An SBM-DEA model with parallel computing design for environmental efficiency evaluation in the big data context: a transportation system application

Abstract

In the big data context, decision makers usually face the problem of evaluating environmental efficiencies of a massive number of decision making units (DMUs) using the data envelopment analysis (DEA) method. However, standard implementations of the traditional DEA calculation process will consume much time when the data set is very large. To eliminate this limitation of DEA applied to big data, firstly, the slacks-based measure (SBM) model is extended considering undesirable outputs and the variable returns to scale (VRS) assumption for environmental efficiency evaluation of the DMUs. Then, an approach comprised of two algorithms is proposed for environmental efficiency evaluation when the number of DMUs is massive. The set of DMUs is partitioned into subsets, a technique which facilitates the application of a parallel computing mechanism. Algorithm 1 can be used for identifying the environment efficient DMUs in any DMU set. Further, Algorithm 2 (a parallel computing algorithm) shows how to use the proposed model and Algorithm 1 in parallel to find the environmental efficiencies of all DMUs. A simulation shows that the parallel computing design helps to significantly reduce calculation time when completing environmental efficiency evaluation tasks with large data sets, compared with using the traditional calculation processes. Finally, the proposed approach is applied to do environmental efficiency analysis of transportation systems.