需求依赖价格、广告投人和质量控制的供应链模型

研究了需求受零售商销售价格和广告投入以及制造商质量控制影响的供应链协调问题,分析了零售商的广告投入以及制造商的质量控制对市场需求的影响,分别给出了集中决策和分散决策下零售商的最优销售价格、最优订购量和最优广告投入努力水平以及制造商的最优质量控制努力水平和最优批发价格,利用了特许经营契约来使供应链达到完美协调.最后,通过数值算例对模型进行仿真计算与分析.     

具强零售商和广告影响的闭环供应链模型

构建了一个具强零售商和广告影响的闭环供应链博弈模型.首先在集中决策和分散决策两种决策模式下,分别探讨了闭环供应链的定价,广告投入和回收率决策,并分析了广告效应对节点企业各决策变量和利润的影响,以及对比了强零售商下不同回收渠道的优劣.其次,考察了通道费契约对具强零售商的闭环供应链的协调作用.主要结论为: 1)与无广告效应...     

突发事件下两部收费契约协调闭环供应链研究

本文针对由一个制造商和一个零售商组成的零售商负责回收闭环供应链的协调问题,首先设计了稳定环境下两部收费契约协调闭环供应链模型。在此基础上,针对突发事件影响下造成零售商面临的市场需求发生变化时,运用K-T条件对集中式决策下的闭环供应链的最优利润进行求解,给出了最优应对策略。通过研究表明:当突发事件发生时,原适用于稳定环境下的两部收费契约将不再对分散式决策下的闭环供应链起协调作用。为此,本研究给出了两种协调策略,一是在制造商自身承担突发事件引起的偏差成本的情况下,通过对原有的两部收费契约中的批发价格和回收价格进行改进;二是若由零售商承担偏差成本,则可保持原有的两部收费契约中的批发价格和回收价格不变。在两种策略下,制造商和零售商均通过重新讨价还价确定合适的固定费用,可协调突发事件影响下的闭环供应链,并证明了两种协调策略的可行性。     

零售与回收双竞争环境下闭环供应链线性转移支付契约研究

利用博弈理论研究了由单个制造商与n个零售商组成的零售与回收均存在竞争的闭环供应链的协调问题,给出了分散决策与集中决策情形下系统成员的最优决策和收益,发现分散决策使闭环供应链系统收益受损;提出了一种线性转移支付契约,实现了闭环供应链的协调.最后,通过一个数值算例验证了研究结论.     

零售商公平关切下双渠道闭环供应链的协调

在双渠道闭环供应链中考虑零售商具有公平关切行为倾向,针对集中、分散两种决策情形分别建立双渠道闭环供应链定价模型,研究和对比了两种不同决策情形对直销价格、零售价格、回收价格及供应链系统利润的影响.研究表明,分散决策情形的系统利润要低于集中决策情形的系统利润;制造商提供一个由批发价格、直销价格和回收转移价格组成的协调契约可以协调双渠道闭环供应链,但该契约只对零售商有利,对制造商不利,为此,通过增加一个利润共享补充协议或两部定价补充协议可以有效协调双渠道闭环供应链,实现制造商和零售商的双赢;而零售商公平关切行为的存在将增强零售商参与协调时的议价能力,进一步影响零售商利润分享比例或零售商支付给制造商固定费用的变化范围.     

奖惩机制下考虑销售努力的闭环供应链协调

以一个制造商和一个零售商组成的闭环供应链为研究对象,考虑在政府的奖惩机制下需求同时受销售价格和销售努力影响的供应链协调问题.首先,在集中决策下,研究了供应链系统的最优决策,并给出了均衡解存在的条件和奖惩力度所满足的范围;在分散决策下,重点分析了奖惩力度以及销售努力对供应链双方决策的影响.其次,使用特许经营契约能够使供应链达到协调.最后,给出了数值算例和仿真分析.     

政府补贴下考虑规模效应的动力电池梯次利用闭环供应链决策与协调

针对零售商主导的考虑政府补贴和规模效应的动力电池闭环供应链,研究成员最优决策及协调问题。分别在无补贴、补贴零售商、补贴制造商、补贴第三方回收商四种情形下,分析了补贴对象、规模效应、再制造动力电池比例对成员最优决策及利润的影响,并实现了闭环供应链的协调。研究表明:政府补贴能够降低零售价,提高回收率以及各成员利润;补贴第三方回收商相比补贴零售商和补贴制造商而言,回收率以及第三方回收商利润提高更为明显,补贴零售商和补贴制造商相比补贴第三方回收商而言,零售价降低、制造商和零售商利润提高更为明显;可用于再制造的废旧动力电池比例增大能够降低动力电池销售价格,提高动力电池回收率;第三方回收商规模效应的增大有利于降低零售价格,提高动力电池产品回收率及闭环供应链各成员收益。     

非对称信息和模糊需求下的闭环供应链协调决策研究

在模糊需求和非对称销售价格信息下,研究了由单一制造商和零售商组成的两级闭环供应链系统的协调问题。通过建立不确定环境下的集中决策和收益共享-费用共担契约决策模型,分别得到了不同模型下闭环供应链系统的最优策略。并进一步通过算例分析了契约下供应链各方收益随模糊需求和价格的变化情况,以及该契约对整个系统决策效率的影响。结果表明:收益共享-费用共担契约能有效实现模糊闭环供应链系统的协调,实现闭环供应链系统决策的最优化;其次,需求和零售价格的不确定性程度越高,对零售商的最优订购量、供应链成员及系统利润的影响也越大。     

具公平行为的闭环供应链动态均衡分析

针对的闭环供应链由单个制造商和单个零售商组成,研究两者的公平行为对闭环供应链动态均衡的影响.利用微分博弈理论和贝尔曼连续型动态规划理论分别求解了分散、集中以及成员公平等五种决策模式下的供应链绩效.研究发现:1)产品品牌声誉的提升有利于供应链成员利润的增加.2)零售商具公平行为时有利于零售商利润的增加;制造商具公平行为时,供应链绩效会减小.3)供应链成员均具公平行为会导致产品零售价、回收努力、营销努力均减少.     

