A comparative study of fuzzy multi-objective investment project portfolio selection and optimization based on financial return and different risk measurements

Competitiveness in global market is getting more intense. Due to resource and budget constraints, firms need to achieve their expected goals and satisfy all investment constraints under uncertainty within these limitations. Selecting the set of projects among other candidates to get the most efficient portfolio requires a lot of attention from the Decision Makers (DMs) as this consideration no longer relies purely on the financial term. This problem becomes a multi-objective problem under uncertainty where the financial return and risk from uncertainty are required into the trading off consideration. Due to the financial uncertainty, the chance-constrained programming has been employed in this study for defuzzifying and solving uncertain optimization problems at a specified confidence level that is defined by the DMs. This multi-objective project portfolio selection is to optimize the return maximization and risk minimization simultaneously. Various kinds of risk measures, Lower-Semi Variance Index (LSVI), the absolute deviation with the expected Fuzzy Net Present Value (FNPV), and the absolute mean-Conditional Value at Risk (CVaR) gap are provided in the selection of risk measures to show their differences in characteristics and performances in the obtained results. Since, such problems can consist of many project candidates and complex constraints, which may grow beyond the application of the exact optimization approach, a meta-heuristic method, Genetic Algorithm (GA), is introduced to optimize this problem through designing and constructing a decision support tool for the investment portfolio selection and optimization. The applicability of the proposed comparative approach and the constructed tool are illustrated through examples.