Evaluation to fixed-sum-outputs DMUs by non-oriented equilibrium efficient frontier DEA approach with Nash bargaining-based selection. (February 2023) - Yu, Shasha; Lei, Ming; Deng, Honghui
Highlights: The proposed NEEFDEA approach extended the prior input-oriented or output-oriented evaluation to a both-oriented evaluation, able to provide more overall efficiency results. We suggested an algorithm to clarify a vital issue for this branch of approaches, that is, whether the achieved EEF is unique. The proposed bargaining-based selection approach not only opens up a new way to complete the selection of a unique EEF but also guarantees the Pareto-optimality of the EEF to further enhance the effectiveness of equilibrium frontier approaches. The NEEFDEA approach has advantages to help managers to evaluate the performance of rival individuals, such as firms in the same industry or participants in the same contest. Abstract: Equilibrium efficient frontier DEA (EEFDEA) approaches have been developed specifically for the efficiency assessment of decision-making units (DMUs) with fixed-sum outputs in recent years. Still, current EEFDEA approaches can only evaluate either input- or output-oriented efficiency. This paper proposes a new non-oriented EEFDEA (NEEFDEA) approach, which measures efficiency by capturing input excesses and output shortfalls simultaneously. However, the NEEFDEA approach also encounters the difficulty of guaranteeing the uniqueness of the common equilibrium efficient frontier (EEF). To address the problem, we further present a new bargaining-based selection method to deal with multiple feasible EEFs. By regarding DMUs as game players to seek to optimize their own evaluation results, the screening process of EEFs is formulated as a bargaining game, it can generate a unique and Pareto-optimal EEF by solving the game. Such an EEF is essential to bring all DMUs to a consensus on the final evaluation results. Finally, to present the performance of our model, we apply the proposed approaches to conduct an empirical study of 30 companies in the vehicle industry in 2020.