Joint Mail‐In Rebate Decisions in Supply Chains Under Demand Uncertainty

We study the joint decisions of offering mail‐in rebates (MIRs) in a single‐manufacturer–single‐retailer supply chain using a game theoretic framework. Either party can offer an MIR to the end consumer if it is in his best interest. The consumer demand is stochastic and depends on the product price and the amount of MIRs. When the retail price is exogenous, we show the existence of a unique Nash equilibrium under both additive and multiplicative demand functions and characterize it completely. We show that any of the following four scenarios can be the equilibrium: both parties offer MIR, only one party offers MIR, none offers MIR. When the retail price is a decision variable for the retailer and the rebate redemption rate increases with the amount of MIR, we once again prove the existence of a unique Nash equilibrium where both the retailer and the manufacturer offer MIRs. Using a numerical study, we show that the average post‐purchase price of the product is higher not only than the perceived pre‐purchase price but also than the newsvendor optimal price without an MIR. This implies that an MIR makes a product look cheaper while the consumers actually pay more on average.     

Retailer's Response to Alternate Manufacturer's Incentives Under a Single‐Period,Price‐Dependent,Stochastic‐Demand Framework*

This article considers the joint development of the optimal pricing and ordering policies of a profit‐maximizing retailer, faced with (i) a manufacturer trade incentive in the form of a price discount for itself or a rebate directly to the end customer; (ii) a stochastic consumer demand dependent upon the magnitude of the selling price and of the trade incentive, that is contrasted with a riskless demand, which is the expected value of the stochastic demand; and (iii) a single‐period newsvendor‐type framework. Additional analysis includes the development of equal profit policies in either form of trade incentive, an assessment of the conditions under which a one‐dollar discount is more profitable than a one‐dollar rebate, and an evaluation of the impact upon the retailer‐expected profits of changes in either incentive or in the degree of demand uncertainty. A numerical example highlights the main features of the model. The analytical and numerical results clearly show that, as compared to the results for the riskless demand, dealing with uncertainty through a stochastic demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower (higher) pass throughs if additive (multiplicative) error, (iii) higher claw backs in both error structures wherever applicable, and (iv) higher rebates to achieve equivalent profits in both error structures.     

Multiperiod Models with Capacities in Competitive Supply Chain

This paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make‐to‐stock setting where the retailer can carry inventory. The retailer faces exogenous, price‐dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.     

基于电子市场的供应链双渠道冲突与协调的契约设计

研究了一个制造商通过传统零售渠道销售产品的同时开辟网上直销渠道,采取混合双渠道来销售产品的供应链渠道结构。从分析消费者效用出发,建立了双渠道环境下需求依赖价格变化的需求函数,运用博弈论建立决策模型。结果表明制造商在保持传统渠道的同时,开辟电子渠道将导致传统零售商的市场份额减少,利润降低,引起渠道冲突。为了解决混合双渠道的冲突和协调,设计了批发价加电子渠道价格的合同实现了双渠道供应链的协调,通过改进的收入共享契约不但实现了双渠道供应链的协调,而且实现了开辟电子渠道后供应链各成员利润的帕累托改进,从而实现了供应链双渠道冲突的协调问题。     

风险规避型供应链的收益共享机制研究

探讨了由风险规避型零售商与风险规避型供应商组成的两级供应链协作激励问题.首先研究了Stackelberg主从对策模型下风险规避型零售商与风险规避型供应商的决策行为,并分析了双方的风险规避系数对双方决策行为的影响.然后,研究了垂直一体化模型下风险规避型供应链的决策行为,同样分析了双方风险规避系数对供应链决策行为的影响程度.最后,提出采用收益共享契约机制来协调该供应链.并通过数值实验进一步分析供应商与零售商的风险规避系数对双方的决策行为及收益共享系数的影响程度.     

Competition and Coordination in a Two‐Channel Supply Chain

We study competition and coordination in a supply chain in which a single supplier both operates a direct channel and sells its product through multiple differentiated retailers. We study analytically the supply chain with symmetric retailers and find that the supplier prefers to have as many retailers as possible in the market, even if the retailers' equilibrium retail price is lower than that of the supplier, and even if the number of retailers and their cost or market advantage prevent sales through the direct channel. We find that the two‐channel supply chain may be subject to inefficiencies not present in the single‐channel supply chain. We show that several contracts known to coordinate a single‐channel supply chain do not coordinate the two‐channel supply chain; thus we propose a linear quantity discount contract and demonstrate its ability to perfectly coordinate the two‐channel supply chain with symmetric retailers. We provide some analytical results for the supply chain with asymmetric retailers and propose an efficient solution approach for finding the equilibrium. We find numerically that the supplier still benefits from having more retailers in the market and that linear quantity discount contracts can mitigate supply chain inefficiency, though they no longer achieve perfect coordination.     

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.     

