An improved equilibrium efficient frontier data envelopment analysis approach for evaluating decision-making units with fixed-sum outputs

Abstract

In recent years, significant development has been made in efficiency evaluation for Decision-Making Units (DMUs) with fixed-sum outputs. The Generalized Equilibrium Efficient Frontier Data Envelopment Analysis (GEEFDEA) approach introduced by Yang et al. (2015) is one of the most representative methods. In the GEEFDEA approach, all DMUs are adjusted to become efficient under the same set of weights, indicating that the Equilibrium Efficient Frontier (EEF) constructed consists of only one hyperplane. However, in practical scenarios under the Variable Return to Scale (VRS) assumption, the production frontier always consists of multiple hyperplanes, presenting a more complex shape. To fill this research gap, we propose an improved Equilibrium Efficient Frontier Data Envelopment Analysis approach. Our approach allows DMUs to have different weights for inputs, variable-sum outputs, and fixed-sum outputs, resulting in an EEF with multiple hyperplanes. It is noted that our new approach uses a non-linear model to obtain the EEF. We show that the model can be linearized in the case of a single fixed-sum output. In situations involving multiple fixed-sum outputs, we propose an algorithm based on the Expectation Maximization (EM) mechanism to solve the model to obtain an EEF. Finally, we illustrate the advantages of our new approach through a numerical example and a case study in the global motor vehicle industry.