创新产品扩散的多阶段动态模型

本文在决策理论框架下应用动态分析方法建立了一个包括价格与广告影响因素的多阶段创新产品扩散模式.在耐用品情形下,扩散系统是稳定的,免费商品只能影响产品的扩散进程,但不能影响其最大采用数量.在重复购买情形下,并在一定条件下,扩散系统会趋向于创新产品与竞争产品共存.分析表明多阶段模型包括了Mesak模型与Bass模型为其特例.最后以Internet采用进行了实证分析,结果表明拟合比现有研究更加符合实际.     

免费商品对独立产品扩散的影响分析

以低值易耗品为研究对象, 基于传统的Bass扩散模型, 在价格营销策略下建立了多时期免费商品赠送水平的优化模型群, 将重复购买、批量购买等众多因素引入模型中, 应用灵敏度分析探讨了参数变化时最优解的稳定性, 结果表明: 免费商品的赠送会加快独立产品的扩散过程; 在价格策略选择时, 采用渗透策略的结果最好; 免费商品在首期赠送的效果要优于其他时期赠送, 形成了"首期赠样效应"; 当消费者需要批量购买时, 就需要更多的免费商品的赠送使得消费者对本商品的了解程度增加, 但在批量购买较高时赠送水平会维持在一个稳定水平下. 在此基础之上, 为企业的实际应用给出了基本操作步骤.     

Stochastic Optimal Control Problem in Advertising Model with Delay

This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.     

带有两种营销模式的供应链合作广告协调模型

本文考虑了带有直营店和代理商两种营销模式的Newsvendor型产品合作广告问题,分别建立了分散决策和集中控制下制造商和代理商的最优广告决策模型,分析了需求的随机性及直营店的营销模式对供应链双方广告决策的影响．给出了一个基于地方促销广告费用分摊的策略以实现供应链协调．最后,用数值仿真验证了本文的相关结论并得到一些重要的管理启示．     

供应链中耐用品的广告投入和零售价策略分析

针对供应链中制造商和零售商关于耐用商品的合作广告和零售价定价问题,本文构建了一个微分博弈模型. 将市场累计销售量作为状态变量,并把广告和价格因素引入到市场累计销售量的动态方程中. 运用汉密尔顿-雅可比-贝尔曼方程,分别得到了零售商的最优定价和广告投入策略以及制造商对零售商广告成本的最优分担比例;发现零售商的最优定价和制造商的分担比例均为常数,而零售商的广告投入随市场累计销售量的增加而递减;并且给出了制造商对零售商进行广告补贴的阈值. 最后,给出了各厂商决策变量的比较静态分析.     

随机需求下单制造商两零售商合作广告协调模型

考虑了由单个制造商两个零售商所组成的供应链生产销售Newsvendor型产品的合作广告问题.分析了制造商的品牌广告投入及两个竞争零售商的地方促销广告投入对每个零售商需求的影响,分别给出了分散决策和一体化决策下制造商的最优广告投入,两个竞争零售商的最优地方促销广告投入及销售期初的最优订购批量,利用利润共享契约使得供应链达到协调,并从供应链各成员风险偏好的角度对渠道收益的分配问题进行了探讨.     

广告竞争模型的最优控制策略研究

考虑了竞争性和信息性两种广告对企业市场份额不同作用,提出一个在两强竞争情况下的动态广告投入模型,运用动态规划的Bellman方程求出模型的闭环Nash均衡解,得到企业应采取的广告最优控制策略,并进一步研究Nash均衡解有经济意义的参数范围以及Nash均衡解收敛的条件.最后用一个数值例子分析了Nash均衡下的广告策略.     

