Supply Contract Design for Competing Heterogeneous Suppliers under Asymmetric Information

This study considers a supply chain with two heterogeneous suppliers and a common retailer whose type is either low‐volume or high‐volume. The retailer's type is unknown to the suppliers. The flexible supplier has a high variable cost and a low fixed cost, while the efficient supplier has a low variable cost and a high fixed cost. Each supplier offers the retailer a menu of contracts. The retailer chooses the contract that maximizes its expected profit. For this setting, we characterize the equilibrium contract menus offered by the suppliers to the retailer. We find that the equilibrium contract menus depend on which supplier–retailer match can generate the highest supply chain profit and on how much information rent the supplier may need to pay. An important feature of the equilibrium contract menus is that the contract assigned to the more profitable retailer will coordinate the supply chain, while the contract assigned to the less profitable retailer may not. In addition, in some circumstances, the flexible supplier may choose not to serve the high‐volume retailer, in order to avoid excessive information rent.     

Coordination in a Single‐Supplier,Multi‐Retailer Distribution System: Supplier‐Facilitated Transshipments

We consider supplier‐facilitated transshipments for achieving supply chain coordination in a single supplier, multi‐retailer distribution system with non‐cooperative retailers. The previous transshipment literature has focused on coordination through retailer‐negotiated transshipments and thus does not consider the supplier's decision‐making. In contrast, in this study, we assume the supplier is an active participant in the system and we seek to understand how the supplier can facilitate the implementation of coordinating transshipments. We study a two‐period model with wholesale orders at the start of the first period and preventive transshipments performed at the start of the second period. Inspired by a supplier‐facilitated transshipment scheme observed in practice, we assume the supplier implements transshipments through a bi‐directional adjustment contract. Under this contract, each retailer can either buy additional inventory from, or sell back excess inventory to, the supplier. We show that coordination can be achieved through carefully designed contracts with state‐dependent adjustment prices and a wholesale price menu. We demonstrate that the supplier's role in facilitating coordinating transshipments is critical. In addition, we use our understanding of the coordinating contract form to derive some simpler and easier‐to‐implement heuristic contracts. We use a numerical study to demonstrate the value, to the supplier, of using the coordinating adjustment and wholesale prices, and to evaluate the heuristics’ performance.     

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.     

消费者低碳偏好下的供应链收益共享契约研究

在消费者对低碳产品存在偏好并且企业自愿减排的假定下,探讨了在由单个供应商与单个零售商构成的两级供应链中零售商确定最佳订货水平和供应商选择减少碳排放水平的决策问题。研究发现单位产品碳排放过大时,供应商不会选择减排;当单位排放较低时,选择减排战略会改善供应商和零售商的收益状况,可以实现供应链成员收益的帕累托改进;而当单位排放处于两者之间时,选择减排战略会使供应商的收益状况变差,使零售商的收益和供应链总体收益增加,虽然存在着改善供应链渠道收益状况的空间,但供应商没有减排动力,减排无法实施。针对这一问题,本文设计了收益共享契约来协调两者之间的关系,实现了帕累托改进。最后,利用Rubinstein讨价还价模型来分析分成比例在给定区间确定问题。     

Designing Supply Contracts Considering Profit Targets and Risk

Managers at all stages of a supply chain are concerned about meeting profit targets. We study contract design for a buyer–supplier supply chain, with each party maximizing expected profit subject to a chance constraint on meeting his respective profit target. We derive the optimal contract form (across all contract types) with randomized and deterministic payments. The best contract has the property that, if the chance constraints are binding, at most one party fails to satisfy his profit target for any given demand realization. This implies that “least risk sharing,”that is, minimizing the probability of outcomes for which both parties fail to achieve their profit targets, is optimal, contrary to the usual expectations of “risk sharing.” We show that an optimal contract can possess only two of the following three properties simultaneously: (i) supply chain coordination, (ii) truth‐telling, and (iii) non‐randomized payments. We discuss methods to mitigate the consequent implementation challenges. We also derive the optimal contract form when chance constraints are incorporated into several simpler and easier‐to‐implement contracts. From a numerical study, we find that an incremental returns contract (in which the marginal rebate rate depends on the return quantity) performs quite well across a relatively broad range of conditions.     

Push and Pull Contracts in a Local Supply Chain with an Outside Market*

Wholesale price contracts are widely studied in a single supplier‐single retailer supply chain, but without considering an outside market where the supplier may sell if he gets a high enough price and the retailer may buy if the price is low enough. We fill this gap in the literature by studying push and pull contracts in a local supplier–retailer supply chain with the presence of an outside market. Taking the local supplier's maximum production capacity and the outside market barriers into account, we identify the Pareto set of the push and/or pull contracts and draw managerial implications. The main results include the following. First, the most inefficient point of the pull Pareto set cannot always be removed by considering both the push and pull contracts. Second, the supplier's production capacity plays a significant role in the presence of an outside market; it affects the supplier's negotiating power with the retailer and the coordination of the supply chain can be accomplished only with a large enough capacity. Third, the import and export barriers influence the supply chain significantly: (i) an export barrier in the local market and the supplier's production capacity influence the supplier's export strategy; (ii) a low import (resp., export) barrier in the local market can improve the local supply chain's efficiency by use of a push (resp., pull) contract; and (iii) a high import (resp., export) barrier in the local market encourages the supplier (resp., retailer) to bear more inventory risk.     

