Dynamic Slotting and Pricing Decisions in a Durable Product Supply Chain

We consider a supply chain in which a manufacturer sells an innovative durable product to an independent retailer over its life cycle. We assume that the product demand follows a Bass-type diffusion process and that it is determined by the market influences, retail price of the product, and shelf space allocated to it. We consider the following retailer profit optimization strategies: (i) the myopic strategy of maximizing the current-period profit and (ii) the far-sighted strategy of maximizing the life-cycle profit. We characterize the optimal dynamic shelf-space allocation and retail pricing policies for the retailer and wholesale pricing policies for the manufacturer. We compute also these policies numerically. Surprisingly, we find that the manufacturer, and sometimes even the retailer, is better off with a myopic retailer strategy in some cases.     

双渠道供应链中合作广告与定价的动态模型

基于单个制造商与单个零售商所组成的双渠道供应链结构,利用微分对策方法,分别考察了动态架构中Stackelberg博弈与合作博弈情形下渠道成员的最优定价和广告策略,并对此两种博弈结构下的反馈均衡结果进行了分析比较.研究发现,两种博弈相比,制造商的直销价格相同,零售商在合作博弈下选择更小的零售价格;制造商在合作博弈下对广告的投入更多,而零售商在两种博弈下的广告投入水平取决于零售商的广告竞争强度与两个渠道销售价格竞争强度的关系;两种博弈下供应链系统利润的大小关系依赖于系统参数.     

供应链互补产品广告投入和捆绑销售联合决策研究

以一个制造商和一个零售商的供应链为研究对象,制造商生产两种互补产品,零售商可选择分开或捆绑两种销售策略。考虑互补品的负交叉弹性和广告外部性的特点,构建基于溢出效应的需求模型,运用博弈论的方法,求解零售商采取分开和捆绑两种销售策略时的均衡结果。通过比较不同销售策略下的均衡结果及利润关系,探讨在分散式和集中式两种情况下,零售商的最优广告投入和捆绑销售的联合决策问题。最后,通过数值算例,讨论产品互补程度和广告成本系数对决策结果的影响。研究结果表明,无论是在分散式还是集中式决策下,当产品互补程度较高或广告成本系数低时,分开销售是占优策略而广告费用较高;当产品互补程度较低且广告成本系数高时,捆绑销售是占优策略且广告费用较低。     

一种电子商务环境下耐用品的动态定价模型与策略

针对电子商务环境下消费者对价格歧视的抗拒问题,以及耐用品生命周期长、产品需求依赖于时间、价格等特点,提出了一种动态定价模型与策略。该模型通过构造转移概率矩阵,推导出在线消费者浏览到耐用品的不同价格状态下的概率,接着根据消费者多阶段效用函数分析消费者的购买决策行为,进而给出零售商利润达到最大化时的最优定价策略集合。为了验证模型与策略的有效性,通过数值模拟实验,分析模型主要参数变化对最优定价策略的影响。研究发现当效用折扣因子越高,零售商应该降低促销频率和高价格并且提高低价格,从而诱导高端消费者在高价格购买产品。折扣效用因子大小还决定了网上零售商是否要隐藏自己的促销概率。     

Optimal Advertising and Pricing in a New-Product Adoption Model

A model of new-product adoption is proposed that incorporates price and advertising effects. An optimal control problem that uses the model as its dynamics is solved explicitly to obtain the optimal price and advertising effort over time. The model has a great potential to be used in obtaining solutions and insights in a variety of differential game settings. The authors thank Anshuman Chutani for help with the figures.     

供应中断下具有随机需求的闭环供应链最优差别定价模型

研究了在供应中断下具有随机需求的闭环供应链系统的最优差别定价模型.基于博弈论的理论和方法分别在集中式和分散式决策情形下,确定了最优批发价、最优销售价、最优订购量及系统利润.最后通过数值例子对最优差别定价模型进行了实证分析.     