模仿者基于一定市场份额条件下产品进入市场时间的确定

新产品进入市场时间的确定问题是现代市场营销领域重要的研究课题，利用Bass首次购买扩散模型，借助马尔柯夫过程分析率先创新企业和拷贝式模仿创新企业在创新产品进入市场后不同时刻各自的市场份额，解决模仿者基于保持一定市场份额条件下市场进入时间的确定问题，同时指出Bass模型描述的创新扩散速度会受到品牌忠诚度的阻滞。     

Cooperative advertising and pricing models in a dynamic marketing channel

This paper studies dynamic pricing and cooperative advertising strategies in a two-member channel of distribution. We propose differential game models that incorporate the carryover effects of advertising over time for both manufacturer and retailer. Two different models are studied. Firstly, we discussed a non-cooperative differential game which the manufacturer supports partially the cost of the promotion activities. Secondly, both channel members cooperatively determine their respective strategies. In these two cases, dynamic cooperative advertising and pricing strategies are characterized. Then numerical simulation method is applied to analyze the sensitivity of main model parameters and compare the main results of the two models. The simulation results show that the cooperative model achieves better coordination than the non-cooperative model with the following features： all channel members achieve higher advertising efforts and profit level in the cooperative case rather than in the non-cooperative case.     

基于比较利益下农业生产模式的模型研究

在连续时间的假设下,研究了农业产出量服从几何布朗运动的最优控制问题。首先借助于马尔可夫过程理论确定出转移概率密度,再利用分布参数系统模型来描述某个地域的粮食和经济作物的产出量在随机变化的情况下,农业生产的分布模型。最后探讨了在均衡条件下农业生产者以寻求利益最大化为目的的最优控制方程。同时给出了某地域粮食及经济作物的产量预测分析模型。参9。     

An optimal dynamic advertising model with inverse inventory sensitive demand effect for deteriorating items

This paper proposes a dynamic advertising model for deteriorating items, and the demand is influenced by goodwill and inventory level. The goodwill affected by advertising effort has a positive effect on demand while the inventory level has a negative effect on demand, which is named as inverse inventory sensitive demand effect. We assume that the deteriorating rate could be influenced by the inventory level and we determine the deteriorating rate formulation based on this assumption. The optimal advertising effort and inventory level are obtained by solving the optimization problem based on Pontryagin’s maximum principle. Furthermore, numerical studies are provided and some managerial insights are presented.     

知识项目价值与企业效益间的动态关系模型

知识项目价值与企业效益密切相关,准确估价知识项目价值有助于更好地管理企业知识、辅助企业决策。根据知识的可扩散、贬值、增值特点,结合ABC模型和Bass模型对知识项目价值和企业效益间的动态关系进行了探究,并给出了相应的动态关系变化模型。     

考虑库存能力约束的批量问题与定价的联合决策

针对多周期离散时间情形,研究了库存能力约束下如何有效地协调定价决策与批量决策,使得企业利润最大化。建立了非线性混合整数规划模型。分析了最优解的特征,详细讨论了子问题的求解方法。提出了基于动态规划的精确算法,可以在多项式时间内求解出联合决策问题的最优定价与最优生产计划。实验结果分析了库存能力与最优利润、最优生产计划之间的关系。     

Coordinating Pricing,Ordering and Advertising for Perishable Products Over an Infinite Horizon

Numerous empirical studies show that advertising effort can stimulate demand in both current and future periods, and there is an interaction between pricing, advertising and ordering decisions. How do these decisions interact with each other and what is the effect of advertising on pricing and ordering decisions? To understand this interaction, we consider a newsvendor-type firm that sells a perishable product in a stable market and dynamically determines the joint ordering, pricing and advertising strategies. The problem is modeled as an infinite horizon newsvendor problem with an advertising carryover effect and price-sensitive demand. We characterize the optimal pricing, advertising and inventory strategies and their comparative statics, and consider how this policy differs from the traditional approach without the advertising effect. We show that the optimal effective advertising level is monotonically increasing with the effective advertising level in the previous period, and hence the optimal strategies (advertising, pricing, inventory level) globally converge to the steady states in the long run. We numerically show that the optimal policy can reap significant profit, which underscores the importance of the advertising-driven ordering and pricing strategies.     

损失规避零售商订货量与广告费用的联合决策

针对实际的决策偏差,研究了损失规避零售商在不确定性需求下的广告费用和订货量的联合决策问题,并基于前景理论 框架下的损失规避效用函数建立了相应的联合决策模型.研究结果表明:在一定条件下,损失规避零售商的最优订货量和广告 费用均低于风险中性零售商的最优订货量和广告费用,而且随着缺货成本的增加,损失规避零售商会逐步减少广告投入但却 增加订货量.还通过理论分析和数值实验,研究了模型参数变化对最优订货量和广告费用的影响.     

