Modeling for delay of risk propagation in divisible project portfolio selection based on the project interaction

• The concept of risk propagation delay in a portfolio was proposed for the first time. • Complex network theory and diffusion dynamics theory are applied to describe the relationships between projects and the risk propagation intensity. • A divisible portfolio selection model considering the risk propagation delay in the project portfolio network is established. • A reinvestment coefficient is provided, allowing managers to adjust the reinvestment ratio based on actual conditions. • Provides a decision support tool for corporate managers with risk warning and resource allocation optimization, offering guidance for controlling the propagation of safety risks in projects. With the increasing enterprise environment uncertainty and project scale, the relationship between projects becomes more complex, which makes risk management a significant challenge in portfolio selection. This study focuses on the issue of risk propagation in the project portfolio selection process within dynamic and complex environments. Existing research lacks an in-depth discussion on the temporal delays in risk propagation. To assist decision-makers in timely capturing potential threats and improving the overall performance of the portfolio, this paper innovatively introduces the concept of risk propagation delay . Using complex network theory and diffusion dynamics theory, the study analyzes the interactions between projects and the mechanisms of risk propagation. A project portfolio selection model considering risk propagation delays is developed, and a comparative model is designed to analyze and verify the effectiveness of the proposed model. The research findings suggest that considering risk propagation delays helps companies avoid projects with potential risks during the selection process, reducing losses; project managers can assess the losses of projects at each stage and, by actively interrupting projects, rationally allocate the execution proportions of projects at each stage to maximize returns. The conclusions of this study have important practical value for enhancing the stability of project portfolios and the sustainable development capacity of enterprises.