Supply Chain Coordination in the Presence of Gray Markets and Strategic Consumers

The practice of diverting genuine products to unauthorized gray markets continues to challenge companies in various industries and creates intense competition for authorized channels. Recent industry surveys report that the abuse of channel incentives is a primary reason for the growth of gray market activities. Therefore, it is crucial that companies take the presence of gray markets into consideration when they design contracts to distribute products through authorized retailers. This issue has received little attention in the extensive literature on contracting and supply chain coordination. In this study, we analyze the impacts of gray markets on two classic contracts, wholesale price and quantity discount, in a supply chain with one manufacturer and one retailer when the retailer has the opportunity to sell to a domestic gray market. Our analysis provides interesting and counterintuitive results. First, a classic quantity‐discount contract that normally coordinates the supply chain can perform so poorly in the presence of a gray market that the supply chain would be better off using a wholesale price contract instead. Second, the presence of gray market can also degrade the performance of the wholesale price contract; therefore, a more sophisticated contract is needed for coordinating the supply chain. We show that contracts that solely depend on retailer's order quantity cannot coordinate the supply chain, and provide the conditions for coordinating the supply chain with price‐dependent quantity discount contracts. We also provide comparative statics and show that when there is a gray market, coordinating the supply chain enhances total consumer welfare.     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.     

Price competition,cost and demand disruptions and coordination of a supply chain with one manufacturer and two competing retailers

This paper studies the coordination of a supply chain with one manufacturer and two competing retailers after the production cost of the manufacturer was disrupted. We consider two coordination mechanisms: an all-unit quantity discount and an incremental quantity discount. For each mechanism, we develop the conditions under which the supply chain is coordinated and discuss how the cost disruption may affect the coordination mechanisms. For the all-unit quantity discount scheme, we find that the manufacturer charges the lower-cost retailer for a lower unit wholesale price in order to induce him to order more products. If the costs of two retailers have a remarkable difference, then the all-unit quantity discount scheme cannot coordinate the supply chain with disruptions. While the cost disruption may affect the wholesale prices, order quantities as well as retail prices, it is optimal for the supply chain to keep the original coordination mechanism if the production cost change is sufficiently small. The model is also extended to the case with both cost and demand disruptions. The equilibrium strategies of the retailers are investigated when the manufacturer cannot timely react to the disruptions such that she has to keep the original mechanism. We illustrate the results by numerical examples.     

Discount Pricing Policies and the Coordination of Decentralized Distribution Systems*

A challenge of supply chain management is to align the objectives, and hence coordinate the activities, of independent supply chain members. In this study, we approach this problem in a simple way by extending traditional quantity discounts that are based solely on buyers' individual order size to discount policies that are based on both buyers' individual order size and their annual volume. We show that discount policies are able to achieve nearly optimal system profit and, hence, provide effective coordination, for a decentralized two‐echelon distribution system, whereby a supplier sells a product to a group of heterogeneous and independent retailers each facing a downward‐sloping demand curve of its retail price. When buyers are heterogeneous, a critical issue of coordination is to motivate different customers to increase their demand and lot size according to their potential so as to improve profits. We show that market heterogeneity presents an effective discriminating factor for the supplier to segment customers in the design of a coordination mechanism.     

Coordinating contracts for a financially constrained supply chain

We consider a financially constrained supply chain in which a supplier (leader) sells products to a retailer (follower) who has no access to bank financing due to her low credit rating. However, the supplier can borrow from a bank and offer trade credit to the retailer to alleviate her financial constraint. Failure to pay off a bank loan or trade credit incurs a variable default cost. We analyze the centralized version of the supply chain to obtain new coordination requirements. We then examine whether revenue-sharing, buyback, and all-unit quantity discount contracts can coordinate our supply chain. We show that the all-unit quantity discount contract fails to coordinate. However, the revenue-sharing and buyback contracts can coordinate the supply chain, but only when the supply chain has a sufficient total working capital. Moreover, they cannot allocate profit flexibly unless the supplier has a large enough working capital. Finally, we design a generalized revenue-sharing contract that coordinates the supply chain with flexible profit allocation, and also show by numerical examples its superiority over the revenue-sharing and buyback contracts.     

