A Unified Maximum-Margin Framework for Data Envelopment Analysis: Theoretical Foundations and Numerical Evidence

Abstract

Data Envelopment Analysis (DEA) is a widely used non-parametric method for evaluating the relative efficiency of decision-making units (DMUs). However, the classic Charnes-Cooper-Rhodes (CCR) model often suffers from a lack of discriminatory power, particularly when the number of input and output variables is large relative to the number of DMUs. Under such conditions, many DMUs are evaluated as "CCR-efficient" with a score of unity, making it difficult to rank or distinguish between top performers. To address this limitation, we propose a novel Maximum-Margin DEA (MM-DEA) model that integrates the concept of "margin maximization" -- inspired by structural risk minimization in machine learning -- directly into the efficiency measurement framework. Like the traditional super-efficiency model, the proposed MM-DEA model excludes the target DMU from the reference set used to evaluate it; unlike the super-efficiency model, however, MM-DEA imposes an explicit upper bound on the target DMU's own score, ensuring that every score remains within the standard $[0,1]$ range rather than potentially exceeding one. We theoretically demonstrate that the MM-DEA model is a generalized extension of the CCR model, reducing to the latter when the trade-off parameter $α$ is zero. Furthermore, we show that the fractional programming formulation of MM-DEA can be rigorously transformed into a linear programming (LP) problem, ensuring computational efficiency. In our numerical experiments, MM-DEA produced a unique ranking for a high-dimensional synthetic dataset on which the CCR model failed to discriminate among any of the DMUs. Our results suggest that the "margin" serves as a critical metric for managerial resilience and competitive advantage.