Joint Optimization of Robust Portfolio Selection and Risk Response in R&D Project Management

Selecting appropriate research and development (R&D) projects under budget constraints is a critical yet challenging task for enterprises. During development, these projects are inevitably exposed to risky events, which may lead to performance loss, turning the optimal “here-and-now” selection decisions into suboptimal operational outcomes. We propose a joint optimization framework for project portfolio selection and risk response in uncertain environments, explicitly accounting for their interdependencies and budget trade-offs. A two-stage robust optimization (TSRO) model is developed to protect against worst-case scenarios. A key feature is a decisiondependent budgeted uncertainty set capturing the endogenous dependence of performance loss on portfolio selection decisions, together with a non-linear function characterizing the effects of risk response. We devise a tailored solution method to transform the original complex model into a single-level mixed-integer linear program solvable with off-the-shelf solvers. Extensive numerical experiments are conducted based on a 50-project R&D case. The proposed TSRO model consistently outperforms benchmark methods, particularly under worst-case scenarios. Sensitivity analyses further reveal that optimal solutions are highly responsive to the decay rate (representing the risk response effectiveness) while remaining relatively robust to the residual rate of failed projects' values. Moreover, the results suggest that under tight budgets, managers should prioritize a smaller set of projects with intensive risk response, whereas with generous budgets, a broader portfolio becomes optimal. Overall, this study offers an integrated framework that not only enhances decision quality in project portfolio management but also provides actionable insights for balancing selection and risk response.