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.     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

The benefit of horizontal decentralization in durable good procurement

A conventional wisdom in industry and academia is that firms suffer from decentralized procurement. In this paper, we demonstrate an important and counter-intuitive benefit of procurement decentralization in a common setting where a firm with multiple divisions procures a durable good from a supplier. We start with a two-period model and obtain analytic equilibrium results on the supplier's wholesale prices, and the firm's procurement quantities and profits under procurement centralization and decentralization. These results show that the firm's profit will benefit from decentralization if and only if the product is durable. We further show that the profit improvement always increases in durability and the number of divisions. To generalize the basic model with two periods, we design an iterative algorithm to compute the equilibrium results for any number of periods. Our extensive numerical simulations show the robustness of our analytic results and managerial insights.     

Revenue Management in Order‐Driven Production Systems

This article investigates the effectiveness of a tactical demand‐capacity management policy to guide operational decisions in order‐driven production systems. The policy is implemented via a heuristic that attempts to maximize revenue by selectively accepting or rejecting customer orders for multiple product classes when demand exceeds capacity constantly over the short term. The performance of the heuristic is evaluated in terms of its ability to generate a higher profit compared to a first‐come‐first‐served (FCFS) policy. The policies are compared over a wide range of conditions characterized by variations in both internal (firm) and external (market) factors. The heuristic, when used with a Whole Lot order‐processing approach, produces higher profit compared to FCFS when profit margins of products are substantially different from each other and demand exceeds capacity by a large amount. In other cases it is better to use the heuristic in conjunction with the Split Lot order‐processing approach.     

A Model for Partial Product Complementarity and Strategic Production Decisions under Demand Uncertainty

This paper considers a general industrial setting where multiple manufacturers each produce a different product and sell it to the markets. These products are partially complementary in the sense that there is a common demand stream that requests all these products as complementary sets and there are streams of individual demands each requesting only one of the products. All demands are uncertain and may follow any general, joint distributions. Facing demand uncertainties, the manufacturers each choose a production quantity for its product with an objective to maximize its own expected profit. We formulate the problem as a non‐cooperative game to study the strategic interactions of such firms and their implications to supply chain performance. We show that such a game may have numerous equilibria. Among all the possible equilibria, however, we prove that there always exists a unique one that maximizes each and every manufacturer's profit, and we derive an explicit solution for this Pareto‐optimal equilibrium point. We further study the optimal solution for a centralized system and compare it with the decentralized solution. Managerial insights are drawn as to how system parameters and control mechanisms affect firms' decisions and performance.     

现货价格和需求关联时期权组合合约模式下采购风险管理策略

在现货价格和客户端需求关联的情形下,本文引用期权组合合约建立现货市场供应量有限时的两阶段采购风险管理模型,以期最大化零售商的期望收益。文中先用逆向归纳法列出零售商第二阶段的最优策略,采用标准扰动定理得出有效合约应满足的最优性条件,并将原模型转化为单调的最短路径问题,应用动态规划求解最优的采购策略。最后用算例分析了现货价格与需求的相关系数及现货市场的供应量对最优策略的影响,发现当供应量一定时,各有效合约的最优预订量及有效合约的总预订量都随着相关系数的增大而提高,并且有效合约受相关系数的影响大小取决于合约的灵活性;并且,当相关系数一定时,有效合约的总预订量及执行价格最低的有效合约的最优预订量都随着供应量的增加而单调减少。     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

基于需求转移的易逝性产品最优动态定价策略

本文针对易逝性产品中新产品对老产品需求的转移作用,应用收入管理方法得出老产品的最优动态定价策略,并应用最大凹向包络理论给出了简化算法的方法.数值算例表明在存在需求转移的情况下,应更早的提供较低的价格.最后作者给出了包含生产和定价的综合模型.     

