A Numerical Approach to measure Performance Big Data in Cross-Efficiency

Abstract

Big Data Envelopment Analysis (Big DEA) and Cross-Efficiency (CE) evaluation are two important topics in Data Envelopment Analysis (DEA).However, it should be noted the CE evaluation can be computationally intensive, particularly when dealing with large data sets or a large number of DMUs. In this research, we propose a numerical approach to CE evaluation that can be applied to data sets of any size and has a reasonable run-time. Additionally, we suggest a complementary method to find the set of efficient units, which is a crucial component of most Big DEA algorithms. To test the proposed methods, we simulated large data sets with different scenarios involving varying numbers of units, inputs, and outputs. We found that the proposed numerical method was successful in CE evaluation and approximating the efficiency of DEA-efficiency with a high degree of confidence for data with dimensions less than five, regardless of the number of units. However, for data with dimensions greater than five to ten, its ability to find the set of efficient units decreased proportionally. This was compensated by the complementary method.