基于无缺陷退货的网上销售易逝品供应链协调模型

本文针对网上在线销售易逝品的无缺陷退货现象,考虑了供应链的最优订购协调问题。利用一个两阶段动态规划来描述动态市场环境下网上销售商的两次订购行为,在假定在两个销售阶段都发生无缺陷退货现象的前提下,分别建立了集中和分散决策模型,同时设计了价格保护契约以实现供应链的协调运作。最后,利用数值仿真得出了一些重要的管理启示。通过研究发现：（1）当不确定性较大时,网上销售商需要在第1阶段多订购产品以应对需求风险,因此导致了较低的系统期望利润。并且,需求的不确定性越大,供应链协调越有价值。（2）当第1阶段或第2阶段退货率或两阶段退货率都增加时,两个阶段的最优订购量均减小。（3）对于需求波动性较高的产品,顾客的退货率越小或者可服务退货率越大,价值越高（即对供应链系统期望利润的提高越显著）。     

服务水平约束下基于顾客策略性退货的供应链契约协调研究

研究由一个制造商和一个零售商及一组顾客群组成的单周期供应链的协调决策问题。建立了顾客策略性退货模型,并确定了服务水平约束下,集中式和分散式决策模式下,商品的最优价格、最优订货量和最优退货价格。为了解决分散式决策的双重边际化效应,设计了一般的回购契约、基于差别定价的回购契约和销售回扣契约对供应链进行协调,并探讨了三种契约的协调机制。结果表明,一般的回购契约及销售回扣契约不能实现包含顾客退货的供应链的协调,而基于差别定价的回购契约可以实现供应链协调。最后,通过数值算例,分析了服务水平约束对供应链总体利润的影响以及差别定价回购契约的协调效果。     

电子商务环境下双渠道供应链协调的补偿策略研究

构建了电子商务环境下由一个制造商与一个零售商组成的双渠道供应链模型,分析、比较了集中式决策与分散式决策下双渠道供应链的最优价格,从电子渠道与传统渠道合作的角度出发,研究了双渠道供应链协调的补偿策略,论证了这种补偿策略能够实现双渠道供应链协调,且在一定范围内可以保证双渠道供应链成员的双赢.最后通过算例分析,进一步检验了所设计的补偿策略对双渠道供应链协调的有效性.     

不完全信息采购环境下的供应链协调问题： 拍卖机制的应用

本文研究了不完全信息采购环境下供应链的协调问题.拍卖不仅是一种价格确定机制,它也可以作为一种供应链协调的机制.文献已经证明拍卖机制对于参与方的收益及整条供应链的有效性具有显著影响.本文研究了当市场中存在n个供应商1个买者的情形下,拍卖环境满足独立私人值(IPV)条件、且市场反需求函数为对数函数时,批发价格拍卖、目录拍卖及二部合同拍卖为各方所产生的期望收入,并且证明了批发价格拍卖和目录拍卖不能实现渠道协调,而在拥有信息中介的二部合同拍卖机制下系统可以达到渠道协调.     

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.     

Price-setting newsvendor with strategic consumers

We consider a newsvendor who sells a single product over a single season with the objective of determining both the selling price and stock quantity to maximize the expected profit. The customers are strategic and we consider two demand cases: additive and multiplicative. For each case, we derive the newsvendor׳s optimal decisions and demonstrate that neglecting the price-sensitivity of demand leads the newsvendor to make sub-optimal decisions. Moreover, we show that under certain conditions, strategic consumer behavior may positively affect the newsvendor׳s optimal expected profit in the additive demand case.     

网络比价行为下双渠道定价及协调策略研究

本文针对比价行为下部分消费者优先在网络渠道购买产品的现象,研究了双渠道供应链的定价决策及协调策略问题。通过比价消费行为对消费者进行了划分,构建了单渠道和双渠道的供应链决策模型,运用博弈理论求得单（双）渠道情形下产品在零售渠道的批发价格和销售价格、网络渠道的销售价格,及制造商和零售商的最优收益,并通过数值算例对供应链各方的定价决策及利润进行了比较分析。结果表明网络消费者的存在使得零售商收益受损,渠道冲突加剧。为此,本文针对存在网络消费者情形下的双渠道供应链设计了协调机制,实现了双渠道供应链的协调。     

The Role of Revenue‐Focused Managerial Performance Measures in Supply Chain Coordination

Many firms employ revenue‐focused managerial performance measures (RF‐MPMs) that cause managers to worry more about revenues than about costs. Although this can seemingly misalign the interests of a manager, we show that the use of such measures can help supply chain partners to overcome hold‐up issues with respect to capacity and promotion investments. We develop a game theoretic model in which two supply chain partners engage in repeated interactions in which the supplier invests in capacity and the buyer invests in demand promotion. Following the realization of demand in each period, the two firms negotiate over the output quantity and wholesale price. The novelty of our model is that we allow the owners of each firm to delegate decision‐making power and negotiating responsibility to a free‐agent manager. We characterize the conditions under which the owners of both firms employ RF‐MPMs in equilibrium and benefit from doing so. For a special case of our model, we show that for the owners of the buyer, an RF‐MPM is equivalent to a price only relational contract, and that it complements a price and quantity relational contract as a mechanism for mitigating hold‐up issues.     

