Maximize Expected Profits by Dynamic After-Sales Service Investment Strategy Based on Word-of-Mouth Marketing in Social Network Shopping

This paper discusses how word-of-mouth marketing affects the profits of product sales in social network-based shopping under good after-sales service. First, a new word-of-mouth communication model based on silent evaluation, positive evaluation, and negative evaluation is proposed. Second, we use the way of increasing after-sales service to achieve high praise and thereby maximize the expected profits. Thus, the proportion control problem of after-sales service investment is modeled as an optimal control problem. Third, the existence of optimal control is proved, and an optimal control strategy for dynamic proportion of after-sales service investment is proposed. Fourth, through data simulation of different real-world networks, it is verified that the expected profits under the dynamic after-sales service strategy is higher than that under any uniform control strategy. Finally, sensitivity analysis is performed to explore how different parameters affect the expected profits.