Controlling Power Retailer's Gray Activities Through Contract Design

We develop a model that captures dynamic relationships of a supply chain populated by a dominant retailer and a number of fringe retailers. The two types of retailers are asymmetric in buying power, retailing cost, and the ability to service the manufacturer's product. The wholesale prices offered through a quantity discount (QD) schedule can coordinate such a supply chain, but invite channel flow diversion type of gray trading between the dominant retailer and the fringe retailers. Our analysis is focused on how such a channel can be coordinated and the gray market activities be prevented. We propose a dynamic QD contract or a revenue‐sharing contract that the manufacturer can use to fight the gray market activity. The performance of the supply chain and the manufacturer's profit under each of the two contract forms are compared and managerial guidelines are provided to help the manufacturer make a judicious choice.     

Impact of secondary market on consumer return policies and supply chain coordination

In this paper, we develop a unified model to study the inventory management problem of a product and the coordination of the associated supply chain consisting of a single supplier and considerably many retailers in the presence of a secondary market. Specifically, consumer returns are allowed in the initial sales. Then, we introduce a secondary market to salvage the returns and the leftovers from the initial sales. In this secondary market, a discount price will be offered to the consumers but no returns are accepted. Moreover, between the primary and the secondary market, there is an internal market where retailers can trade among themselves so that they are able to adjust their inventory levels to prepare for the sales in the secondary market. We study the retailers' and the supply chain's inventory decision in this case and highlight the impact of the secondary market on the sales as well as on the supply chain coordination contracts. We conclude that the secondary market helps us to increase the total wholesale volume. Numerical examples show that the total sales profit is also increased. However, the secondary market aggravates the incentive conflict between the retailers and the supply chain on deciding the optimal inventory levels and hence requires the supplier to offer more generous buyback or sales rebate contracts for coordination of the supply chain. Finally, we extend our analysis to more general cases and also show that our results are robust to some of the modeling assumptions.     

Potentially self-defeating: Group buying in a two-tier supply chain

Retailers have an incentive to cooperate in the form of group buying (GB) when a supplier provides quantity discounts, because wholesale price under GB depends on total purchasing quantity rather than individual purchasing (IP) quantity. Most previous studies on GB focus on the benefits that buyers get but ignore the supplier׳s response to GB. In this paper, we take the supplier׳s response into consideration, and present a game model with a single supplier and two symmetric competing retailers in two systems: the retailers purchase individually, and the retailers group buy. Under a general quantity discount schedule, each system has a unique sub-game perfect equilibrium. The comparison between IP and GB suggests that GB may sabotage the benefits of all members in the supply chain (i.e., the supplier, the retailers, and the consumer). Retailers may hold contradictory attitudes toward GB before and after the publishing of the discount schedule. These insights are shown to be robust for the case when more than two retailers are involved, as well as the case when the supplier enjoys economies of scale based on the order volume. We suggest that a mixed discount schedule may help prevent the potential damage of GB. In addition, with significant economies of scale, the supplier and retailers may be better off under GB. Then GB can be a favorable purchasing strategy.     

两零售商竞争下多因素同时扰动的供应链协调研究

本文研究了由一个制造商两个竞争零售商组成的供应链在百川德博弈下,生产成本、市场需求和价格敏感系数同时扰动的协调机制,考虑了线性数量折扣契约对供应链的协调作用。研究表明,当三因素同时发生扰动后, 集权式供应链中线性数量折扣契约可以协调供应链,而在分散式供应链中,原来的协调契约不具有鲁棒性,制造商只有采用新的线性数量折扣契约,分散式供应链才能实现协调。 最后用一个算例验证了结论。     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

Pay‐Back‐Revenue‐Sharing Contract in Coordinating Supply Chains with Random Yield

