Cross-efficiency aggregation by ordered visibility graph averaging: method, and application in portfolio selection

Abstract

In research and practice of Data Envelopment Analysis (DEA), the arithmetic average is commonly used to aggregate cross-efficiency scores. For this, each decision-making unit (DMU) contributes an equal weight, and many essential decision-making details are lost in the final aggregated cross-efficiency. We propose a novel application of the ordered visibility graph averaging (OVGA) operator for DEA cross-efficiency aggregation and apply the proposed method to study the portfolio selection problem. When solving this problem, several practical concerns, such as a budget, cardinality, buy-in requirements, and restrictions against short selling are also considered. The proposed OVGA aggregated cross-efficiency approach is explained through a numerical example, followed by the formulation of optimal portfolios based on these cross-efficiencies. The suggested method is also tested using empirical data from the Indian banking industry. The results of this study can be used to create the most acceptable portfolio in stock companies, financial institutions, and businesses in the public and private sectors.