考虑随机市场需求的双渠道供应链风险补偿策略研究——从质量与价格竞争视角

在由两个供应商和单个零售商构成的二级双渠道供应链系统中，分析了随机市场需求以及供应商之间同时存在价格与质量竞争的情形下的双渠道供应链协调问题。在供应链集中决策、无风险补偿及有风险补偿三种情境下，构建了基于质量和价格的风险补偿模型并求得纳什均衡解。研究结果表明：存在可行的需求风险补偿策略使得供应链达到协调水平，并且需求风险补偿策略对零售商更加有利；在需求风险补偿策略下，需求风险补偿价格与其对应批发价格正相关，与其产品质量水平负相关；价格竞争程度对零售商订货量具有负向影响作用，对供应链总利润影响作用随着竞争程度增加而减弱，质量竞争程度对零售商订货量和供应商产品质量水平具有正向影响作用，对供应链总利润影响呈倒U型关系；需求风险补偿策略能够激励零售商的订货行为，强化价格竞争程度和质量竞争程度对供应商订货量和供应链总利润的影响；在供应链系统中双渠道营销模式下的供应链总利润要优于单渠道营销模式下的供应链总利润。本文结论不仅详细剖析了风险补偿策略对双渠道供应链协调的影响关系，也理清了价格与质量竞争对各方行为策略的影响机理。     

Demand Forecast Sharing in Supply Chains

This paper examines the incentives of a manufacturer and a retailer to share their demand forecasts. The demand at the retailer is a linearly decreasing function of price. The manufacturer sets the wholesale price first, and the retailer sets the retail price after observing the wholesale price. Both players set their prices based on their forecasts of demand. In the make‐to‐order scenario, the manufacturer sets the production quantity after observing the actual demand; in the make‐to‐stock scenario, the manufacturer sets the production quantity before the demand is realized. In the make‐to‐order scenario, we show that sharing the forecast unconditionally by the retailer with the manufacturer benefits the manufacturer but hurts the retailer. We also demonstrate that a side payment contract cannot induce Pareto‐optimal information sharing equilibrium, but a discount based wholesale price contract can. The social welfare as well as consumer surplus is higher under the discount contract, compared with under no information sharing. In the make‐to‐stock scenario, the manufacturer realizes additional benefits in the form of savings in inventory holding and shortage costs when forecasts are shared. If the savings from inventory holding and shortage costs because of information sharing are sufficiently high, then a side payment contract that induces Pareto‐optimal information sharing is feasible in the make‐to‐stock scenario. We also provide additional managerial insights with the help of a computational study.     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

Sales Force and Competition in Financial Product Markets: The Case of Mexico's Social Security Privatization

This paper examines how sales force impacts competition and equilibrium prices in the context of a privatized pension market. We use detailed administrative data on fund manager choices and worker characteristics at the inception of Mexico's privatized social security system, where fund managers had to set prices (management fees) at the national level, but could select sales force levels by local geographic areas. We develop and estimate a model of fund manager choice where sales force can increase or decrease customer price sensitivity. We find exposure to sales force lowered price sensitivity, leading to inelastic demand and high equilibrium fees. We simulate oft proposed policy solutions: a supply‐side policy with a competitive government player and a demand‐side policy that increases price elasticity. We find that demand‐side policies are necessary to foster competition in social safety net markets with large segments of inelastic consumers.     

Vertical Integration with Price‐Setting Competitive Newsvendors*

This article addresses the problem of distribution channel design under demand uncertainty. We consider two manufacturers, each producing a substitutable product and selling it through either a decentralized or an integrated retail store, which is modeled as a price‐setting newsvendor. A multiplicative demand function incorporating a random shock term is assumed. Of primary interest is how demand uncertainty and production cost affect the equilibrium distribution channel structure. Results indicate the following: On the one hand, if the random shock term is uniformly distributed on [0, x], then the equilibrium design does not depend on the variance of the shock. On the other hand, if the random shock term is uniformly distributed on [1 −r, 1 +r], then the equilibrium design does depend on the variance of the shock. In particular, an increase in r favors the integrated structure where both channels are integrated and hurts the decentralized configuration where both channels are decentralized. Additionally, we explain the qualitative similarities and differences between the structural properties of the equilibrium distribution channel structure when demand is, and is not, uncertain. We also establish that production cost always favors the decentralized structure, while it hurts the integrated one. One important managerial implication of our study is that, by reducing the number of decisions made in supply chains, the impact of demand uncertainty can be controlled to a certain extent.