Ranking multiple-input and multiple-output units: A comparative study of data envelopment analysis and rank aggregation

Abstract

Ranking multiple-input and multiple-output units is a critical problem that arises in a broad range of disciplines. While various methods have been proposed and applied, their comparative strengths and weaknesses are not well understood. In this paper, we assess and compare two popular methods, data envelopment analysis (DEA) and heuristic rank aggregation approach (i.e., the Borda method), in the context of ranking multiple-input and multiple-output units. Both methods exploit the output-input ratios, but in different ways. The Borda method sorts the units by taking the arithmetic average of the ranks in terms of individual output-input ratios, whereas DEA ranks the units based on composite output-input ratios. We use simulations to compare Borda rank aggregation and six DEA models, including CCR (Charnes, Cooper, Rhodes), super-efficiency CCR, BCC (Banker, Charnes, Cooper), super-efficiency BCC, SBM (slacks-based measure), and super-efficiency SBM. The simulations are based on Cobb-Douglas and translog production functions with both single output and multiple outputs. We show that the heuristic Borda rank aggregation, though simple to implement, performs better than DEA models for Cobb-Douglas production function under three situations: small sample size, relatively balanced weights for production factors, and presence of multiple outputs. For translog production function, the Borda method generally performs better than the CCR model, but cannot match up to other DEA models. We also demonstrate the performance of different methods via application to the well-known problem of ranking countries by human development. Our research sheds light on the potential of rank aggregation to complement or even supplant DEA under certain conditions.