This paper proposes a comprehensive framework for project selection problem under uncertainty and subject to real-world constraints, like segmentation, logical, and budget constraints. The framework consists of two main phases. In the first phase, the candidate projects are ranked considering the uncertainty, through a Monte Carlo simulation linked to a multi-criteria approach. In the second phase, the overall complete preorder of the projects in different iterations is first determined and then used in another Monte Carlo simulation linked to an integer programming module in order to effectively drive the final portfolio selection while satisfying the budget, segmentation and other logical constraints. The proposed framework is implemented in a case study to show its usefulness and applicability in practice. Finally, a comparison is carried out between the proposed approach and its deterministic counterpart and the corresponding results are discussed.