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.     

Inventory‐Based Dynamic Pricing with Costly Price Adjustment

We study an average‐cost stochastic inventory control problem in which the firm can replenish inventory and adjust the price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size—An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time‐average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory‐based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

The Role of Contract Expirations in Service Parts Management

The majority of after‐sales service providers manage their service parts inventory by focusing on the availability of service parts. This approach, combined with automatic replenishment systems, leads to reactive inventory control policies where base stock levels are adjusted only after a service contract expires. Consequently, service providers often face excess stock of critical service parts that are difficult to dispose due to their specificity. In this study, we address this problem by developing inventory control policies taking into account contract expirations. Our key idea is to reduce the base stock level of the one‐for‐one policy before obsolescence (a full or partial drop in demand rate) occurs and let demand take away excess stock. We refer to this policy as the single‐adjustment policy. We benchmark the single‐adjustment policy with the multiple‐adjustment policy (allowing multiple base stock adjustments) formulated as a dynamic program and verify that for a wide range of instances the single‐adjustment policy is an effective heuristic for the multiple‐adjustment policy. We also compare the single‐adjustment policy with the world‐dependent base stock policy offered by Song and Zipkin (1993) and identify the parameter combinations where both policies yield similar costs. We consider two special cases of the single‐adjustment policy where the base stock level is kept fixed or the base stock adjustment is postponed to the contract expiration time. We find that the initial demand rate, contract expiration time, and size of the drop in demand rate are the three key parameters driving the choice between the single‐adjustment policy and its special cases.     

Motivating Retail Marketing Effort: Optimal Contract Design

We study a distribution channel where a manufacturer relies on a sales agent for selling the product, and for investing in the most appropriate marketing effort. The agent's effort is hard to monitor. In addition, the cost of effort is the agent's private information. These impose challenges to the manufacturer in its endeavor to influence the agent's marketing effort provisions and to allocate profit between the two parties. We propose two contract forms. The franchise fee contract is a two‐part price schedule specifying a variable wholesale price and a fixed franchise fee. The retail price maintenance contract links the allowed retail price that the agent charges customers with total payment to the manufacturer and sales level. Under information asymmetry, for implementing either contract form, the manufacturer needs to offer a menu of contracts, hoping to invoke the “revelation principle” when the agent picks a certain contract from that menu. We show that the two contract forms perform differently, and each party's preference toward a particular contract form is linked with the total reservation profit level and/or the sales agent's cost type. We provide managerial guidelines for the manufacturer in selecting a better contract form under different conditions.     

Managing Slow‐Moving Perishables in the Grocery Industry

We address the value of information and value of centralized control in the context of a two‐echelon, serial supply chain with one retailer and one supplier that provide a single perishable product to consumers. Our analysis is relevant for managing slow‐moving perishable products with fixed lot sizes and expiration dates of a week or less. We evaluate two supply chain structures. In the first structure, referred to as decentralized information sharing, the retailer shares its demand, inventory, and ordering policy with the supplier, yet both facilities make their own profit‐maximizing replenishment decisions. In the second structure, centralized control, incentives are aligned and the replenishment decisions are coordinated. The latter supply chain structure corresponds to the industry practices of company‐owned stores or vendor‐managed inventory. We measure the value of information and value of centralized control as the marginal improvement in expected profits that a supply chain achieves relative to the case when no information is shared and decision making is decentralized. Key assumptions of our model include stochastic demand, lost sales, and fixed order quantities. We establish the importance of information sharing and centralized control in the supply chain and identify conditions under which benefits are realized. As opposed to previous work on the value of information, the major benefit in our setting is driven by the supplier's ability to provide the retailer with fresher product. By isolating the benefit by firm, we show that sharing information is not always Pareto‐improving for both supply chain partners in the decentralized setting.     

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.     

