Marketing strategies developed by merchants on e-commerce platforms are essential tools to increase sales. To attract consumers, merchants often design multiple promotions for their products and allow them to be stacked. However, combining multiple promotions is not always rational, as some may conflict with each other. In these cases, merchants may suffer unnecessary losses, i.e., the combinations of promotions may have loopholes, which need to be urgently addressed. Thus, this paper discusses the risk assessment and optimal design of promotional combinations. A risk assessment model is established by designing heuristic rules and using machine learning. Using this model, we analyze collected marketing data to identify and categorize various types of promotional loopholes. We then construct corresponding mixed-integer linear programming (MILP) optimization models that aim to maximize merchant profits while minimizing risk. Simulation experiments demonstrate the effectiveness of our predictive model in detecting promotional loopholes. Moreover, our optimization framework provides optimal promotional combination strategies that account for both profitability and risk. Compared to optimizing single promotions in isolation, our approach significantly reduces the likelihood of unreasonable promotional strategies. This provides a practical and effective tool for merchants to assess the risks of their marketing strategies and to optimize promotion parameters before implementation.

Marketing optimization plays an important role to enhance user engagement in online Internet platforms. Existing studies usually formulate this problem as a budget allocation problem and solve it by utilizing two fully decoupled stages, i.e., machine learning (ML) and operation research (OR). However, the learning objective in ML does not take account of the downstream optimization task in OR, which causes that the prediction accuracy in ML may be not positively related to the decision quality.