We consider coordination issues in supply chains where supplier's production process is subject to random yield losses. For a simple supply chain with a single supplier and retailer facing deterministic demand, a pay back contract which has the retailer paying a discount price for the supplier's excess units can provide the right incentive for the supplier to increase his production size and achieve coordination. Building upon this result, we consider coordination issues for two other supply chains: one with competing retailers, the other with stochastic demand. When retailers compete for both demand and supply, they tend to over‐order. We show that a combination of a pay back and revenue sharing mechanism can coordinate the supply chain, with the pay back mechanism correcting the supplier's under‐producing problem and the revenue sharing mechanism correcting the retailers' over‐ordering problem. When demand is stochastic, we consider a modified pay‐back‐revenue‐sharing contract under which the retailer agrees to not only purchase the supplier's excess output (beyond the retailer's order), but also share with the supplier a portion of the revenue made from the sales of the excess output. We show that this contract, by giving the supplier additional incentives in the form of revenue share, can achieve coordination.     

具有风险规避销售商的供应链最优回购契约

在销售商风险规避下,运用CVaR方法研究了供应商在直营渠道（集中式供应链）和非直营渠道（分散式供应链）下回购契约的设计问题。刻画了集中式供应链下回购契约完成渠道协调的充要条件,求解了分散式供应链的最优回购契约。比较分析了集中式和分散式供应链下回购契约的差异,得到以下结论：相对于集中式供应链,供应商在分散式供应链中趋向于设定更高的批发价格,或更低的回购价格。讨论了销售商的风险规避度对契约设计和供应商收益的影响,研究表明：销售商越规避风险,供应商的收益越低。最后提供一个案例讨论了模型在现实中的应用。     

零售商退出风险的供应链冲击与协调契约分析

零售商退出会导致供应链合作关系的终止,冲击供应链合作运营的基础,供应链企业需要合作应对吗?本文以数量折扣契约下的协调供应链为研究框架,研究存在零售商退出风险时传统数量折扣契约的供应链运作,并构建改进契约下的供应链协调模型。通过理论推演与仿真分析发现,零售商退出风险对供应链运作可能造成巨大的冲击,同时也惊讶地发现,虽然数量折扣契约在冲击下不能协调运作,但运作效率非常高。建议契约调整成本不高的供应链可选择我们改进后的协调数量折扣契约。     

Wholesale Pricing under Mild and Privately Known Concerns for Fairness

This article studies the performance of wholesale pricing when the supply chain partners' fairness concerns are private information. We find that some properties of wholesale pricing established under complete information hold under incomplete information as well. First, wholesale pricing can coordinate the supply chain, despite the information asymmetry, when fairness concerns are strong enough. Second, in the case when an equitable profit split does not imply that the retailers profit must be higher than that of the supplier, the suppliers' equilibrium offer is never rejected. Overall, the study makes two primary contributions. First, it provides a partial characterization of the equilibrium when the conditions required for coordination do not hold, that is, when fairness concerns are mild. In this case, the model predicts that the expected market price must be exactly the same as under complete information. The channel efficiency, nevertheless, is strictly lower than under complete information. The distribution‐free lower bound on channel efficiency suggests that this efficiency loss should be quite small, though. Second, it provides an experimental test of the models' predictions as well as a direct validation of the assumptions of preferences heterogeneity and mildness by obtaining the empirical distribution of the preferences.     

考虑公平关切行为下竞争零售商的最优联合购买策略研究

本文考虑一个由两个竞争的零售商和一个供应商组成的两级供应链,其中供应商可通过提供批量折扣契约向两家竞争的零售商销售产品,而零售商表现出纵向公平关切(即当获得利润小于供应商的利润时,其获得一个负效用)。并且,考虑的两个零售商为了获得较低的批发价格可能更喜欢团购,进而它们将选择最佳订单数量来最大化其自身的效用。利用经典的纳什议价解决方案作为公平参考点,本文主要研究竞争与公平关切行为将如何影响零售商的联合购买策略。研究发现,当零售商追求公平时,联合购买策略优于单独购买策略,且越大竞争强度使得使用联合购买策略的优势越明显。此外,当零售商表现出不同的公平关切程度时,若批量折扣比例比较低,对公平关切敏感的零售商的效用总是小于对公平关切不敏感的零售商的效用;否则,对公平关切敏感的零售商的效用总是大于对公平关切不敏感的零售商的效用。     