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。     

A delay-in-payment contract for Pareto improvement of a supply chain with stochastic demand

We consider a supply chain consisting of a single supplier and a single retailer with stochastic customer demand, which is operated over an infinite horizon. We propose a delay-in-payment contract to coordinate the supply chain. With this contract, the supplier allows the retailer to pay partial order cost at the ordering epoch, and to pay the remaining portion after a permissible number of periods. The system is formulated as a stochastic dynamic programming problem. It is shown that there exists a base-stock policy to be optimal. Compared with the traditional wholesale-price contract, the delay-in-payment contract with appropriate parameters can achieve a Pareto improvement (i.e., the performances of both the supplier and the retailer using the delay-in-payment contract are better than those using the wholesale-price contract). Numerical studies are performed to investigate both the effectiveness of the Pareto improvement, and the impact of the major parameters of the delay-in-payment contract on the system performance.     

价格柔性合同下的原材料采购策略及风险分析

为了降低原材料价格波动给采购-供应双方企业带来的风险,供应链企业通常采用签订价格合同的方式来共同分担原材料价格波动的风险。本文通过设计价格柔性合同,利用Stackelberg主从博弈模型研究了由一个供应商和一个制造商组成的采购系统的最优采购策略及原材料价格波动风险的分担机制。研究表明,通过实施价格柔性合同可以降低供应双方的风险,且通过设置合理的价格柔性系数可以提高双方的收益。     

Stable and Coordinating Contracts for a Supply Chain with Multiple Risk‐Averse Suppliers

We analyze a decentralized supply chain with a single risk‐averse retailer and multiple risk‐averse suppliers under a Conditional Value at Risk objective. We define coordinating contracts and show that the supply chain is coordinated only when the least risk‐averse agent bears the entire risk and the lowest‐cost supplier handles all production. However, due to competition, not all coordinating contracts are stable. Thus, we introduce the notion of contract core, which reflects the agents' “bargaining power” and restricts the set of coordinating contracts to a subset which is “credible.” We also study the concept of contract equilibrium, which helps to characterize contracts that are immune to opportunistic renegotiation. We show that, the concept of contract core imposes conditions on the share of profit among different agents, while the concept of contract equilibrium provide conditions on how the payment changes with the order quantity.     

Distributional and Peer‐Induced Fairness in Supply Chain Contract Design

Members of a supply chain often make profit comparisons. A retailer exhibits peer‐induced fairness concerns when his own profit is behind that of a peer retailer interacting with the same supplier. In addition, a retailer exhibits distributional fairness when his supplier's share of total profit is larger than his own. While existing research focuses exclusively on distributional fairness concerns, this study investigates how both types of fairness might interact and influence economic outcomes in a supply chain. We consider a one‐supplier and two‐retailer supply chain setting, and we show that (i) in the presence of distributional fairness alone, the wholesale price offer is lower than the standard wholesale price offer; (ii) in the presence of both types of fairness, the second wholesale price is higher than the first wholesale price; and (iii) in the presence of both types of fairness, the second retailer makes a lower profit and has a lower share of the total supply chain profit than the first retailer. We run controlled experiments with subjects motivated by substantial monetary incentives and show that subject behaviors are consistent with the model predictions. Structural estimation on the data suggests that peer‐induced fairness is more salient than distributional fairness.     

考虑风险规避的资金约束供应链最优信用契约设计

本文针对零售商的资金约束问题,研究了风险规避的供应商如何通过设计信用契约影响零售商的融资结构。构建了包含供应商、零售商以及银行在内的供应链融资模型,给出了供应商的最优信用契约决策、零售商的最优库存决策以及银行的最优利率决策。进一步分析了供应商的风险规避程度对最优信用契约决策的影响。研究表明：当供应商的风险规避程度低于某个临界值时,供应商偏好提供全额信用,从而零售商的融资结构为单一的交易信用融资;而当供应商的风险规避程度高于该临界值时,供应商偏好提供部分信用,从而零售商的融资结构为组合融资。最后,通过数值算例验证了本文的结论。本研究一定程度上丰富了现有供应链金融的理论研究,为供应链核心企业与银行的决策提供了依据与参考。     

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.     

