A fuzzy multidimensional multiple-choice knapsack model for project portfolio selection using an evolutionary algorithm

Project portfolio selection problems are inherently complex problems with multiple and often conflicting objectives. Numerous analytical techniques ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve these problems with precise data. However, the project data in real-world problems are often imprecise or ambiguous. We propose a fuzzy Multidimensional Multiple-choice Knapsack Problem (MMKP) formulation for project portfolio selection. The proposed model is composed of an Efficient Epsilon-Constraint (EEC) method and a customized multi-objective evolutionary algorithm. A Data Envelopment Analysis (DEA) model is used to prune the generated solutions into a limited and manageable set of implementable alternatives. Statistical analysis is performed to investigate the effectiveness of the proposed approach in comparison with the competing methods in the literature. A case study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms.