A benefit-to-cost ratio based approach for portfolio selection under multiple criteria with incomplete preference information

Benefit-to-cost ratio (BCR) measuring is a useful approach for selecting portfolios of projects when they are evaluated applying multiple and conflicting criteria. A multiattribute value function can be used to measure the benefit of each project, which allows one to evaluate the BCRs, rank projects, and select them according to the available budget. However, here, there is a significant difficulty associated with the inaccuracy in the values of criteria scaling constants, which may not be exactly known by decision makers (DMs). Considering this, the present work is directed at overcoming this difficulty by developing a BCR-based model for selecting portfolios under incomplete information about criteria scaling constants. During the elicitation process, DMs answer questions on preferences by considering tradeoffs amongst criteria. The provided information is converted into inequalities forming a space of criteria weights. These inequalities serve as constraints for linear programming models, which are processed to find dominance relations between projects, considering their BCRs. The process is supported by developed computing tools. The formation of a portfolio of research and development projects, which are to be executed by a Brazilian electric energy utility, is presented to illustrate the paper results and their practical applicability.