Multi-stage diffusion dynamics based on optimal control theory

In this relentlessly innovative market, product diffusion has a pre-eminent importance for any firm. The comprehend study of the adoption process assists the manufacturer to facilitate the growth of their product. It is observed that the adoption of the product goes through multiple stages before the actual adoption occurs. As market shows dynamic behavior, the fluctuating price acts as a vital characteristic in the consumer buying decisions. In the present paper, a multi-stage innovation diffusion model is formulated where the evolution of sales takes place in three stages, namely, development of innovation awareness, motivation and ultimate adoption. The proposed model showcases the impact of dynamic pricing policy of the product on the motivation for actual adoption by the potential consumers. For this purpose, an optimization model based on optimal control theory problem is formulated. In addition, analytical results for the optimal pricing policy for an innovation are also investigated. The proposed model is further tested on different real life sales data sets for validation purpose and results provide empirical support to the model. The paper also provides the numerical illustration of the discrete model of proposed problem to evaluate the influence of price, the marketing factor on the company's new product introduction approach.