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The consideration of the substitution phenomenon in the project portfolio selection problem can improve the robustness of project portfolio selection and help enterprises better achieve their strategic objectives. However, the existence of inter-project risk propagation will have a negative impact on project substitution. This paper proposes a new framework for project portfolio selection and constructs a risk propagation model based on strategic objectives to study the impact of risk propagation on substitution in the project portfolio.

The authors first construct a risk propagation model based on strategic objectives to describe the risk propagation between projects. Then the project substitution phenomenon based on risk propagation is put forward, and the calculation method of substitution loss is given. Finally, a robust project portfolio selection framework based on strategic objectives considering risk propagation is constructed.

The analysis of a case study demonstrates that (1) With the increase of risk intensity, the strategic loss of the same project portfolio increases linearly, and under the same risk intensity, the more projects in the portfolio, the stronger the robustness. (2) Considering risk propagation, the effect of project substitution is significantly weakened, and the strategic loss rate of the project portfolio is significantly increased compared with that of a direct attack.

This study is the first to take the project substitution into account in the project portfolio selection process. Moreover, the authors describe inter-project risk propagation and analyze the impact of risk propagation on the project substitution phenomenon. Finally, the authors extend the evaluation index of robustness. This paper puts forward a new way to solve the problem of project portfolio selection.

This study aims to examine the roles of principal resilience (psychological, social and spiritual) and trust in colleagues in predicting the flourishing of school principals, considering different career stages.

Utilising multigroup structural equation modelling and mediation analysis, data were collected from a sample of 1,274 school principals in China. The study investigates the direct impact of resilience on flourishing and the mediating role of trust in colleagues, with a focus on variations across different career stages.

The findings reveal that all aspects of a principal’s resilience significantly impact their flourishing, with trust serving as a partial mediator. Notably, the influence of spiritual resilience on flourishing is significant only for principals in the later stages of their careers.

This research contributes to the expanding body of literature on educational leadership by highlighting the importance of resilience and trust in fostering principal flourishing. The insights gained offer valuable knowledge for developing support strategies to enhance the flourishing experiences of school principals throughout their careers.