Pareto analysis of supply chain contracts under satisficing objectives

Supply chain coordination has become critical to firms as increased pressure is placed on them to improve performance. We evaluate the performance of Push, Pull, and Advance-purchase discount (APD) contracts in a manufacturer-retailer supply chain where one or both firms have a satisficing objective of maximizing the probability of achieving a target profit. We identify the resulting operational modes of the supply chain and potential conflicts over the preferred contracts under the Push, Pull, and APD contracts. When both firms are satisficing, conflict over the preferred contract arises when the manufacturer has an ambitious profit target or the retailer has a low profit target. We show that the Push contract can result in a large decrease in the expected profit of a risk-neutral manufacturer when the retailer maximizes the probability of achieving her maximum expected profit. We find that a modified buy-back and profit guarantee contracts can provide significant Pareto improvement over Push or APD contracts when the manufacturer is risk-neutral and the retailer is satisficing, while revenue-sharing contracts cannot. In contrast, revenue sharing and modified buy-back contracts are Pareto dominant under certain conditions when the manufacturer is satisficing and the retailer is risk-neutral.     

产出不确定性的三级供应链风险分担组合契约设计

研究了供应商和制造商产出随机且零售商面临随机需求的三级供应链协调模型,决策变量为供应商的原材料投入量、制造商的订购量和零售商的订购量。分析了集中决策下供应链协调基准的唯一性,论证了回购契约及其与产出风险分担组合契约的协调性。研究结果表明,对于产出和需求不确定的三级供应链,仅考虑在制造商和零售商之间采用回购契约可改善供应链绩效,但并不能实现供应链的全局最优化,而从风险分担的角度设计的回购和产出风险分担组合契约不仅能有效的协调供应链,且在一定条件下,各供应链成员的利润还能获得帕累托改进。通过算例验证了以上结论的正确性,并分析了回购价格对订购量、原材料投入量和利润的影响,以及各供应链成员对契约的偏好。     

Wholesale-price contract of supply chain with information gathering

This paper investigates a wholesale-price contract of supply chain under the endogenous information structure. This supply chain consists of one supplier and one retailer during the selling season. The retailer does not know his selling cost but can spend resources to acquire information. The supplier offers a contract, which induces the retailer to gather information and generate more production orders with beta costs. We find that there exists an upper bound of the information gathering cost such that the supplier induces the retailer to gather information. The increasing cost of information gathering may decrease the order quantity and wholesale price. Moreover, the cost beta has an impact on the expected profits of the two parties. With the increasing cost of information gathering, the supplier’s expected profit is reduced, while that of the retailer becomes ambiguous in terms of the distribution function and the interval of selling cost information. Finally, a numerical example is presented to explain the main results.     

Inventory competition and allocation in a multi-channel distribution system

Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.     

Manufacturer’s revenue-sharing contract and retail competition

This paper investigates a revenue-sharing contract for coordinating a supply chain comprising one manufacturer and two competing retailers. The manufacturer, as a Stackelberg leader, offers a revenue-sharing contract to two competing retailers who face stochastic demand before the selling season. Under the offered contract terms, the competing retailers are to determine the quantities to be ordered from the manufacturer, prior to the season, and the retail price at which to sell the items during the season. The process of pricing and ordering is expected to result in an equilibrium as in the Bayesian Nash game. On the basis of anticipated responses and actions of the retailers, the manufacturer designs the revenue-sharing contract. Adopting the classic newsvendor problem model framework and using numerical methods, the study finds that the provision of revenue-sharing in the contract can obtain better performance than a price-only contract. However, the benefits earned under the revenue-sharing contract by different supply chain partners differ because of the impact of demand variability and price-sensitivity factors. The paper also analyses the impact of demand variability on decisions about optimal retail price, order quantity and profit sharing between the manufacturer and the retailers. Lastly, it investigates how the competition (between retailers) factor influences the decision-making of supply chain members in response to uncertain demand and profit variability.     