The Dynamics of Domestic Gray Markets and Its Impact on Supply Chains

Gray markets are created by unauthorized retailers selling manufacturer's branded products. Similar to international gray markets, domestic gray markets are a growing phenomenon whose impact on supply chains is not clear. We consider a supply chain with one manufacturer and several authorized retailers who face a newsvendor problem and a domestic gray market. While a gray market provides an opportunity for retailers to clear their excess inventory (inventory‐correction effect), it also can be a threat to their demand (demand‐cannibalization effect). We first characterize the emerging equilibrium by assuming an MSRP environment. Comparing a decentralized and centralized system, we show that a wholesale pricing contract is quite efficient in a gray market environment; we explain the underlying mechanism and note some of the operational decisions that could hurt that efficiency. We show that the gray market price determines the degree of both the negative effects of demand‐cannibalization and the positive effects of inventory correction, which in turn determines the net impact of gray markets on the retailer's stocking choice and, ultimately, the manufacturer's profit. We then study the authorized retailers' problem as a price‐setting newsvendor. We observe that the gray market creates price competition between the authorized and unauthorized retailers, causing a drop in the primary market price. However, this price competition can be counteracted by the authorized retailers' stocking decision. Finally, we extend our model to consider the cases where the demand can be correlated across retailers.     

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.     

A Mobile Platform's In‐App Advertising Contract Under Agency Pricing for App Sales

Unlike advertising in traditional media, a mobile platform's in‐app advertising market exhibits two unique features—split structure of the mobile platform with a platform owner and an app developer jointly provisioning in‐app advertising, and agency pricing for app sales. We develop a two‐sided market model to analyze the role of these two unique features in determining the platform owner's optimal advertising revenue‐sharing contract. Our results reveal an interesting N‐shaped dynamic regarding the platform owner's optimal choice of her ad revenue share with respect to the overall advertisers’ valuation of in‐app ads. We identify a between‐agent subsidization strategy for the platform owner, where she finds it optimal to subsidize the developer via the advertising channel, leading to greater profits for both of them. We find that the advertising revenue‐sharing contract under agency pricing for app sales leads to a higher app price than would be offered by the integrated platform found in traditional advertising. However, the ad price is coordinated under the platform owner's optimal choice of ad revenue share when she obtains revenue from both the advertising and app sales channels, leading to an alignment of her interest with the app developer's on ad level.     

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.     

Managing Inventory with Cash Register Information: Sales Recorded but Not Demands

Inventory inaccuracy is common in many businesses. While retailers employ cash registers to enter incoming orders and outgoing sales, inaccuracy arises because they do not record invisible demand such as spoilage, damage, pilferage, or returns. This setting results in incomplete inventory and demand information. An important inventory control problem therefore is to maximize the total expected discounted profit under this setting. Allowing for dependence between demand and invisible demand, we obtain the associated dynamic programming equation with an infinite‐dimensional state space, and reduce it to a simpler form by employing the concept of unnormalized probability. We develop an analytical upper bound on the optimal profit as well as an iterative algorithm for an approximate solution of the problem. We compare profits of the iterative solution and the myopic solution, and then to the upper bound. We see that the iterative solution performs better than the myopic solution, and significantly so in many cases. Furthermore, it gives a profit not far from the upper bound, and is therefore close to optimal. Using our results, we also discuss meeting inventory service levels.     

供应商保鲜努力的生鲜农产品双渠道供应链协调决策研究

在互联网迅猛发展的时代,生鲜农产品双渠道营销模式是供应商的最佳选择,如何发挥双渠道优势,实现渠道共赢是目前研究的热点。以供应商主导的双渠道供应链为研究对象,考虑新鲜度衰减且扰动需求和供应商保鲜努力,对比分析集中和分散决策模型,论证构建协调模型的必要性。从渠道合作和利润最大化的角度出发,设计两部定价契约、批发价协调契约和由成本分担与补偿策略构成的混合协调契约,三种契约均能在一定范围内有效实现供应链协调,提高各成员的利润。最后,对比分析所设计协调契约以认识其本质,并通过数值分析验证其有效性。     

效率参数不可观测下的SaaS云外包合约研究

客户企业在实施SaaS（软件即服务,Software as a Service）云外包时,面临因效率参数不可观测所引发的云服务提供商（Cloud Service Provider,CSP）道德风险问题。针对该问题,以激励机制设计方法为基础,以客户企业期望收益最大化为目标,在服务产出为公共信息,而效率参数信息为CSP私人信息下研究如何通过外包合约的设计诱使CSP显示出真实的信息,并付出最优的努力水平。研究表明,最优努力水平、服务报酬支付是效率参数的减函数;客户企业向CSP提供的最优合约可以用线性合约表示;在由固定服务报酬及收益共享构成的线性合约中,效率参数与固定服务报酬支付正相关,与收益共享系数负相关。     