Hierarchical Screening for Capacity Allocation in Supply Chains: The Role of Distributors

We consider a two‐stage principal–agent screening environment in a decentralized supply chain with retailers, distributors, and a supplier. The retailers possess private information regarding their local market profitabilities. The distributors can partially observe the retailers' profitabilities and are heterogeneous with regard to the precision of that information. The supplier determines the level of production, but knows neither the local market profitabilities nor the precision of the distributors' information. The supplier first allocates finished products to distributors, and the distributors then contract with local retailers with a capacity constraint. We find that due to the distributors' superior information, the quantity distortion on the retailers' side is mitigated, and the upstream information asymmetry subsequently affects the quantity allocation among the downstream retailers. The supplier may not benefit from contracting with the distributors. In addition, no distributor is excluded based on the heterogeneity of the information precision, even though some distributors do not have better information than the supplier. In the numerical examples, we further analyze how the local market heterogeneity and inventory costs affect the capacity allocation, the retailers' payoffs, and the supply chain profits. We document some counter‐intuitive quantity allocation rules that arise from the distributors' information advantage.     

多零售商供应链应对突发事件的协调机制研究

本文针对一个供应商和n个Cournot竞争零售商组成的供应链系统,从系统优化和企业管理的角度研究了该供应链系统如何应对突发事件。首先证明稳定条件下的收益共享合约能实现该供应链协调。但突发事件引起的成本和需求的扰动会打破供应链协调,当突发事件导致供应链的市场需求增加而生产成本减少时,供应商必须通过增加生产来应对突发事件;当突发事件导致供应链的市场需求减少而生产成本增加时,供应商必须通过减少生产来应对突发事件;并通过求解突发事件下供应链系统最优利润的Karush-Kuhn-Tucker(KKT)条件,提出了供应链在一体化时应对突发事件的最优策略。进一步证明了改进的收益共享合约可以协调突发事件下分散化决策的供应链系统。最后运用数值实验对模型进行了验证。     

Channel Coordination with a Risk‐Neutral Supplier and a Downside‐Risk‐Averse Retailer

We investigate how a supply chain involving a risk‐neutral supplier and a downside‐risk‐averse retailer can be coordinated with a supply contract. We show that the standard buy‐back or revenue‐sharing contracts may not coordinate such a channel. Using a definition of coordination of supply chains proposed earlier by the authors, we design a risk‐sharing contract that offers the desired downside protection to the retailer, provides respective reservation profits to the agents, and accomplishes channel coordination.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

Channel Coordination for a Supply Chain with a Risk‐Neutral Manufacturer and a Loss‐Averse Retailer*

This articles considers a decentralized supply chain in which a single manufacturer is selling a perishable product to a single retailer facing uncertain demand. It differs from traditional supply chain contract models in two ways. First, while traditional supply chain models are based on risk neutrality, this article takes the viewpoint of behavioral principal–agency theory and assumes the manufacturer is risk neutral and the retailer is loss averse. Second, while gain/loss (GL) sharing is common in practice, there is a lack of analysis of GL‐sharing contracts in the supply chain contract literature. This article investigates the role of a GL‐sharing provision for mitigating the loss‐aversion effect, which drives down the retailer order quantity and total supply chain profit. We analyze contracts that include GL‐sharing‐and‐buyback (GLB) credit provisions as well as the special cases of GL contracts and buyback contracts. Our analytical and numerical results lend insight into how a manufacturer can design a contract to improve total supply chain, manufacturer, and retailer performance. In particular, we show that there exists a special class of distribution‐free GLB contracts that can coordinate the supply chain and arbitrarily allocate the expected supply chain profit between the manufacturer and retailer; in contrast with other contracts, the parameter values for contracts in this class do not depend on the probability distribution of market demand. This feature is meaningful in practice because (i) the probability distribution of demand faced by a retailer is typically unknown by the manufacturer and (ii) a manufacturer can offer the same contract to multiple noncompeting retailers that differ by demand distribution and still coordinate the supply chains.