随机需求下考虑不同竞争情形的网约车平台动态定价

针对乘车需求波动下网约车平台间存在乘车需求竞争和乘运供应竞争的最优定价问题,以平台期望收益最大化为目标,运用最优控制论方法,构建不同竞争情形下的网约车平台动态定价模型,并利用哈密尔顿函数及模型推导,求得最优动态竞争价格解以及乘运供应率与需求率的变化轨迹。结果表明：平台最优动态竞争价格随市场需求的波动而动态变化,且最优价格可以有效调控平台供应能力,促使平台供需匹配,优化平台期望收益。此外,乘车需求市场竞争越激烈,平台最优价格越低,而乘运供应市场竞争越激烈,最优价格越高。平台间竞争的加剧将降低平台的期望收益,且平台期望收益随着固定佣金报酬率的提高先增大后减小。     

基于数量柔性契约的双源应急物资采购定价模型

针对灾害事件发生的不确定性以及灾害发生后应急物资需求量的爆发式增长,本文设计了一个政府主导的基于数量柔性契约的双源应急物资采购模型。在存在一个现货市场的情况下,政府除了常规采购外,还会与供应方签订一份数量柔性契约,用以建立政企联合储备应急物资的合作关系。通过数理推导,本文发现灾害事件发生概率,政府自身储备量,现货市场采购价格会对双方决策产生重要影响,并给出三个影响因素在满足不同条件时政企双方的最优决策,同时进一步分析了这三个因素对政府采购成本与供应方利润的影响。最后,通过数值模拟的方式对所得结论进行了验证。本文的研究为政府与企业构建联合储备应急物资的合作关系提供了指导与依据。     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.     

存在战略购买需求的定价、供给、机制选择和配给研究

本文研究存在战略购买需求的易逝资产销售策略问题。垄断厂商基于利润最大化目标确定易逝资产定价、供给、机制选择和配给策略,战略消费者通过锚定预期价格安排战略购买时机。不同于通常基于效用理论研究定价的思路,本文首先基于锚定效应和跨期价格均衡思想探寻不同战略等待购买规模的市场预期需求曲线和动静态定价区域;其次在众多预期需求曲线中寻找市场有效定价前沿（即有效预期需求曲线）;再次在利润曲面上找出与有效定价前沿对应的容量扩展线（即最大利润曲线）;最后沿容量扩展线和有效定价前沿搜寻最大期望利润及相应策略。研究表明,消费者保留价异质和需求不确定性是动态定价和战略购买存在的根本原因;市场在不同战略等待购买规模状态拥有不同预期需求曲线,最大战略等待购买规模状态预期需求曲线是市场有效定价前沿。动静态定价机制各有其所适用的容量和价格空间,消费者保留价水平和战略消费者规模决定动态定价空间大小,随机需求分布差异只影响动态定价空间形状（即影响需求弹性）。在跨期价格均衡区域内,提价和扩容都会加剧消费者战略购买程度,供给越大定价往往越低。战略购买不仅会降低厂商供给、定价和利润水平,改变不同类型消费者之间高低价购买机会,甚至还可能影响定价机制选择和配给策略。压缩过度供给和虚高价格空间可降低战略购买导致的利润损失。本文研究结果可为考虑消费者行为的需求价格理论研究和运营管理实践提供参考。     

存在信息更新时的双源采购和后备生产结合策略研究

在现实的采购运作中,双源采购和后备生产是两种最常见的风险应对策略。本文在考虑信息更新的情况下,探讨了一个两阶段动态采购决策模型：第一阶段,制造商向存在供应风险的一个或两个主供应商订货;第二阶段,制造商根据主供应商风险信息的更新,决定是否向供应可靠但价格较高的后备供应商订货。本文得到了两阶段的最优采购策略,分析发现,当固定采购成本较低时：若潜在市场需求较小,双源采购将排斥后备生产;若潜在市场需求较大,双源采购和后备生产共存;若潜在市场需求适中,后备生产可能排斥双源采购,两者也可能共存。特别地,在潜在市场需求适中时,可靠性改进概率的增大或后备供应商生产成本的降低,将使后备生产趋于排斥双源采购;反之,可靠性改进概率的减小、固定采购成本的降低或后备生产成本的增加,将使两者趋于共存。     

