Efficiency evaluation of very large-scale samples: Data envelopment analysis with angle-index synthesis

Abstract

In the era of big data, the rapid solution of large-scale data envelopment analysis model has attracted extensive attention of scholars. Finding efficient DMUs has become a key consideration in large-scale evaluation. The parallel building hull method and the framework method offer good performance in terms of finding efficient DMUs. However, with the surge in time series data and high-frequency data, the evaluation problem of large-scale samples has put forward the requirement for faster and larger scale solutions for traditional methods. In this study, we propose a prescoring method for DMUs by synthesizing the angle and the index, hereafter called the angle-index synthesis method. Meanwhile, we combine this proposed method with the framework method to obtain all efficient DMUs. Numerical experiments and a real application to the bankruptcy data of Polish companies show the significant advantages of our algorithm in terms of computational time in the large-scale sampling context, and optimal parameters can be ignored. Finally, in the Monte Carlo simulation of very large-scale samples, we show that our algorithm has linear increasing trend for the computational time and good validity even in 1 billion DMUs.