基于巴斯模型的消费者推荐奖励和广告投入动态定价决策  

Optimal Dynamic Pricing of Consumer Referral Reward and Advertising Investment Based on Bass Model

作　　者：段永瑞[1] 尹佳 DUAN Yong-rui;YIN Jia(School of Economics and Management,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学经济与管理学院,上海200092

出　　处：《中国管理科学》2020年第8期65-75,共11页Chinese Journal of Management Science

基　　金：国家自然科学基金资助项目(71371139,71771179,71532015,71502088);上海市曙光人才计划(13SG24)。

摘　　要：本文从新产品扩散的过程出发,构建了同时考虑口碑效应和广告效应的产品扩散模型,研究企业推荐奖励和广告投入的动态定价问题。利用汉密尔顿函数和最大值原理得到最优解,并结合多个关键参数对最优解进行了敏感性分析。研究发现:最优推荐奖励呈先减少后增加趋势,最优广告投入则是逐渐减少;对于高价值产品,企业应采取高价格高奖励的策略;企业的推荐奖励策略和广告投入策略会受到推荐奖励效率、广告效率、自发购买比率和传统口碑效的影响。本文的研究结论对企业的推荐奖励和广告策略设计有一定的理论指导意义。With the rapid development of mobile internet,consumers are willing to share ideas about product,service or shopping experience and spread word of mouth on the internet.The consumer referral reward program(RRP)has been widely applied in online sales.There is no deny the fact that the company which has adopted the RRP does not stop advertising their products at the same time.In this paper,a product diffusion model is formulated which considers both the word-of-mouth effect and the advertising effect,and a dynamic pricing problem of the consumer referral reward and the advertising investment is studied.Assume the population size is 1.In our dynamic model,the state of the system is the cumulative sales,while the instantaneous sales rate has four resources:new consumers from innovation,advertisement,the WOM and reward referral.First,as for this optimal control problem,an optimal solution of the consumer referral reward and the advertising investment is obtained based on the Hamiltonian function and the maximum principle.It shows that the optimal trajectory for referral reward is decreased first and then increased,while the optimal trajectory for advertising investment is reduced gradually.Furthermore,numerical examples,comparing the coefficients from previous research,are provided,together with sensitivity analysis of the optimal solution with respect to major parameters.The consumer referral reward strategy and advertising investment strategy will be influenced by the reward efficiency,advertising efficiency,spontaneous purchase ratio and traditional word of mouth.(1)For high value products,it is advisable for enterprises to adopt a high-price-high-reward strategy.(2)When the referral is effective,the referral bonus and advertisement input should be higher.(3)It’s better to sustain the high level of referral reward when the advertising doesn’t work.(4)A high spontaneous purchase ratio means the product has advantages in quality,brand or something else.In such circumstance,it’s wise to provide a lower referral

关 键 词：消费者推荐奖励 广告 口碑效应 巴斯模型 最优控制问题 

分 类 号：F270[经济管理—企业管理]