碳排放交易机制下的供应链运作策略及协调研究

碳排放权交易是控制和减少碳排放的有效工具,同时也使得企业的运作成本增加,供应链的决策管理更复杂。考虑由零售商和制造商组成的二阶段供应链,研究不同碳排放权交易政策(供应链成员内部碳排放权交易、外部市场碳排放权交易)下基于数量折扣契约的供应链协调问题,并与无碳排放约束的情形进行比较。研究结果表明:在不同碳排放权交易政策下,数量折扣契约能够实现供应链的协调;无碳排放约束的供应链最优订货量大于外部碳排放权交易的供应链最优订货量,成员内部碳排放交易下的供应链最优订货量和供应链期望利润随着碳排放配额的增加最终等于无碳排放约束下的供应链最优订货量和供应链期望利润;外部市场碳排放交易政策下供应链的期望利润随着碳排放配额的增加而增加。     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

强制减排规制下基于碳减排利润增量分享契约的供应链协调研究

碳减排会增加制造商的成本,导致批发价和零售价提高,从而抑制市场需求。以此为背景,本文针对由一个制造商和一个零售商组成的供应链,研究了强制减排规制下考虑消费者低碳偏好时的供应链决策与协调。通过设计碳减排利润增量分享契约协调制造商和零售商的决策,实现帕累托改进,利用Rubinstein讨价还价模型最终确定减排利润分享比例。研究发现,实施碳减排利润分享契约能有效提高零售商的订货量,并降低批发价格;制造商的利润随着消费者低碳意识提高而提高;当净化率较低时,零售商的利润随消费者低碳意识提高而提高;当净化率较高时,零售商的利润随消费者低碳意识提高而降低;最后,论文通过数值模拟验证了碳减排利润分享契约的有效性。     

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.     

碳限额与交易机制下受资金约束的供应链优化

在碳限额与交易机制下,研究零售商受资金约束的供应链优化问题。构建了制造商占优的两级供应链Stackelberg博弈模型,通过引入减排成本分担机制,分别给出了分散决策和集中决策的最优解。通过收益共享契约,实现了供应链协调和供应链成员利润的帕累托改善。通过算例分析了不同减排成本分担系数、碳交易价格对供应链利润和订购量、碳减排决策的影响,为供应链各成员开展减排合作提供了理论依据。研究结果表明,供应链成员的合作不仅可以提高供应链总绩效,而且有利于为消费者提供更多、更绿色的产品;碳价格的提高,促使供应链更加努力减排,从而提高了供应链总利润。     

需求不确定下制造商为核心的三级供应链协调

在需求不确定的情境下,研究由单一供应商、制造商和销售商组成的三级供应链系统的协调问题。设计了制造商—销售商采用期权契约,制造商—供应商采用回购契约的联合契约协调机制,分析了集中控制、分散控制和协调机制下供应链系统的最优决策。最后,通过数值算例说明了机制设计的有效性,并对分析结果进行验证。研究结果表明,通过制定合理的契约参数可以使供应链各成员的期望利润相比分散决策时有帕累托改进,从而实现三级供应链系统的协调。     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Analysis of the impact of price-sensitivity factors on the returns policy in coordinating supply chain

This paper analyzes the impact of price-sensitivity factors on characteristics of returns policy contracts in a single-period product supply chain. The contract considers stochastic and price-dependent demand. We present an analytical model and then use numerical methods with the Stackelberg game to identify the contract properties. We numerically show that a returns policy indeed improves supply chain performance. However, the benefits earned from the returns policy, under price-sensitive and variable demand, are different for different supply chain partners. First, when price-sensitivity is high, profit of the manufacturer decreases with increase in demand variability. Second, when price-sensitivity is sufficiently high and demand variability increases, the manufacturer has to surrender part of the profits to the retailer, in order to continue sales. However, even after surrendering part of the profits to the retailer, the manufacturer still earns profits that are higher than those available in a wholesale price contract. Last, from the perspective of division of channel profits, the retailer is always worse off in case of returns policies than in a wholesale price contract. Therefore, to apply this form of incentive in practice, managements should consider the impact of price-sensitivity on the returns policy and its performance.     

具有价格粘性的供应链动态模型及其协调策略

本文针对由一个制造商和一个零售商构成的供应链系统,在市场价格具有粘性的情况下,利用动态博弈理论分析了制造商和零售商如何确定其最优的批发价格和产品订购量以实现自身长期利润的最大化。本文首先利用汉密尔顿-雅可比-贝尔曼方程分别求解了供应链系统在Stackelberg博弈下的最优批发价格和最优产品订购数量。然后,利用数值算例说明了该供应链系统协调的必要性。最后,利用数量折扣契约协调了该供应链系统,并证明了协调的有效性。     

Supply chains in the presence of store brands

Increased competition from store brands is forcing manufacturers to re-evaluate their strategies in regard to pricing and contracting with trade intermediaries. We analyze a supply chain in which a retailer accepts (with the appropriate contractual agreements) a national brand for resale and then determines whether to introduce a store brand, how to price the store brand, and what quantities of the product(s) to order. We show that when the national brand’s cost per unit quality (CPUQ) is larger than the store brand’s CPUQ, then the retailer seeks to introduce the store brand (SB) and the national brand (NB) manufacturer/supplier is unable to deter him from doing so. We find that the efficiency loss in the decentralized supply chain becomes smaller when a store brand is introduced. Recognizing the inadequacy of standard contracts in coordinating this supply chain, we propose a simple minimum order quantity contract that can coordinate this supply chain.     

