Closest reference point on the strong efficient frontier in data envelopment analysis

Akbar Moradi; Alireza Amirteimoori; Sohrab Kordrostami; Mohsen Vaez-Ghasemi; Akbar Moradi; Alireza Amirteimoori; Sohrab Kordrostami; Mohsen Vaez-Ghasemi

doi:10.3934/math.2020055

AIMS Mathematics

2020, Volume 5, Issue 2: 811-827. doi: 10.3934/math.2020055

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Research article

Closest reference point on the strong efficient frontier in data envelopment analysis

1.
Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
2.
Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Received: 03 September 2019 Accepted: 19 December 2019 Published: 27 December 2019
MSC : 90B30

Data envelopment analysis (DEA) is a data-oriented procedure to evaluate the relative performances of a set of homogenous decision making units (DMUs) with multiple incommensurate inputs and outputs. Performance measurement using tools such as DEA needs to construct an empirical production technology set. In this analysis, DMUs are partitioned into two groups: efficient and inefficient. Inefficient DMUs are projected onto efficient frontier in such a way that their inputs are reduced and their outputs are increased. In this sense, finding a projection point with the shortest distance is important and it is a most frequently studied subject in the field of DEA. In this paper, a two-steps procedure is proposed to determine a projection point on the efficient frontier with closest distance. The reference point is constructed in such a way that it is located on the strong defining hyperplane of the DEA technology set. As we will show, the low computational efforts and the guarantee of determining an efficient projection point on the strong efficient frontier are the two important advantages of the proposed model.To show the applicability of the proposed approach, a real case on 28 international airlines is given.
- data envelopment analysis,
- efficiency,
- input-output,
- closest distance
Citation: Akbar Moradi, Alireza Amirteimoori, Sohrab Kordrostami, Mohsen Vaez-Ghasemi. Closest reference point on the strong efficient frontier in data envelopment analysis[J]. AIMS Mathematics, 2020, 5(2): 811-827. doi: 10.3934/math.2020055

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Abstract

Data envelopment analysis (DEA) is a data-oriented procedure to evaluate the relative performances of a set of homogenous decision making units (DMUs) with multiple incommensurate inputs and outputs. Performance measurement using tools such as DEA needs to construct an empirical production technology set. In this analysis, DMUs are partitioned into two groups: efficient and inefficient. Inefficient DMUs are projected onto efficient frontier in such a way that their inputs are reduced and their outputs are increased. In this sense, finding a projection point with the shortest distance is important and it is a most frequently studied subject in the field of DEA. In this paper, a two-steps procedure is proposed to determine a projection point on the efficient frontier with closest distance. The reference point is constructed in such a way that it is located on the strong defining hyperplane of the DEA technology set. As we will show, the low computational efforts and the guarantee of determining an efficient projection point on the strong efficient frontier are the two important advantages of the proposed model.To show the applicability of the proposed approach, a real case on 28 international airlines is given.

References

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