Robust optimization for identifying the most efficient decision making unit in data envelopment analysis

Subject Areas : International Journal of Data Envelopment Analysis

Reza Akhlaghi ¹ , Mohsen Rostamy-Malkhalifeh ² , Alireza Amirteimoori ³ , Sohrab Kordrostami ⁴

1 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
4 - Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Received: 2023-02-12 Accepted : 2023-04-19 Published : 2023-05-01

Keywords: Optimistic Counterpart, Uncertainty, Data envelopment analysis (DEA), Interval data, robust optimization,

Abstract :

Due to the nonlinear and discrete nature of BCC (Banker, Charnes, and Cooper, [11]) models for determining the most efficient decision-making unit, it is practically impossible to evaluate the models' dual and, consequently, optimistic case. Thus, in this paper, the linear model with linear constraints proposed by Akhlaghi et al. [2] is used to investigate the dual equality of the model's robust problem and the optimistic case of the new model's dual under VRS uncertainty. The model proposed in this paper is novel in comparison to previous models because it solves the most efficient decision-making unit only once, without relying on uncertain data to determine its rank. The paper demonstrates how the proposed robust model can also ascertain the most efficient decision-making unit when uncertainty exists. Furthermore, the dual issues raised by robust counterparts in the new linear programming (LP) model are addressed to identify the most efficient decision-making unit. The robust counterpart is demonstrated to be equivalent to a linear program under interval uncertainty, and the dual of the robust counterpart is shown to be equal to the optimistic counterpart of the dual problem. Consequently, this study aims to demonstrate that the dual problem is equivalent to a decision-maker operating under optimal data, whereas the primal robust problem is equivalent to a decision-maker operating through the worst-case possible data scenario.