A new parallel framework algorithm for solving large-scale DEA models

Abstract

With the rapid development of social informatization and platform economy, evaluating high-frequency and large-scale data has attracted widespread attention. One relevant and current research topic deals with finding high-quality decision-making units (DMUs) and scoring each DMU using a shorter computing time. The Framework method (Khezrimotlagh et al., 2019) has the fastest computing time so far. We propose a new parallel framework algorithm in this study. This algorithm effectively reduces the calculation time for finding all efficient DMUs and evaluate all DMUs in the BCC (Banker, Charnes and Cooper) model, the CCR (Charnes, Cooper and Rhodes) model, FG (Färe and Grosskopf) model and ST (Seiford and Thrall) model. The proposed algorithm has a reasonable selection method and optimal numbers of initial hull which can decrease the running time effectively. The extensive experimental results presented in this study show that when the input and output data are generated by uniform approach or normal approach, the density will increase with the increase of input and output dimensions, and show a growth trend like that of the S curve, which is similar to the distribution function of the Gamma distribution. We also tested our method using a real-life dataset. Compared with the previous methods, our method is shown to be more suitable for the input and output data generated by normal approach and decreases the calculation time by at least 12.52%. Furthermore, it has strong advantages in decreasing calculation time of solving the CCR model irrespective of whether the input data and output data are uniformly distributed or normally distributed.