A new dynamic two-stage mathematical programming model under uncertainty for project evaluation and selection

•Project selection is a complex task involving several stakeholders and multiple criteria under uncertainty.•We propose a two-stage multi-criteria decision making and mixed integer linear programming approach.•We first use fuzzy TOPSIS to evaluate projects while handling the uncertainty factor.•We then formulate a bi-objective mixed integer linear program to optimize profit and qualitative criteria.•We demonstrate the applicability of the proposed model in the cybersecurity industry. Project portfolio evaluation and selection is a complex task involving an exhaustive assessment of competing projects with interdependencies and synergies based on multiple and often conflicting criteria. The additional factor of uncertainty further complicates this complex task. This study proposes a two-stage hybrid multi-criteria decision making and mixed-integer linear programming for evaluating and selecting projects with interdependencies under uncertainty. In Stage I, we use the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) to evaluate the alternative projects under uncertainty. In Stage II, we formulate a bi-objective mixed-integer linear program to optimize profit and qualitative values for each portfolio by considering project synergies, human resources capabilities, and employee training opportunities under different scenarios. The proposed model produces portfolios with quantitative and qualitative values for each scenario under consideration. We demonstrate and validate the applicability and efficacy of the proposed approach through a real-world case study in the cybersecurity industry.