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

Abstract: 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 reward and keep a lower advertisement density. (5)When traditional WOM efficiency is high, it's time to make the best use of WOM strength to sustain both referral reward and advertisement higher.

Key words: consumer referral reward, advertising, word-of-mouth, bass model, optimal control