Managing High‐Tech Capacity Expansion via Reservation Contracts

We study capacity reservation contracts between a high‐tech manufacturer (supplier) and her OEM customer (buyer). The supplier and the buyer are partners who enter a ‘design‐win” agreement to develop the product, and who share the stochastic demand information. To encourage the supplier for more aggressive capacity expansion, the buyer reserves capacity upfront by paying a deductible fee. As capacity expansion demonstrates diseconomy of scale in this context, we assume convex capacity costs. We show that as the buyer's revenue margin decreases, the supplier faces a sequence of four profit scenarios with decreasing desirability. We examine the effects of market size and demand variability to the contract conditions. We propose two channel coordination contracts, and discuss how such contracts can be tailored for situations where the supplier has the option of not complying with the contract, and when the buyer's demand information is only partially updated during the supplier's capacity lead‐time.     

不对称信息下考虑产能约束的供应链合同设计

本文针对由产能约束品牌制造商和零售商组成的供应链系统,考虑市场上消费者对产品的异质性偏好,以及品牌制造商和零售商之间存在信息不对称,研究品牌制造商最优合同设计与零售商定价策略,考察产能约束与不对称信息对产品定价和供应双方合作的影响。研究发现：受到产能约束的品牌制造商有三种合同策略,即低价合同、固定价格合同以及高价合同等三种合同,在低价合同下品牌制造商可以充分利用其产能约束,而在后两种合同下产品有可能滞销;不对称信息会导致"批发价格+一次性转移支付"合同不能完美协调供应链。当品牌制造商和零售商进行信息共享谈判时,若二者在高价合同下进行合作,则品牌制造商与零售商在一定条件下可以达成信息共享谈判,实现"双赢"。     

针对不同类型销售商的长期激励合同设计研究

在制造商雇用销售商销售产品的过程中,双方之间常常存在关于销售商销售能力和销售努力的不对称信息,制造商需要通过设定合同来激励销售商付出实现制造商利润最大化的销售努力。本文建立了信息不对称情况下,制造商在两周期的长期合同设计并同时制定产品价格的模型。虽然不对称信息存在时,制造商在单周期的最优合同策略是分离策略,而本文的两周期模型结果表明,长期合同中第一个周期的最优合同策略并不一定是分离策略,有可能是混同策略,这与第二周期的折现因子有关。而两周期产品价格也与单周期不同,其大于单周期采取混同策略时的价格,小于单周期采取分离策略时的价格。     

Option Contracts and Capacity Management—Enabling Price Discrimination under Demand Uncertainty

We explore using an option contract as a price discrimination tool under demand uncertainty. In our capacity game model, a monopolistic supplier has to build capacity before observing the uncertain demand. The demand is generated by two potential customers, who privately know their own types. The types could be either high or low, differing in willingness to pay for each unit of demand. To discriminate between the customer types, the supplier designs option contracts so that only the high type will buy options in advance. The high type will do so because the options can hedge their risk of demand loss when capacity is tight. The supplier profits in three ways. First, the high type customers pay higher marginal prices on average. Second, the high type customers' demand is satisfied as a first priority, guaranteeing allocation efficiency. Third, the supplier can observe the number of options being purchased and so determine customer types, improving capacity investment efficiency. We compare our results to those of classical second degree price discrimination. We show that our proposed framework guarantees the same level of supplier profit even when the supplier cannot discriminate between the customers by bundling products.     

A Note on Optimal Selling to Asymmetric Retailers

I consider a channel with one manufacturer selling the same product to two retailers engaged in imperfect competition. The retailers are asymmetric because one has a lower marginal selling cost (or a higher demand potential) than the other. I design the manufacturer's optimal selling mechanism, whereby the manufacturer must offer the same contract options to both retailers. I fully characterize the manufacturer's optimal selling mechanism for varying degrees of retailer asymmetry and competition intensity. I find that under certain conditions, the manufacturer is better off selling a larger quantity through the high‐cost (or low‐demand potential) retailer. I also show how the optimal mechanism can be implemented using a menu of two‐part tariffs with quantity controls.     

A Portfolio Approach to Procurement Contracts

The purpose of this paper is to develop a general framework for supply contracts in which portfolios of contracts can be analyzed and optimized. We focus on a multi‐period environment with convex contract, spot market, and inventory holding costs. We specialize the model to the case of a portfolio consisting of option contracts. We characterize the optimal replenishment policy and show that it has a simple structure. Namely, the use of every different option contract and the spot market is dictated by a modified base‐stock policy. In addition, we derive conditions to determine when an option is relatively attractive compared to other options or the spot market. Finally, we present our computational study, where we report the sensitivity of the results to the parameters of the model. Our experiments indicate that portfolio contracts not only increase the manufacturer's expected profit, but can also reduce its financial risk.     

