### Abstract

The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole-unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship.

Original language | English |
---|---|

Pages (from-to) | 70-79 |

Number of pages | 10 |

Journal | Omega (United Kingdom) |

Volume | 83 |

DOIs | |

Publication status | Published - 2019 Mar 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)*,

*83*, 70-79. https://doi.org/10.1016/j.omega.2018.02.004

}

*Omega (United Kingdom)*, vol. 83, pp. 70-79. https://doi.org/10.1016/j.omega.2018.02.004

**Cross efficiency measurement and decomposition in two basic network systems.** / Kao, Chiang; Liu, Shiang Tai.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Cross efficiency measurement and decomposition in two basic network systems

AU - Kao, Chiang

AU - Liu, Shiang Tai

PY - 2019/3/1

Y1 - 2019/3/1

N2 - The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole-unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship.

AB - The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to the system. This paper applies the idea of cross evaluation, which has been demonstrated to be an effective approach in ranking DMUs for systems considered as a whole-unit, to measure the efficiency of the two basic structures of network systems, series and parallel. The proposed model is able to decompose the cross efficiency measure of the system into the product of those of the divisions for the series structure and a weighted average for the parallel structure. The results from two real-world cases, one for the basic series structure and another for the parallel one, show that the cross efficiency measures proposed in this paper not only increase the discriminating power in ranking systems and divisions, but also identify the relationship between the system and division efficiencies. Which division has stronger effects on the performance of the system is reflected from this relationship.

UR - http://www.scopus.com/inward/record.url?scp=85041928284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041928284&partnerID=8YFLogxK

U2 - 10.1016/j.omega.2018.02.004

DO - 10.1016/j.omega.2018.02.004

M3 - Article

AN - SCOPUS:85041928284

VL - 83

SP - 70

EP - 79

JO - Omega

JF - Omega

SN - 0305-0483

ER -