一个考虑回收契约的两级供应链库存决策模型研究

讨论了一个季节性商品销售环境下的两级供应链库存决策模型,在分析传统回收契约模型的基础上,引入了一个特殊的回收契约,讨论不同契约参数下供应链成员的最优决策.研究表明,在该契约下通过合理的契约参数设计,供应链可以实现帕累托改进.用一个算例对结论进行了说明.     

公平感对供应链成员定价决策影响的研究

本文研究公平感对由一个供应商和一个零售商组成的二级供应链中的定价决策的影响,其中供应商决定批发价格,零售商在接受供应商批发价格合同之后决定零售价格,市场需求受到零售价格的线性影响.采用管理实验方法得出,首先,供应商的批发价格和零售商的零售价格均分别低于完全理性假设下的均衡解;供应商是利他性的,即,乐于看到零售商收益的增加,并且,供应商认为零售商是完全理性的,即零售商的决策目标是最大化自身收益;然而,零售商却是刻毒性的,即乐于看到供应商收益的减少.其次,批发价格的变异度大于零售价格的,即供应商决策的难度大于零售商的.给管理者的启示是:供应商应考虑零售商的刻毒性的特征,降低批发价格,以提高零售商接受供应商所提批发价格的概率;此外,还应该为供应商提供辅助决策手段,以降低批发价格的变异度,提高决策的准确性     

考虑初创企业的供应链融资与期权交易策略

考虑单供应商、单零售商组成的二级供应链，零售商作为初创企业面临资金短缺，但可以通过供应商贷款获得资金。除了提供资金支持，供应商还为零售商提供期权合约供其采购产品。通过对供应商期权价格和贷款利率，以及零售商的采购和融资策略进行分析，结论显示当产品生产成本较高时，供应商会设置较高的期权价格和贷款利率，获取整个供应链的利润。零售商期望利润为0并且面临较高的破产风险，而此时的博弈均衡是不稳定的。为了获得稳定博弈均衡，供应商需要稍微降低期权价格或贷款利率，以使零售商获得正的期望利润，此时零售商采购量会趋近于一个固定值。当生产成本较低时，供应商和零售商之间能够达到稳定的均衡解，且双方均有正的期望利润。     

Contracting and Coordination under Asymmetric Production Cost Information

We analyze a supply chain consisting of a supplier and a retailer. The supplier's unit production cost, which characterizes his type, is only privately known to him. When trading with the retailer, the supplier demands a reservation profit that depends on his unit production cost. We model this problem as a game of adverse selection. In this model, the retailer offers a menu of contracts, each of which consists of two parameters: the ordering quantity and the supplier's share of the channel profit. We show that the optimal contract depends critically on a surrogate measure—the ratio of the types’ reservation profit differential to their production cost differential. An important implication from our analysis is that information asymmetry alone does not necessarily induce loss in channel efficiency. The optimal contract can coordinate the supply chain as long as the low‐cost supplier's cost efficiency is neither much overvalued nor much undervalued in the outside market. We further discuss the retailer's preference of the supplier's type under different market conditions, as well as evaluate the effects of the supplier's reservation profit, the retail price, and the demand uncertainty on the optimal contract.     

Role of Random Capacity Risk and the Retailer in Decentralized Supply Chains with Competing Suppliers

This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers’ wholesale price competition and the incentive for reducing capacity uncertainty. In this dual‐sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single‐supplier case and a supplier‐duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single‐supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition.     

随机产出与需求下农产品供应链协调的收益共享合同研究

生鲜农产品生产受季节性和天气等影响,投入一定农资后产出呈随机分布。本文考虑产出和需求扰动服从均匀分布情形下,单个生产商和零售商的供应链协调问题。在收益共享合同模式下,生产商决定农资投入数(e)并将单一产品以低于生产成本的价格(ω)全部出售给零售商,零售商制定销售价格(p)进行销售并支付约定比例(1-Ф)的收益补偿生产商。在分析供应链协调的条件后,说明了合同参数ω与Ф的关系和Ф设定范围。研究结果表明,收益共享合同能有效地协调供应链,且协调的p和e与需求价格弹性有关;并且Ф取值范围随影响产出的随机变量的期望值变大而增大。最后以数值算例说明了分析结果的正确性。     

Enabling Opportunism: Revenue Sharing when Sales Revenues are Unobservable

We consider a supply chain with a supplier that sells to a retailer under a revenue‐sharing arrangement. Demand is uncertain and unobservable to the supplier. We assume that the retailer is rational, that is, the retailer behaves opportunistically and underreports sales revenues to the supplier whenever such underreporting is profitable. Assuming the supplier has the ability to audit the retailer and learn about the actual sales revenues, we show that the supplier will never find it optimal to audit to the point that ensures truthful reporting for all demand realizations. By committing to an auditing policy, the supplier can exploit retailer opportunism and derive profits that at times even exceed those that could be obtained when dealing with a retailer that always strictly adheres to the agreed‐upon contract terms. We also show that the retailer's opportunistic behavior can increase total supply chain profits.