### Abstract

Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.

Original language | English |
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Article number | 102192 |

Journal | Omega (United Kingdom) |

DOIs | |

Publication status | Accepted/In press - 2020 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Strategy and Management
- Management Science and Operations Research
- Information Systems and Management

### Cite this

*Omega (United Kingdom)*, [102192]. https://doi.org/10.1016/j.omega.2020.102192

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**A slacks-based measure model for calculating cross efficiency in data envelopment analysis.** / Kao, Chiang; Liu, Shiang Tai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A slacks-based measure model for calculating cross efficiency in data envelopment analysis

AU - Kao, Chiang

AU - Liu, Shiang Tai

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.

AB - Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to provide appropriate efficiency scores for weakly efficient DMUs. Second, the efficiencies measured from the input and output sides under variable returns to scale are different which may cause difficulties in subsequent analyses. Third, negative values may appear when the efficiency is measured from the input side. To solve these problems, this paper proposes a slacks-based measure to calculate efficiency. The basic idea is the same as that of the radial measure using the frontier corresponding to a DMU to measure the efficiency of all DMUs, except that the efficiency measure is slacks-based instead of radial. Due to the nature of the slacks-based efficiency measure, the problems caused by weak efficiency and difference in input and output radial measures do not exist. More importantly, negative efficiencies are not produced. The proposed method is applied to a real case involving the selection of the most efficient robot to use for production. The results help identify the top-ranked robot.

UR - http://www.scopus.com/inward/record.url?scp=85077932362&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077932362&partnerID=8YFLogxK

U2 - 10.1016/j.omega.2020.102192

DO - 10.1016/j.omega.2020.102192

M3 - Article

AN - SCOPUS:85077932362

JO - Omega

JF - Omega

SN - 0305-0483

M1 - 102192

ER -