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DEA-based allocations of fixed costs in a fuzzy environment: fuzzy expected values and max–min satisfaction degree approaches.

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Title: DEA-based allocations of fixed costs in a fuzzy environment: fuzzy expected values and max–min satisfaction degree approaches.
Authors: Wang, Xu1 (AUTHOR) sugarwang0813@163.com, Wang, Yingming2,3 (AUTHOR), Lan, Yixin2 (AUTHOR)
Source: RAIRO: Operations Research (2804-7303). 2025, Vol. 59 Issue 4, p2303-2324. 22p.
Subjects: Overhead costs, Cost allocation, Satisfaction, Cost analysis, Dilemma, Data envelopment analysis
Abstract: Due to incomplete and unattainable information, the data of inputs and outputs in production often cannot be obtained crisply but are represented by fuzzy data. Therefore, the data envelopment analysis (DEA) approach with precise data to fixed cost allocation is not applicable anymore, and the fuzzy DEA method is necessitated. This paper proposes the fuzzy DEA model based on the fuzzy expected values approach for the first measurement of fixed cost allocation, where the fuzzy inputs and fuzzy outputs are respectively weighted. It proves that there exist feasible allocation schemes that can render each DMU and the collection of all DMUs efficient. Additionally, with the help of the fuzzy expected values approach, the Max-min satisfaction degree principle is utilized to achieve the optimal solution to the fixed cost allocation in the fuzzy scenario. The proposed fuzzy expected values approach based on fuzzy DEA and satisfaction degree for the fixed cost allocation is illustrated by two numerical examples. It shows that the fuzzy DEA approach with the fuzzy expected values can crisply evaluate DMUs and avoid the comparison dilemma of fuzzy efficiencies, as well as determine a precise allocation plan of fixed costs that can make all DMUs DEA efficient. [ABSTRACT FROM AUTHOR]
Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: DEA-based allocations of fixed costs in a fuzzy environment: fuzzy expected values and max–min satisfaction degree approaches.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Xu%22">Wang, Xu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sugarwang0813@163.com</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Yingming%22">Wang, Yingming</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lan%2C+Yixin%22">Lan, Yixin</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22RAIRO%3A+Operations+Research+%282804-7303%29%22">RAIRO: Operations Research (2804-7303)</searchLink>. 2025, Vol. 59 Issue 4, p2303-2324. 22p.
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  Data: <searchLink fieldCode="DE" term="%22Overhead+costs%22">Overhead costs</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+allocation%22">Cost allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Satisfaction%22">Satisfaction</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+analysis%22">Cost analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Dilemma%22">Dilemma</searchLink><br /><searchLink fieldCode="DE" term="%22Data+envelopment+analysis%22">Data envelopment analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Due to incomplete and unattainable information, the data of inputs and outputs in production often cannot be obtained crisply but are represented by fuzzy data. Therefore, the data envelopment analysis (DEA) approach with precise data to fixed cost allocation is not applicable anymore, and the fuzzy DEA method is necessitated. This paper proposes the fuzzy DEA model based on the fuzzy expected values approach for the first measurement of fixed cost allocation, where the fuzzy inputs and fuzzy outputs are respectively weighted. It proves that there exist feasible allocation schemes that can render each DMU and the collection of all DMUs efficient. Additionally, with the help of the fuzzy expected values approach, the Max-min satisfaction degree principle is utilized to achieve the optimal solution to the fixed cost allocation in the fuzzy scenario. The proposed fuzzy expected values approach based on fuzzy DEA and satisfaction degree for the fixed cost allocation is illustrated by two numerical examples. It shows that the fuzzy DEA approach with the fuzzy expected values can crisply evaluate DMUs and avoid the comparison dilemma of fuzzy efficiencies, as well as determine a precise allocation plan of fixed costs that can make all DMUs DEA efficient. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of RAIRO: Operations Research (2804-7303) is the property of EDP Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1051/ro/2025091
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      – Code: eng
        Text: English
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        PageCount: 22
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    Subjects:
      – SubjectFull: Overhead costs
        Type: general
      – SubjectFull: Cost allocation
        Type: general
      – SubjectFull: Satisfaction
        Type: general
      – SubjectFull: Cost analysis
        Type: general
      – SubjectFull: Dilemma
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      – SubjectFull: Data envelopment analysis
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      – TitleFull: DEA-based allocations of fixed costs in a fuzzy environment: fuzzy expected values and max–min satisfaction degree approaches.
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            NameFull: Wang, Yingming
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            NameFull: Lan, Yixin
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            – D: 01
              M: 07
              Text: 2025
              Type: published
              Y: 2025
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