Algorithms for Multi-Criteria Decision-Making and Efficiency Analysis Problems

Abstract: Multi-criteria decision-making (MCDM) problems involve the evaluation of alternatives based on various minimization and maximization criteria. Similarly, efficiency evaluation (EA) methods assess decision-making units (DMUs) by analyzing their input consumption and output production. MCDM and EA methods face challenges in managing alternatives and DMUs with varying capacities across different criteria (inputs and outputs). That leads to performance assessments often skewed by subjective biases in criteria weighting. We introduce two innovative scenarios utilizing linear programming-based Virtual Gap Analysis (VGA) models to address these limitations. This dual-scenario approach aims to mitigate traditional biases, offering robust solutions for comprehensively assessing alternatives and DMUs. Our methodology allows for the influential ranking of alternatives in MCDM problems and enables each DMU to adjust its input and output ratios to achieve efficiency.