考虑延迟现象的质量改进投入和营销努力动态协同策略

利用时滞微分方程刻画质量改进投入对品牌商誉提升的延迟现象,分别构建了制造商和零售商采取非合作博弈、合作博弈以及成本分担的部分合作博弈(制造商参与营销的单向部分合作博弈、零售商参与生产的单向部分合作博弈、制造商参与营销及零售商参与生产的双向部分合作博弈)五种决策模式下的微分博弈模型。借助哈密尔顿极大值原理,求解得到五种情形下的制造商最优质量改进投入策略和零售商的最优营销努力策略以及供应链利润。对比五种博弈模式下的结果发现:1)延时现象会降低制造商进行质量改进投入的积极性,但对零售商营销努力无影响;品牌商誉在延迟现象影响下出现先衰减后提升的演进规律;2)合作博弈对于供应链绩效总是最优的,三种成本分担的部分合作博弈契约虽不能实现供应链的完全协调,但可以对非合作博弈情形进行帕累托改进;3)对比两种单向部分合作博弈,在提高供应链利润方面,制造商参与营销的成本分担契约优于零售商参与生产的成本分担契约;4)三种成本分担契约中,双向合作的部分合作博弈是供应链的最优选择,但随着延迟时间增大,其帕累托改进效果将不再明显。     

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.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Consumer Behaviour and Optimal Advertising

Using Nicosia's formulation of consumer behaviour, optimal advertising strategies are derived. Other studies, using empirical data, have shown that advertising should be concentrated at the early part of the product life cycle and the paper discusses what assumptions about consumer behaviour must be made to obtain that results. Specifically, it is shown under what conditions pulsing advertising campaigns are optimal.     

关键词广告支付模式的研究

关键词广告是主要用于搜索引擎的一种广告销售机制.所谓关键词既指搜索用户在搜索框内输入的检索词,也指机器程序从用户浏览的网页内容中抓取的词.广告主的广告依据关键词触发而展现在相应网页上.对搜索引擎来说,选择广告的支付模式是销售机制的核心命题.在互联网发展的实践中出现了许多支付模式,比如按展现付费(Pay-Per-Impression),接点击付费(Pay-Per-Click),按呼叫付费(Pay-Per-Call)和按销量付费(Pay-Per-Sale)等.如果实现这些支付模式的条件都具备,那么哪一种付费方式对搜索引擎是最有利的?试图回答这个问题.主要结论是对搜索引擎来讲,按点击付费是最优或近似最优的支付模式.     

Modelling Cooperative Advertising Decisions in Franchising

Advertising fee decisions in franchise systems are a frequent source of conflict between franchisors and franchisees. Such disagreements persist because the win-win potential of vertical cooperative advertising is not well appreciated. Our paper introduces a formal normative approach for analyzing, understanding and subsequently making these vertical cooperative advertising decisions within a franchising context in a manner that results in optimal system-wide returns. The model demonstrates that cooperative determination of franchisor's and franchisee's advertising contributions may yield superior payoffs for both exchange partners than the total payoff if the franchisor and franchisee seek to optimize their individual objective functions. Three types of models are developed and evaluated (i.e. deterministic, stochastic and under conditions of differing perceptions of the sales response functions to advertising). Conclusions hold under all three model variants. Industry implications are also presented.     

Advertising strategies in a franchise system

The main question of this research is: Who should undertake promotional and brand-image advertising if the franchisor and franchisees act so as to maximize their respective profits? To address this question, we study a two-stage advertising game between a franchisor and two adjacent franchisees. In the first stage of the game, the franchisor chooses between three advertising models – centralizing or delegating the two types of advertising to the franchisees or delegating only promotional advertising. In the second stage, given the franchisor’s choice of an advertising model, the two franchisees decide whether or not to cooperate. Our main findings are that (1) the franchisees should cooperate if the franchisor delegates either both brand-image and promotional advertising or promotional advertising, although cooperation between franchisees does not necessary improve the franchisor’s profits. (2) The choice of an advertising arrangement critically depends on the margins as well as the costs of performing both promotional and brand-image advertising. We also discuss the conditions under which the three advertising models should be implemented.     

Different Approaches to Advertising Media Selection

Research groups on both sides of the Atlantic are attempting to use the power of mathematics to aid the decision-maker in dealing with the complex media scheduling problem. This paper reviews, compares and critiques several possible approaches. The approaches reviewed are: linear programming, dynamic programming, marginal analysis, heuristic programming and simulation. At least one particular model of each approach is discussed in detail.     

Advertising Events in a Competitive Framework

We study the problem of how to minimize the advertising costs for a one-time entertainment event taking competition into account. Using the concept of Nerlove-Arrow goodwill, we describe a market where two single players organize two different events. A single-player instance of the same problem has been analyzed already in the literature using both the Nerlove-Arrow dynamics and the Bass dynamics, but without considering a competitive framework. In this work, starting from a linear-quadratic model, we consider competition in the market and we study the problem in the settings of linear-quadratic deterministic and stochastic differential games. The analytical tractability of the problem allows us to characterize the Nash equilibria and to study the new features of the competitive scenario. In the deterministic instance of the model, we show that competition decreases efficiency. On the other hand, when the goodwill evolution is stochastic, competition may even increase efficiency by a diversification effect.