A scenario-based mathematical approach to a robust project portfolio selection problem under fuzzy uncertainty

Abstract

As a major concern of chief managers in each organization, project portfolio selection has a special place in their responsibilities. To assist managers in making decisions, applicable optimization models play an essential role in such processes. In this regard, this paper provides a stochastic optimization model for a project portfolio selection problem under different scenarios. Providing the novelty in the model along with making it closer to reality, the interdependency between revenue and cost of projects is considered. Due to the inherent uncertainty of parameters, the revenue and cost of each project, as well as contributed capital, follow triangular fuzzy parameters. Contrary to the previous model, the appreciation of assets is considered in the proposed model as the other novelty of the proposed model. To tackle the uncertainty of parameters, a robust possibilistic approach is used, which has been first-ever devised in such problems. Being both optimistic and pessimistic approaches available for decision-makers, a new measure is introduced to make the model inclusive. Moreover, by considering the confidence level as both parameter and decision variables, the robust possibilistic programming approach is adopted to solve the proposed model. Using the new proposed measure, the optimal average value of robust model are obtained under different confidence level. Finally, solving the optimization model, the results are provided by implementing the realization for uncertain parameters, and regarding the obtained results, discussions are made to provide some insights to the managers.