A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains

Vertical cooperative (co-op) advertising is a marketing strategy in which the retailer runs local advertising and the manufacturer pays for a portion of its entire costs. This paper considers vertical co-op advertising along with pricing decisions in a supply chain; this consists of one manufacturer and one retailer where demand is influenced by both price and advertisement. Four game-theoretic models are established in order to study the effect of supply chain power balance on the optimal decisions of supply chain members. Comparisons and insights are developed. These embrace three non-cooperative games including Nash, Stackelberg-manufacturer and Stackelberg-retailer, and one cooperative game. In the latter case, both the manufacturer and the retailer reach the highest profit level; subsequently, the feasibility of bargaining game is discussed in a bid to determine a scheme to share the extra joint profit.     

Channel incentives in sharing new product demand information and robust contracts

Demand for a new product is often highly uncertain. As the developer of a new product, the manufacturer may reduce the uncertainty of the product’s demand through observing progress in his product development process or receiving demand signals directly from customers. This paper first shows that a centralized channel always benefits from improved demand information. Yet, to realize this benefit in a decentralized manufacturer–retailer channel, the manufacturer needs to disclose his private demand information to the retailer. We show that the manufacturer’s incentive to share his improved demand information depends on the supply contract signed with the retailer. Furthermore, mandating the manufacturer to disclose his improved demand information can actually reduce the total channel profit. We provide managerial insights by analyzing three widely used contract forms. We investigate whether these contracts are robust under an unanticipated demand information update observed by the manufacturer. We show that the quantity flexibility contract with a high return rate is not robust. The buyback contract, however, is robust and always achieves information sharing while preserving channel performance.     

基于流程创新的供应链激励合同研究

针对由一个零售商两个制造商组成的竞争供应链,建立了零售商处于领导地位的Stackelberg博弈模型。分析了收益分享合同和成本分担合同下流程创新效率和竞争强度对流程创新水平和供应链成员利润的影响,并探讨了最优激励合同类型。研究发现,流程创新效率的降低会使得制造商流程创新水平和供应链成员利润降低;竞争强度的增大会使得制造商流程创新水平和供应链成员利润增加。此外,在流程创新效率较高和竞争强度较低时零售商提供收益分享合同有利,在流程创新效率较低和竞争强度较高时零售商提供成本分担合同有利。     

预付款融资下期权契约的协调研究

本文研究零售商占主导、供应商自有资金有限的二级供应链如何通过契约实现协调的问题。在预付款融资的基础上加入期权契约方法,构建用于预付款融资的期权契约模型,并求解出该模型下所能协调供应链的契约参数与此时零售商供应商双方的最优决策系统。研究表明当供应商自有资金大于等于某临界值时通过预付款融资下的期权契约可实现供应链协调。若小于则无法通过该契约协调,并且供应商自有资金约束越大,零售商最优订购数量越多,同时供应商的最优生产数量随着自有资金的减少而减少,供应链的参与者及整个供应链的利润也随着供应商自有资金的减少单调递减;另外,相比于无融资下的期权契约,预付款模式能提高零售商、供应商以及整个供应链的收益。     

A two-echelon supply chain of a returnable product with fuzzy demand

This study investigates the effects of the manufacturer’s refund on retailer’s unsold products for the two-echelon decentralized and centralized supply chains of a short life and returnable product with trapezoidal fuzzy demand, in which retailer returns the unsold and the customer’s unsatisfactory products to the manufacturer. For each returnable chain, we obtain the closed-form solution of order quantity to maximize the total expected profit of the supply chain, and confirm that demand fuzziness does indeed affect the order quantity and the members’ expected profits. We provide a number of managerial insights by comparing both chains and show that each chain is more advantageous to the members depending on certain condition. Our models are appropriate for a supply chain with a returnable product that lacks information about the demand.