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A Linear Bilevel Programming Problem For Obtaining The Closest Targets And Minimum Distance Of A Unit From The Strong Efficient Frontier

Author

Listed:
  • G. R. JAHANSHAHLOO

    (Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran)

  • J. VAKILI

    (Faculty of Mathematical Sciences and Computer, Tabriz University, 29 Bahman Avenue, Tabriz, Iran;
    Faculty of Mathematical and Computer Sciences, Teacher Training University, 599 Taleghani Avenue, 15618 Tehran, Iran)

  • M. ZAREPISHEH

    (Faculty of Mathematical Sciences and Computer, Amirkabir University, Tehran, Iran)

Abstract

Data envelopment analysis (DEA) can be used for assessing the relative efficiency of a number of operating units, finding, for each unit, a target operating point lying on the strong efficient frontier. Most DEA models project an inefficient unit onto a most distant target, which makes its attainment more difficult. In this paper, a linear bilevel programming problem for obtaining the closest targets and minimum distance of a unit from the strong efficient frontier by different norms is provided. The idea behind this approach is that closer targets determine less demanding levels of operation for the inputs and outputs of the units to perform efficiently. Finally, it will be shown that the proposed method is an extension of the existing methods.

Suggested Citation

  • G. R. Jahanshahloo & J. Vakili & M. Zarepisheh, 2012. "A Linear Bilevel Programming Problem For Obtaining The Closest Targets And Minimum Distance Of A Unit From The Strong Efficient Frontier," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(02), pages 1-19.
    • Handle: RePEc:wsi:apjorx:v:29:y:2012:i:02:n:s021759591250011x
    DOI: 10.1142/S021759591250011X
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    Citations

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    Cited by:

    1. J. Vakili & R. Sadighi Dizaji, 2021. "The closest strong efficient targets in the FDH technology: an enumeration method," Journal of Productivity Analysis, Springer, vol. 55(2), pages 91-105, April.
    2. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    3. Mustapha Daruwana Ibrahim & Sahand Daneshvar & Hüseyin Güden & Bela Vizvari, 2020. "Target setting in data envelopment analysis: efficiency improvement models with predefined inputs/outputs," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1319-1336, December.
    4. Ling Wang & Zhongchang Chen & Dalai Ma & Pei Zhao, 2013. "Measuring Carbon Emissions Performance in 123 Countries: Application of Minimum Distance to the Strong Efficiency Frontier Analysis," Sustainability, MDPI, vol. 5(12), pages 1-14, December.
    5. Lozano, Sebastián & Khezri, Somayeh, 2021. "Network DEA smallest improvement approach," Omega, Elsevier, vol. 98(C).
    6. Javad Vakili & Hanieh Amirmoshiri & Rashed Khanjani Shiraz & Hirofumi Fukuyama, 2020. "A modified distance friction minimization approach in data envelopment analysis," Annals of Operations Research, Springer, vol. 288(2), pages 789-804, May.
    7. Somayeh Razipour-GhalehJough & Farhad Hosseinzadeh Lotfi & Gholamreza Jahanshahloo & Mohsen Rostamy-malkhalifeh & Hamid Sharafi, 2020. "Finding closest target for bank branches in the presence of weight restrictions using data envelopment analysis," Annals of Operations Research, Springer, vol. 288(2), pages 755-787, May.
    8. Kao, Chiang, 2024. "Maximum slacks-based measure of efficiency in network data envelopment analysis: A case of garment manufacturing," Omega, Elsevier, vol. 123(C).

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