On the Unimodality of the Profit Function of the Pricing Newsvendor

In this note, we study the price‐setting newsvendor problem. We use three conditions, the log‐convexity of the coefficient of variation, the log‐concavity of the deterministic profit function, and the log‐convexity of the random noise's expectation conditional on having leftover inventory to establish the log‐concavity of the retailer's expected profit function. This new result is complementary to existing results and removes some assumptions in the pricing and inventory coordination literature. It also addresses the conjecture made by Petruzzi and Dada (1999), and can be applied in the pricing game.     

不确定需求环境下多级库存系统优化与协调模型研究

论文首先将模糊随机变量扩展为混合随机变量,并用来描述不确定需求.然后对多级单周期库存系统在模糊随机和混合随机需求环境下的优化与协调问题作了研究,提出了通过集成库存管理使库存系统整体收益期望值最大化的优化模型和协调合作伙伴利益的数量折扣契约模型,并根据遗传算法理论和计算机模拟技术设计了求解模型的智能算法.最后通过实例对模型进行了仿真分析.     

On the Effects of Capacity Agent on Market Equilibrium

We consider a setting of two firms and one capacity agent. Each firm serves a primary market, and the capacity agent sustains a common market to draw demand for capacity from the external firms. The firms can partner with the capacity agent under her contract to serve the common market. When they use the common market mainly as an outlet for their unused capacities, the capacity agent will only specify a variable fee for each capacity unit deployed through her, and prefer to partner with one firm in most circumstances. When the firms adjust capacities to accommodate the businesses created by serving the common market, the capacity agent will specify a lump‐sum payment and a variable fee, and will be more likely to incentivize only one firm to partner with her, when the common market is sufficiently large or the demands in the common and primary markets are strongly correlated. She will always use a fixed fee to extract, while not necessarily all, the profit gains to the firms serving the common market, but will use a variable fee only when partnering with both firms. The key results are robust with respect to market configuration and contract type.     

Quality Management in Multi‐Level Supply Chains with Outsourced Manufacturing

Outsourcing stretches supply chains longer with added contract manufacturers responsible for the manufacturing of parts and final products. Should a firm change its quality management approach as its supply chain becomes longer with outsourced manufacturing? This paper studies a brand owner's optimal choice between two commonly used quality management approaches: an inspection‐based approach and an external failure‐based approach, in two supply chains – a dyadic supply chain and a multi‐level supply chain where the brand owner outsources manufacturing to an independent contract manufacturer. Our study finds that the brand owner's optimal choice between the two quality management approaches could be opposite in the two supply chains. Specifically, we show that if agency costs exist between the contract manufacturer and the brand owner, the brand owner may prefer an inspection‐based approach in the multi‐level supply chain in contrast to preferring an external failure‐based approach in the dyadic supply chain. In particular, inspections can be effective for the brand owner to limit the manufacturer's profit by excluding defective finished products and components, which in turn reduce agency costs in the multi‐level supply chain. Hence, the efficiency of an inspection‐based approach relative to an external failure‐based approach can be higher in the multi‐level supply chain as compared to the dyadic one. Our findings suggest that firms should adjust to changes in supply chain structures and re‐evaluate the efficiencies of different quality management approaches accordingly.     

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.     

Willingness to Pay for Shifting Inventory Risk: The Role of Contractual Form

In order to reduce their inventory risk, firms can attempt to contract with their suppliers for shorter supply lead‐times, with their buyers for longer demand lead‐times, or both. We designed a controlled laboratory experiment to study contracts that shift a focal firm's inventory risk to its supply chain partners and address two questions. First, is it more effective if the cost of shifting inventory risk is framed as a fixed fee or in per‐unit cost terms? We find that, generally, our participants are willing to pay more to avoid supply–demand mismatches than the expected costs from such mismatches. This tendency to overpay is mitigated under fixed fee schemes. Second, does it matter whether the option to reduce inventory risk is the outcome of either increased responsiveness from the upstream supplier or advanced demand information from the downstream buyer? Our results suggest that this difference, when only a matter of framing, has no significant effect on willingness‐to‐pay.