多因素干扰下的供应链最优定价与订货决策

在信息不对称条件下,市场需求、价格和风险厌恶等因素同时干扰时,构建数量折扣契约的供应链博弈模型,寻找其实现供应链协调的内在约束条件。根据显示原理,构建信息不对称条件下多因素干扰的CVaR模型并求解,然后用算例仿真,结果表明:供应商隐瞒生产成本信息会带来额外收益,但给零售商造成额外损失。价格随机与零售商厌恶风险的耦合作用是导致供应链上各决策变量发生分岔现象的内因,与信息是否对称无关。但信息不对称会损害供应链系统的稳定性。在分岔突变区域内供应链失调,在区域之外供应链协调。零售商风险中性的态度和提高信息透明度有利于提高整个供应链的绩效。     

考虑公平偏好的供应链最优信用期和定价策略研究

论文将公平偏好引入商业信用供应链的运作中,研究公平偏好如何影响供应链的商业信用和定价策略。论文在三种情况下,即仅供应商关注公平,仅零售商关注公平和双方均关注公平,运用Stackelberg博弈分析了供应商的最优商业信用期及零售商的最优零售价格。研究发现,当零售商具有公平偏好时,零售价格与其公平偏好程度无关;零售商的公平偏好程度越大,供应商提供的商业信用期限越长。当仅供应商具有公平偏好时,供应商的公平偏好程度越大,零售商的零售价格越大,供应商提供的商业信用期限越短;当双方都具有公平偏好时,零售商的零售价格关于双方偏好均为增函数;供应商的商业信用期限为自身偏好系数的增函数,为零售商偏好系数的减函数。供应链成员的效用为自身偏好系数的增函数,对方偏好系数的减函数;双方具有公平偏好时,供应链利润小于无公平偏好时的供应链利润。     

Optimal Distributed Dynamic Advertising

We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem. The first author gratefully acknowledges financial support by the NSF, the DAAD, the SFB 611 (Bonn), and the Max-Planck-Institut für Mathematik (Leipzig) through an IPDE fellowship.     

免费更换策略下耐用品垄断厂商的定价研究

耐用品厂商向消费者提供一定时间期限的免费更换服务已成为一种市场销售策略.免费更换服务期限和所需的更换成本又影响着耐用品的销售价格和销售量.针对耐用品厂商提供免费更换服务的情况,通过建立动态决策模型利用最优控制理论研究垄断厂商有关耐用品最优定价和免费更换服务期限等问题.研究得到:免费更换服务期越长,耐用品最优销售价格越高,而耐用品最优销售量越低;在以最优价格销售耐用品时,免费更换服务期和更换成本均与产品耐用度成正比例关系.     

Feedback Nash Equilibrium for Dynamic Brand and Channel Advertising in Dual Channel Supply Chain

This paper investigates dynamic brand and channel advertising and their effects on market expansion and market share in a dual channel supply chain by using differential game theory. Nash equilibrium of the differential game will be obtained by the feedback approach. A sensitivity analysis was performed to assess the impact of key parameters on optimal strategies and to characterize behaviors of both the manufacturer and retailer over time. Comparative statistics show that a higher compatibility of a product with online marketing leads to a higher advertising effort for the online channel by the manufacturer, an enhanced steady state for demand of the brand as well as greater sales in the steady state through the online channel.     

随机中断和随机需求下闭环供应链最优回收定价模型

讨论了由一个制造商、一个零售商和一个第三方回收商组成的闭环供应链的差别定价问题.基于博弈论的理论和方法在集中式和分散式决策情形下分别建立了第三方回收定价模型,并给出了随机中断和随机需求下闭环供应链的最优定价策略组合,最后通过数值例子分析了供应中断对最优批发价和零售价的影响.     

线上结合线下的供应链动态服务与定价决策研究

本文研究由一个传统电商企业和线下实体零售商组成的线上结合线下的供应链系统。由于线下服务努力能同时增加线上和线下的销售量,于是传统电商纷纷开设线下实体店,或者与已有的实体店进行合作。这两种模式分别对应集中决策和分散决策模式,因此本文构建了线上结合线下的供应链动态模型并研究这两种决策模式下的最优服务和定价决策。结果表明:(1)当线下渠道偏好增加时,无论是集中决策下还是分散决策模式下,企业都应该提高线下价格而降低线上价格以获得最优利润,而在分散决策模式下,传统电商还应该提高其批发价格;(2)成本分担策略能够提高线下实体店对服务的投入,从而提高服务和商誉水平;(3)成本分担策略能使线下零售店和传统电商的利润水平都得到了提高,实现了帕累托改进;(4)当满足一定条件时,成本分担-收益分担机制能够实现供应链的协调。     