Quality improvement and pricing with reference quality effect

This article studies a problem of joint pricing and dynamic product quality investment with consumers’ reference quality effect under the existence of quality inflation. Optimal control models are constructed to maximize the total profit with a limited quality investment capacity, where the demand is sensitive to historical product quality level. The optimal quality investment strategies for finite and infinite planning horizon are given respectively by solving these optimal control models on the basis of Pontryagin’s maximum principle, which enables the exact trajectory of the optimal quality investment with the reference quality effect over time to be depicted. In addition, an effective algorithm is designed to generate the optimal joint pricing and dynamic quality investment policy for the system. The main difference between the strategy of finite planning horizon and that of infinite planning horizon is that the latter is a constant. Our study indicates that it is never optimal for firm to increase quality investment all the way throughout the planning horizon. The level of quality investment is higher when taking into account the impact of reference quality. Moreover, numerical example is given to illustrate the validness of the theoretical results. Also, sensitivity analysis is carried out to show how system parameters affect the optimal policies, and some managerial suggestions are presented.     

考虑商户广告投资的网上交易平台定价

在商户广告投资内生化和双边平台特性下,建立两阶段动态博弈模型,研究网上交易平台的最优定价及利润.研究表明:1)平台定价策略受广告效果和平台固有效果两种作用的影响.广告效果相对平台固有效果较小时,商户实力(与投资预算有关)的相对差距较小,平台定价策略倾向于让所有商户都加入;广告效果相对较大时,平台会根据商户实力的相对差距制定定价策略,差距越小(大),平台希望吸引的商户就越多(少).2)商户价格敏感性较高时,平台定价较低,利润较小.商户外部性较大时,平台应吸引更多的商户.特别地,广告效果相对较小时,商户外部性越大,平台定价越高.     

社会网络下更新产品扩散的投放时机和种子优化

近年来，更新产品的延期投放成为许多企业的产品运营策略。目前关于产品投放时机的研究主要基于Bass模型，假定同质用户，没有考虑具体的社会网络，也没有优化初始的投放种子选择。基于社会影响力最大化模型的更新产品投放时机和种子优化问题：在一个已存在旧产品的社会网络 中，产品以扩散模型 的形式传播其影响力，但更新产品投放时旧产品停止扩散，如何选择投放阶段 和 个更新产品的种子使得新旧产品利润之和最大化。在本文的扩散模型中，如果用户来自已购买产品的邻居影响力超过某一确定阈值，则该用户保持激活并影响其未激活邻居，当未有新的激活用户时停止扩散。本文建立了更新产品扩散的投放时机和种子优化问题的整数规划模型，设计了求解大规模问题的多阶段贪婪算法。计算实验显示，相比传统贪婪算法，该算法具有更高的求解效率，相比度数下降算法、随机算法，该算法具有更好的求解质量。同时在一个真实网络中进行扩散模拟，发现：更新产品利润小、种子数量少、计划阶段限制大时，延期投放容易使厂商获得更高的利润和市场效果。     

经常购买模型及其参数的极大似然估计

在分析巴斯模型和重复购买的产品生命周期模型等的基础上，提出经常购买模型，详细讨论该模型的参数的极大似然估计法，并采用实例检验模型及参数估计方法，分析模型的参数估计结果，在此基础上使用模型做产品销量预测，表明模型的参数估计方法及预测方法的有效性。     

基于学习理论的产品重新设计策略

为研究在单一产品生产环境中产品重新设计对价值、成本和质量管理有关问题的影响，我们提出了一个动态规划模型，该模型可以确定企业最优的产品重新设计深度和实施重新设计的最优时间，这样能使累积的净产品价值最大化。该模型可以使用不同的学习率和不同的成本数据进行计算，最后的结果表明，早期实施最优产品重新设计策略提高了产品的累积净价值。