Multi-Objective Fuzzy Project Portfolio Optimization with Divisibility: Integrating Financial Return, Downside Risk, and Societal Impact

Abstract

This study develops a fuzzy multi-objective project portfolio selection model to support investment decision-making under uncertainty. The framework incorporates project divisibility and multi-period planning, enabling flexible allocation and scheduling of investments across competing projects. Investment costs and cash flows are represented as triangular fuzzy numbers to capture forecasting imprecision. The model simultaneously maximizes expected return while minimizing downside risk and societal impact. Expected return is evaluated using discounted cash flows, downside risk is measured through period-wise deviations below expected performance, and societal impact is assessed to support responsible investment decisions beyond purely financial criteria. A Zimmermann-based fuzzy linear programming approach is employed to obtain a compromise solution without predefined objective weights. By integrating uncertainty, project divisibility, and multi-period flexibility, the framework provides a robust decision-support tool for complex investment environments. Results show that project divisibility enhances portfolio flexibility and efficiency compared with non-divisible approaches. Partial project execution across multiple periods improves budget utilization, reduces risk concentration, and allows investments to be postponed or scaled as conditions change. Consequently, more projects can be included while satisfying financial and risk constraints, producing portfolios that better balance return, downside risk, and societal impact under uncertainty.