云服务供应链技术创新与动态定价的微分博弈分析

考虑了时间因素对产品技术先进度的影响,引入微分博弈的方法在动态框架下研究云服务产品动态定价及技术创新问题。分别探讨了两种合作研发模式(创新成本分担契约和收益共享契约)下的微分博弈模型及均衡结果。结果表明,技术先进度敏感系数的增加会提高技术创新投入、云产品价格以及云服务供应链各成员利润;对于整个云服务供应链来说,选择低创新成本分担比例或高收益共享比例更加有利;当云服务供应链内部成员意见不一致时,可使用一次性转让合同来协调两方的行为。最后通过数值算例展示了模型的有效性。     

A Game-Theoretic Analysis for Coordinating Cooperative Advertising in a Supply Chain

In this paper, we investigate the coordination of cooperative advertising decisions in a supply chain with one manufacturer and one retailer. The manufacturer and the retailer invest in national and local advertising, respectively. The manufacturer also agrees to share part of the total local-advertising costs with the retailer. The model is analyzed using game theory. We also compare the results of our analysis with similar results from the literature developed for cooperative advertising.     

Pricing and Advertising of Private and National Brands in a Dynamic Marketing Channel

We consider a marketing channel where a retailer sells, along the manufacturer’s brand, its own store brand. We assume that each player invests in advertising in order to build the brand’s goodwill. One distinctive feature of this paper is the introduction of the negative effect of own advertising on other player’s goodwill stock evolution. We characterize feedback-Nash pricing and advertising strategies and assess the impact of the store brand and national brand’s goodwill stocks on these strategies in different settings. The main findings suggest first that investing in building up some equity for each brand reduces the price competition between them and propels the market power for both. Second, the retailer will pass to consumer an increase in its purchasing cost of the national brand in all situations as no coordination is taken into account to counter the double marginalization problem. Finally, the higher the brand equity of the store brand, the more the retailer invests in advertising.     

考虑服务水平的双渠道供应链定价策略研究

研究单个制造商与单个零售商组成的双渠道供应链系统定价问题.在分散决策和集中决策条件下讨论了零售商传统销售渠道和制造商开拓网上销售渠道分别以不同服务水平销售产品的双渠道供应链,从而得到了在集中式决策和分散式决策条件下的最优定价,并分析了服务水平对定价决策和渠道需求的影响.研究表明,当零售商渠道服务水平增加时,批发价也随之增加.本渠道的服务水平对本渠道的价格影响会大于对竞争渠道的价格的影响.渠道服务水平的提高会导致本渠道销售价格和本渠道需求的提高,也会对另一渠道产生一定的溢出效应.     

随机需求下具有不对称信息的闭环供应链的最优差别定价模型

在随机需求条件下建立了由一个制造商和一个零售商所组成的闭环供应链差别定价模型。在制造商成本信息对称和信息不对称情况下,分别讨论了闭环供应链的最优差别定价问题,得到了在不同信息条件下的最优定价组合以及最优的订购量.最后通过数值算例分析了成本信息不对称对两种产品的零售价以及订购量的影响.     

共享平台下供应链闲置资源动态优化配置策略

随着共享经济的发展,其领域已从消费环节延伸到供应链层面。供应链上闲置资源如何重新配置,以实现共享,提高资源利用率,是共享供应链企业面临的新问题。本文考虑基于共享平台的供应链闲置资源匹配过程的动态性,利用微分博弈和动态规划原理分别建立集中式决策下、无成本分担和有成本分担契约的分散式决策下共享供应链闲置资源的优化配置模型,并构建对应的哈密顿-雅克比-贝尔曼(HJB)方程,求解和分析三种情形下资源供应方、共享平台和需求方关于供应链共享闲置资源的最优配置策略。结果表明,成本分担契约在一定条件下可提高供应链闲置资源参与方的积极性,并使供应链上各参与方利润增加,实现共享供应链的Pareto改进。     

基于双边平台匹配努力的共享供应链动态定价策略研究

考虑在一个由双边平台、制造商和零售商组成的共享供应链中,研究双边平台匹配努力下的共享供应链动态定价问题。其中制造商通过平台共享其剩余产能,平台为动态地匹配制造商和零售商的供需资源而付出匹配努力,以此改变其服务水平,进而影响共享平台的交易费用、制造商的批发价格和零售商的零售价格。利用HJB方程构建微分博弈模型,分别探讨集中和分散式共享供应链中最优平台匹配努力和各成员的动态定价策略,得到不同情形下的动态定价轨迹,并分析了关键参数对定价策略的影响。结果表明,平台匹配努力通过影响其服务水平对最优/均衡解有正向影响,供应链各成员的定价策略取决于平台初始服务水平和稳态服务水平之间的关系。