供应商价格折扣契约与零售商承诺订购契约的两阶段供应链契约协调机制,证明了两阶段协调机制能够实现供应链的帕累托改进。算例分析表明了两阶段契约协调机制的有效性,并发现能够实现供应链完美协调的契约参数不一定在帕累托集合内,供应链不一定能够达到完美协调;且由于零售商与供应商的最优契约参数不同,需要通过零售商与供应商之间的谈判达到纳什均衡。     

A spatiotemporal Data Envelopment Analysis (S-T DEA) approach: the need to assess evolving units

We consider a two-stage supply chain with one supplier and one manufacturer. The manufacturer faces a Poisson demand process where the arrival rate depends on the selling price, the announced delivery time, and the delivery reliability defined as the probability of satisfying the announced delivery time. Such a demand model generalizes the works in the literature by simultaneously considering the above three demand sensitivity factors. The main purpose of this paper is to study the equilibrium decisions in the supply chain with an all-unit quantity discount contract. We consider four scenarios regarding whether the leadtime standard, the delivery reliability standard, and the manufacturer’s capacity are endogenous, and whether the manufacturer’s production cost is its private information. We find that an all-unit quantity discount scheme can coordinate the supply chain for most cases. Managerial insights are observed regarding the impact of the three demand sensitivity factors. For example, the breakpoint in an optimal quantity discount contract always increases with the delivery reliability sensitivity under an exogenous delivery reliability, but may decrease under an endogenous delivery reliability; with asymmetric information, a higher variance of the manufacturer’s unit production costs leads to a lower unit wholesale price for the low-cost manufacturer.     

Random yield supply chain with a yield dependent secondary market

This paper considers a simple supply chain with one supplier and one retailer where the supplier’s production is subject to random yield and the retailer faces uncertain demand. There exists a secondary market for acquiring or disposing products by the supplier. We study both the centralized and decentralized systems. In the decentralized system, a no risk sharing contract and a risk sharing minimum commitment contract are analyzed. The supply chain with the risk sharing contract is further analyzed with a constant secondary market price and a yield dependent secondary market price. We present both the supplier’s and the retailer’s optimal strategies and provide insights for managers when making decisions under random yield risk and demand uncertainty. We find that the secondary market generally has a positive impact on supply chain performance and the actual effect of random yield risk on the supply chain performance depends on cost parameters and supply chain contract settings. Under certain conditions, reducing yield randomness may weaken the double marginalization effect and improve the chain performance. From the numerical study, we also show that there exists an optimal commitment level for the supply chain.     

Coordination mechanism for the supply chain with leadtime consideration and price-dependent demand

We study a coordination contract for a supplier–retailer channel producing and selling a fashionable product exhibiting a stochastic price-dependent demand. The product’s selling season is short, and the supply chain faces great demand uncertainty. We consider a scenario where the supplier reserves production capacity for the retailer in advance, and permits the retailer to place an order not exceeding the reserved capacity after a demand information update during a leadtime. We formulate a two-stage optimization problem in which the supplier decides the amount of capacity reservation in the first stage, and the retailer determines the order quantity and the retail price after observing the demand information in the second stage. We propose a three-parameter risk and profit sharing contract that coordinates the supply chain. The proposed contract permits any agreed-upon division of the supply-chain profit between the channel members.     

Study on the coordination contract in supply chain under trade credit based on risk compensation

Trade credit changes the inventory risk between supplier and retailer. This leads to failure in the coordination of the supply chain. Considering that the supplier bears the retailer’s inventory risk under the credit condition, in this paper, the contract is constructed by combining the risk compensation and quantity discount contract to re-coordinate the supply chain and analyze the contract. The results show that the contract can achieve voluntary supply chain coordination; and when the seller’s funds is within a certain range, the coordinate contract can perform in the form of the wholesale price contract, and the wholesale price is influenced by its own funds and product value. In the end, a numerical example is given to verify this conclusion.     

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.     

非对称信息下供应商-零售商供应链的批量折扣决策

在供应链管理的文献中,许多工作研究供应商如何使用激励手段,如数量折扣,去影响零售商的订货行为以增加供应商的利润(与整个供应链的利润).多种形式的激励策略模型已有许多,但通常有一个关键的假设,即,供应商关于零售商的成本结构具有完全信息.本文研究了在非对称信息下供应商的最优数量折扣决策问题,得到了最优策略,并与完全信息的情形进行了比较.