A Nonatomic‐Game Approach to Dynamic Pricing under Competition

We study a revenue management problem involving competing firms. We assume the presence of a continuum of infinitesimal firms where no individual firm has any discernable influence over the evolution of the overall market condition. Under this nonatomic‐game approach, the unanimous adoption of an equilibrium pricing policy by all firms will yield a market‐condition process that in turn will elicit the said policy as one of the best individual responses. For both deterministic‐ and stochastic‐demand cases, we show the existence of equilibrium pricing policies that exhibit well‐behaving monotone trends. Our computational study reveals many useful insights, including the fact that only a reasonable number of firms are needed for our approach to produce near‐rational pricing policies.     

两阶段供应链碳排放目标减排量分配研究

由于不同企业减排成本和减排效率有所差异,将目标减排量在供应链企业间进行合理分配是顺利完成减排目标的关键。本文研究了制造商和零售商组成的两阶段供应链的既定目标减排量分配问题,考虑企业减排对产品需求有正向影响,根据制造商分配和零售商分配两种分配方式,以及制造商领导、零售商领导和垂直纳什三种渠道权力结构,构建了六种决策模型,分析分配方式和渠道权力结构对分配决策和供应链成员以及系统利润的影响。研究表明,在三种渠道权利中：由减排对需求影响大的企业进行分配,制造商和零售商会分摊减排量,由减排对需求影响小的企业进行分配,减排量全部由对方企业承担,市场需求更大;作为领导者比作为跟随者承担更多减排量;由减排对需求影响大且减排效率低的企业分配减排量,可以实现减排量在供应链企业间分摊以及系统利润最大化,由减排对需求影响小且减排效率低或略高于对方的企业分配减排量,虽然系统利润最优,但是以单个企业承担全部减排量为代价。     

Demand switching criteria for multiple products: An inventory cost analysis

In this paper, we consider the problem of demand switching and show how a firm can take advantage of the risk-pooling effect to gain more profit. We examine the case of three products under various switching criteria; a model based on the heuristic approach is developed to determine the switching paths and the corresponding switching rates that yield the optimal profit. A constrained model with limited amount of the switched demand is also developed. In general, the profit increases as a result of higher profit margin or smaller demand variation and correlation. Our result indicates that the profit does not necessarily increase as the switching rate increases; in some cases the profit may even decrease as a result of demand switching. Numerical examples are also included to illustrate the derived models. The developed analytical approach may help practitioners to gain more insight in demand switching and facilitate inventory related decision-making process as well.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

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.     

Rationing Capacity Between Two Product Classes*

In this paper, we study the capacity allocation problem faced by make-to-order manufacturing firms encountering expected total demand in excess of available capacity. Specifically, we focus on firms' manufacturing short-life-cycle or seasonal products such as high fashion apparel. Using a decision-theory-based approach, we develop a capacity allocation policy that allows such firms to discriminate between two classes of products (one yielding a higher profit contribution per unit of capacity allocated to it than the other), resulting in selective rejection of orders for the class with the lower unit contribution. The effectiveness of capacity rationing is investigated under a wide array of conditions characterized by variations in factors such as the ratio of unit profit contributions of the two product classes, the ratio of total available capacity to expected total demand, the ratio of expected demands between the two classes, and the variability in demand for each product class. The results indicate that capacity rationing is very effective in increasing the total profit, and could therefore serve as a valuable decision tool for managers in such firms.     

面向价值共创的服务衍生供需决策优化研究

针对制造企业服务衍生时,制造企业与客户间可能存在的"双重边际效应"问题,以制造企业服务衍生特征刻画为基础,构建了服务衍生供需价值创造模型,比较分析了分散和集中两种决策情形下的价值创造,发现集中决策下供需双方能够创造整体更高的价值,但制造企业存在陷入"服务悖论"的风险,由此,设计了有助于协调供需价值分配的收益共享契约。研究表明,收益共享契约能够缓解制造企业与客户间的"双重边际效应",契约能够激发制造企业以更为积极主动的态度改进服务衍生方案,提升方案的性价比,并由此促进市场需求,实现供需双方的价值共创。