Achieving MAX-MIN Fair Cross-efficiency scores in Data Envelopment Analysis

Abstract

Algorithmic decision making is gaining popularity in today's business. The need for fast, accurate, and complex decisions forces decision-makers to take advantage of algorithms. However, algorithms can create unwanted bias or undesired consequences that can be averted. In this paper, we propose a MAX-MIN fair cross-efficiency data envelopment analysis (DEA) model that solves the problem of high variance cross-efficiency scores. The MAX-MIN cross-efficiency procedure is in accordance with John Rawls's Theory of justice by allowing efficiency and cross-efficiency estimation such that the greatest benefit of the least-advantaged decision making unit is achieved. The proposed mathematical model is tested on a healthcare related dataset. The results suggest that the proposed method solves several issues of cross-efficiency scores. First, it enables full rankings by having the ability to discriminate between the efficiency scores of DMUs. Second, the variance of cross-efficiency scores is reduced, and finally, fairness is introduced through optimization of the minimal efficiency scores.