New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA

Vakili, Javad

doi:10.1142/s021759591750035x

Cited by 5 publications

(2 citation statements)

References 31 publications

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“…Ebrahimnejad et al (2013) proposed an approach that requires solving a mixed integer quadratic program to find the closest efficient target. In contrast to strongly efficient target, Vakili (2017) developed a mixed integer linear bi-level program to find the closest weakly efficient target to the assessed DMU in terms of Hölder norms, which is very difficult to solve.…”

Section: Introductionmentioning

confidence: 99%

Closest target on the frontier of the free disposal hull

Kao

2024

Preprint

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In data envelopment analysis (DEA) the production possibility set (PPS) constructed from the observed decision making units (DMUs) under only the free disposability postulate is referred to as the free disposal hull (FDH), based on which efficiencies are measured. The conventional non-radial DEA models that take both the inputs and outputs into consideration seek the target on the FDH frontier that is farthest to the DMU to be assessed to measure efficiency. A consequence is that greater effort is needed to make an inefficient DMU efficient. This paper proposes a method to find the target on the frontier that is closest to the assessed DMU. The target is found by examining only the orthogonal projection points of the assessed DMU on the frontier and the weakly efficient corner points of the PPS that dominate the assessed DMU. The effort needed to reach this point is the least. The case of twenty-four non-life insurance companies in Taiwan widely used in the literature is used in this paper for illustrative purposes. Surprisingly, the difference between the longest and shortest distances can be hundreds of times, which implies that the effort for an inefficient DMU to become efficient can be reduced to less than one-hundredth of what is usually needed. JEL Classification C61, C67

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Section: Introductionmentioning

confidence: 99%

Closest target on the frontier of the free disposal hull

Kao

2024

Preprint

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“…Using the definition in Vakili J. (2017) [8] for reference, the non-cash risk measure is defined as follows.…”

Section: Introductions Of Non-cash Risk Measurementioning

confidence: 99%

Non-Cash Risk Measure on Nonconvex Sets

Cong

Zhao

2018

Mathematics

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Monetary risk measures are interpreted as the smallest amount of external cash that must be added to a financial position to make the position acceptable. In this paper, A new concept: non-cash risk measure is proposed and this measure provides an approach to transform the unacceptable positions into the acceptable positions in a nonconvex set. Non-cash risk measure uses not only cash but also other kinds of assets to adjust the position. This risk measure is nonconvex due to the use of optimization problem in L 1 norm. A convex extension of the nonconvex risk measure is derived and the relationship between the convex extension and the non-cash risk measure is detailed.

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The closest strong efficient targets in the FDH technology: an enumeration method

Vakili

Dizaji

2021

J Prod Anal

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New Models for Computing the Distance of DMUs to the Weak Efficient Boundary of Convex and Nonconvex PPSs in DEA

Cited by 5 publications

References 31 publications

Closest target on the frontier of the free disposal hull

Closest target on the frontier of the free disposal hull

Non-Cash Risk Measure on Nonconvex Sets

The closest strong efficient targets in the FDH technology: an enumeration method

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