Equilibrium Wage‐Tenure Contracts

In this study we consider a labor market matching model where firms post wage‐tenure contracts and workers, both employed and unemployed, search for new job opportunities. Given workers are risk averse, we establish there is a unique equilibrium in the environment considered. Although firms in the market make different offers in equilibrium, all post a wage‐tenure contract that implies a worker's wage increases smoothly with tenure at the firm. As firms make different offers, there is job turnover, as employed workers move jobs as the opportunity arises. This implies the increase in a worker's wage can be due to job‐to‐job movements as well as wage‐tenure effects. Further, there is a nondegenerate equilibrium distribution of initial wage offers that is differentiable on its support except for a mass point at the lowest initial wage. We also show that relevant characteristics of the equilibrium can be written as explicit functions of preferences and the other market parameters.     

不对称信息下“农超对接”供应链定价及合同设计

农超对接"模式有助于缩减农产品流通环节,缓解农户农产品"卖难"和消费者"买贵"同时存在的矛盾。本文针对由一个农户（或合作社）和一个超市组成的"农超对接"系统,考虑消费者对农产品质量偏好的异质性,且消费者偏好与农产品质量之间的不匹配成本为不对称信息,研究农产品供应链定价及合同设计问题。研究结果表明,在对称信息下,农产品总是不会滞销,农户通过"批发价格+一次性转移支付"的合同设计能够实现农产品供应链的完美协调;在不对称信息下,农户存在低批发价格合同、固定批发价格合同以及高批发价格合同等三种策略,在后两种策略下,农产品有可能滞销;不对称信息的存在总是会给农户造成损失,给超市带来额外信息租金,但不一定会造成消费者剩余或社会福利的损失;当农户选择高批发价格合同时,若满足一定条件,则超市与农户能够达成信息共享谈判而共同分享整个农产品供应链的利润。     

A Theory of the Firm with Non‐binding Employment Contracts

This paper examines an employment relation in which individual workers enjoy some bargaining power vis‐a‐vis the firm although they are not unionized. The main elements of the situations studied here are that the employment contracts are non‐binding across periods of production and that the firm has opportunities to replace workers. The paper analyzes a dynamic model in which the processes of contracting and recontracting between the firm and its workers are intertwined with the dynamic evolution of the firm's workforce. The analysis of the model is somewhat complicated because the employment level is a nondegenerate state variable that evolves over time and is affected by past decisions. The main analytical results characterize certain important equilibria: the profit maximizing and stationary equilibria. The unique stationary equilibrium is markedly inefficient: it exhibits inefficient over‐employment and the steady state wages coincide with the workers' reservation wage. It confirms earlier results derived by Stole and Zwiebel (1996a, b) in the context of a static model and shows that they are very robust even when the firm has nearly frictionless hiring opportunities. In contrast, in the profit maximizing equilibrium the outcome is nearly efficient and the wage exhibits a mark‐up over the reservation wage.     

A Note on the Relationship Among Capacity,Pricing, and Inventory in a Make‐to‐Stock System

We address the simultaneous determination of pricing, production, and capacity investment decisions by a monopolistic firm in a multi‐period setting under demand uncertainty. We analyze the optimal decision with particular emphasis on the relationship between price and capacity. We consider models that allow for either bi‐directional price changes or models with markdowns only, and in the latter case we prove that capacity and price are strategic substitutes.     

Optimizing Customer Forecasts for Forecast‐Commitment Contracts

We study a “Forecast‐Commitment” contract motivated by a manufacturer's desire to provide good service in the form of delivery commitments in exchange for reasonable forecasts and a purchase commitment from the customer. The customer provides a forecast for a future order and a guarantee to purchase a portion of it. In return, the supplier commits to satisfy some or all of the forecast. The supplier pays penalties for shortfalls of the commitment quantity from the forecast, and for shortfalls of the delivered quantity from the customer's final order (not exceeding the commitment quantity). These penalties allow differential service among customers. In Durango‐Cohen and Yano (2006), we analyzed the supplier's problem for a given customer forecast. In this paper, we analyze the customer's problem under symmetric information, both when the customer is honest and when he strategically orders more than his demand when doing so is advantageous. We show that the customer gains little from lying, so the supplier can use his control over the contract parameters to encourage honesty. When the customer is honest, the contract achieves (near‐)coordination of the supply chain in a great majority of instances, and thus provides both excellent performance and flexibility in structuring contracts.     

Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy

Branch selection is a key decision in a cadet's military career. Cadets at USMA can increase their branch priorities at a fraction of slots by extending their service agreement. This real‐life matching problem fills an important gap in the market design literature, providing strong empirical legitimacy to a series of elegant theoretical works on matching with contracts. Although priorities fail a key substitutes condition, the agent‐optimal stable mechanism is well defined, and in contrast to the current USMA mechanism it is fair, stable, strategy‐proof, and respects improvements in cadet priorities. Adoption of this mechanism benefits cadets and the Army. This new application shows that the matching with contracts model is practically relevant beyond traditional domains that satisfy the substitutes condition.     

