The Most Efficient Unit in Data Envelopment Analysis Using Genetic Algorithm

Subject Areas : Applied Mathematics

M. Matin Nejati ¹ , Mohsen Rostamy-Malkhalifeh ² , R. Kargar ³ , R. Mehrjoo ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran , Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran , Iran
3 - Department of Mathematics, Qom Branch, Islamic Azad University, Tehran , Iran
4 - Department of Mathematics, Shahr-e-Gods Branch, Islamic Azad University, Tehran , Iran

Received: 2019-02-17 Accepted : 2019-02-17 Published : 2018-12-01

Keywords: Genetic Algorithm, Data envelopment analysis, Hyperplane, Efficient Unit,

Abstract :

Data Envelopment Analysis (DEA) is actually to obtain the efficiency using inputs and outputs, which can determine efficient and inefficient units with the help of performance calculations such that the efficiency for efficient DMUs is one and less than one for inefficient DMUs [1]. In some cases, the ranking of the decision-making units are not important for decision-makers, and they are only looking to obtain the most efficient DMUs, so that they can directly achieve the most efficient DMU from all existing DMUs. In a number of papers regarding this subject, several steps were taken to find the most efficient DMU, [2,3], which later examined the problems of these models and other models were announced by the researchers to resolve them. Some of the problems that can be mentioned:1. Solving the model took place in two steps and could not directly reach the final answer.2. Many unnecessary conjunctions were used in the models.Other models were proposed to solve the problems that could eliminate unnecessary conjunctions and solve the problem in two phases [5].Therefore, in this paper, it has been tried to provide a model that avoids unnecessary conjunctions, and most importantly, maximizes the distance between the other DMUs of an efficient DMU [6].