Accelerating Data Envelopment Analysis Calculations with Big Data

Abstract

The conventional approach in Data Envelopment Analysis (DEA) involves solving n linear programming (LP) problems to evaluate the efficiency of Decision-Making Units (DMUs), based on m inputs and s outputs, where n is the total number of DMUs. As the number of inputs, outputs, or DMUs increases, the computational complexity grows, leading to a steep rise in processing time for solving the standard models. This paper proposes an innovative method that significantly reduces computation time by leveraging parallel processing. The methodology consists of five distinct stages: (1) selecting a subset of DMUs using a specialized algorithm; (2) identifying the top-performing DMUs within the selected subset; (3) isolating non-essential DMUs located in the convex hull of the subset; (4) iteratively refining the selection to exclude additional inefficient units; and (5) determining the full set of efficient DMUs. By systematically introducing and filtering subsets, the proposed approach reduces the problem's dimensionality, making it more computationally tractable. The effectiveness of the method is demonstrated through its application to a dataset and is compared against existing approaches.