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.     

信息不对称下委托代理契约纳什实施性研究

针对代理人逆向选择导致委托人无法将契约与代理人类型状态直接关联的矛盾,研究了信息不对称下委托代理契约的纳什实施性问题。通过建立信号空间上的纳什均衡与有效配置的映射关系,将委托人契约与代理人状态联系起来,并以完全信息下委托人的最优契约和逆向选择下的次优契约为例,研究分析委托人契约纳什实施的性质,当且仅当委托契约满足激励相容约束时,才具备纳什实施的惟一性,该结果为实务契约设计逼近激励可行契约提供了新的途径。     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

基于补偿合约的供应链定价与能力设计的协调问题研究

研究和分析了在需求不确定并且受价格影响的情况下,供应链中制造商与供应商的产品定价与能力设计的协调问题。制造商从供应商处采购用于产品生产的关键零部件,供应链面临的潜在需求服从随机分布,有效需求则受产品定价的影响。当供应商的生产能力出现约束时,制造商可以从外部其他渠道获取关键零部件,但是需要付出一个更高的采购价格。制造商确定产品的销售价格,供应商确定生产能力。分析比较了在集成供应链与独立决策的供应链中的定价与能力计划策略,提出了一种能够有效协调制造商和供应商的决策行为的补偿合约。最后,进行了数值分析,证明补偿合约的有效性。     

A Note on Job Tenure and Collective Contracts

Abstract. This paper analyses the relationship between individual tenure and the application of collective contracts at the firm level under the specific institutional settings in Germany. The empirical approach is based on a multilevel model and a linked employer–employee data set for the years 1990, 1995, and 2001. The main result is that elapsed tenure is longer in firms applying collective contracts than in companies with individual wage setting: workers in firms with collective contracts benefit not only from higher wages, but also from higher job stability. Furthermore, we find no significant changes in mean tenure during the 1990s as well as stable differences across wage‐setting regimes.     

对多产品销售的激励合同设计及定价研究

在制造商雇用销售商销售多种产品的市场背景下,本文分析了当制造商面临的销售商有关于销售能力的私有信息时,制造商如何制订多种产品的销售价格并设定多产品的激励合同问题。模型中,制造商通过提供多个规定目标销售量的合同供销售商进行选择,在销售商选择后,制造商了解到销售商的真实销售能力。由于制造商和销售商之间存在不对称信息,制造商需要付出一定的信息成本才能获得销售商的销售能力。研究发现,制造商能够通过合适地设定不同产品的销售价格,以获得在不同产品上的分配销售商销售努力的权力。进一步,在一定的条件下制造商可以根据自己的需要任意设定合同中不同产品的目标销售量而不影响其最终期望利润。本文找到了上述最优销售价格以及多种产品目标销售量所需要满足的条件。     

Shareholders' Wealth‐Maximizing Operating Decisions and Risk Management Practices in a Mixed Contracts Economy

This paper establishes a critically important positive role for operations management practices and financial hedging. We show that operations management decisions and financial hedging are intertwined, and we advance a framework that can identify their combined effects on investors' wealth. We show that: (a) firms (publicly traded corporations) will optimally hold adequate riskless working capital (e.g., cash) to minimize the cost of obtaining non‐financial inputs, and the magnitude of this cash holding depends on operating details, and (b) operations management and financial hedging can lower firms' cash requirements, and boost productivity, defined as the wealth created in the firm per dollar of invested capital. Productivity‐enhancing practices—by “freeing up” some of the firm's cash—can maximize the investors' wealth. We show that these results obtain because firms' contracts with many of the providers of non‐financial inputs are not traded, and because investors can invest not just in public corporations but also in businesses “outside the markets” (e.g., proprietorships, partnerships, and private equity).     

基于讨价还价博弈下的供应链回购合同研究

分析了由一个供应商和一个零售商组成的系统.不确定性需求实现之后,系统成员能够对交易合同参数进行讨价还价,从而确定双方之间的收益分配比例.研究得出,首先,相对于分散控制系统,基于讨价还价下的分散控制系统中,成员之间讨价还价会对供应商收益产生负面影响;而对于供应链系统和零售商而言,收益变化趋势取决于双方之间的讨价还价能力的大小.其次,相对于回购控制系统中,在对回购价格进行讨价还价的回购控制系统中,供应商和零售商在期初所签订的回购合同具有抗讨价还价性;而在对批发价格进行讨价还价的回购控制系统中,回购合同是否具有抗讨价还价性,取决于零售商和供应商之间的相对谈判权利.