IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v250y2017i1d10.1007_s10479-015-2042-y.html
   My bibliography  Save this article

Data envelopment analysis and its related linear programming models

Author

Listed:
  • Rolf Färe

    (Oregon State University
    Oregon State University)

  • Shawna Grosskopf

    (Oregon State University)

  • Giannis Karagiannis

    (University of Macedonia)

  • Dimitris Margaritis

    (University of Auckland)

Abstract

We provide a unifying framework synthesizing the dual spaces of production and value used in DEA efficiency measurement with some well-known linear programming (LP) problems. Specifically, we make use of the technology matrix to map intensity variables into input–output space, and the adjoint transformation of the technology matrix to map input–output prices into prices of intensity variables. We show how the diet problem, a classical LP problem, is related to DEA and also use the adjoint matrix to demonstrate a procedure for pricing efficient decision-making units. We further illustrate the relationship between benefit-of-the-doubt aggregation and the diet problem.

Suggested Citation

  • Rolf Färe & Shawna Grosskopf & Giannis Karagiannis & Dimitris Margaritis, 2017. "Data envelopment analysis and its related linear programming models," Annals of Operations Research, Springer, vol. 250(1), pages 37-43, March.
    • Handle: RePEc:spr:annopr:v:250:y:2017:i:1:d:10.1007_s10479-015-2042-y
    DOI: 10.1007/s10479-015-2042-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-015-2042-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-015-2042-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liu, W.B. & Zhang, D.Q. & Meng, W. & Li, X.X. & Xu, F., 2011. "A study of DEA models without explicit inputs," Omega, Elsevier, vol. 39(5), pages 472-480, October.
    2. Laurens Cherchye & Willem Moesen & Nicky Rogge & Tom Puyenbroeck, 2007. "An Introduction to ‘Benefit of the Doubt’ Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 82(1), pages 111-145, May.
    3. Lovell, C. A. Knox & Pastor, Jesus T., 1999. "Radial DEA models without inputs or without outputs," European Journal of Operational Research, Elsevier, vol. 118(1), pages 46-51, October.
    4. R F&aauml;re & S Grosskopf & D Margaritis, 2013. "Pricing decision-making units," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(4), pages 619-621, April.
    5. Rolf Färe & Shawna Grosskopf, 2002. "Two Perspectives on DEA: Unveiling the Link between CCR and Shephard," Journal of Productivity Analysis, Springer, vol. 17(1), pages 41-47, January.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. George J. Stigler, 1945. "The Cost of Subsistence," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 27(2), pages 303-314.
    8. Rolf F&aauml;re & Valentin Zelenyuk, 2015. "Pricing of decision-making units under non-constant returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 172-173, January.
    9. Färe, Rolf & Karagiannis, Giannis, 2014. "Benefit-of-the-doubt aggregation and the diet problem," Omega, Elsevier, vol. 47(C), pages 33-35.
    10. R Färe & S Grosskopf & D Margaritis, 2011. "The diet problem and DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1420-1422, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Färe, Rolf & Karagiannis, Giannis & Hasannasab, Maryam & Margaritis, Dimitris, 2019. "A benefit-of-the-doubt model with reverse indicators," European Journal of Operational Research, Elsevier, vol. 278(2), pages 394-400.
    2. Shokhrukh-Mirzo Jalilov & Mohammed Mainuddin & Md. Maniruzzaman & Md. Mahbubul Alam & Md. Towfiqul Islam & Md. Jahangir Kabir, 2019. "Efficiency in the Rice Farming: Evidence from Northwest Bangladesh," Agriculture, MDPI, vol. 9(11), pages 1-14, November.
    3. Qingxian An & Fanyong Meng & Beibei Xiong & Zongrun Wang & Xiaohong Chen, 2020. "Assessing the relative efficiency of Chinese high-tech industries: a dynamic network data envelopment analysis approach," Annals of Operations Research, Springer, vol. 290(1), pages 707-729, July.
    4. Subrata Mitra & Balram Avittathur, 2018. "Application of linear programming in optimizing the procurement and movement of coal for an Indian coal-fired power-generating company," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 45(3), pages 207-224, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Färe, Rolf & Karagiannis, Giannis, 2014. "Benefit-of-the-doubt aggregation and the diet problem," Omega, Elsevier, vol. 47(C), pages 33-35.
    2. Tom Puyenbroeck, 2018. "On the Output Orientation of the Benefit-of-the-Doubt-Model," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(2), pages 415-431, September.
    3. Nguyen, Trang Thi Thuy & Pham, Binh Thai & Prior, Diego & van Hemmen, Stefan, 2022. "Performance of tax simplification around the world: A panel frontier analysis," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    4. Karagiannis, Roxani & Karagiannis, Giannis, 2018. "Intra- and inter-group composite indicators using the BoD model," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 44-51.
    5. Färe, Rolf & Karagiannis, Giannis & Hasannasab, Maryam & Margaritis, Dimitris, 2019. "A benefit-of-the-doubt model with reverse indicators," European Journal of Operational Research, Elsevier, vol. 278(2), pages 394-400.
    6. Giannis Karagiannis & Georgia Paschalidou, 2017. "Assessing research effectiveness: a comparison of alternative nonparametric models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 456-468, April.
    7. Antonio García-Romero & Daniel Santín & Gabriela Sicilia, 2016. "Another brick in the wall: a new ranking of academic journals in Economics using FDH," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(1), pages 91-101, April.
    8. Cook, Wade D. & Ruiz, José L. & Sirvent, Inmaculada & Zhu, Joe, 2017. "Within-group common benchmarking using DEA," European Journal of Operational Research, Elsevier, vol. 256(3), pages 901-910.
    9. Giménez, Víctor & Thieme, Claudio & Prior, Diego & Tortosa-Ausina, Emili, 2022. "Evaluation and determinants of preschool effectiveness in Chile," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    10. De Witte, Kristof & Schiltz, Fritz, 2018. "Measuring and explaining organizational effectiveness of school districts: Evidence from a robust and conditional Benefit-of-the-Doubt approach," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1172-1181.
    11. Jamal Ouenniche & Skarleth Carrales, 2018. "Assessing efficiency profiles of UK commercial banks: a DEA analysis with regression-based feedback," Annals of Operations Research, Springer, vol. 266(1), pages 551-587, July.
    12. Giuseppe Coco & Raffaele Lagravinese & Giuliano Resce, 2020. "Beyond the weights: a multicriteria approach to evaluate inequality in education," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(4), pages 469-489, December.
    13. Fernández-Macho, Javier & González, Pilar & Virto, Jorge, 2016. "An index to assess maritime importance in the European Atlantic economy," Marine Policy, Elsevier, vol. 64(C), pages 72-81.
    14. Cesaroni, Giovanni & Kerstens, Kristiaan & Van de Woestyne, Ignace, 2019. "Short- and long-run plant capacity notions: Definitions and comparison," European Journal of Operational Research, Elsevier, vol. 275(1), pages 387-397.
    15. Tüselmann, Heinz & Sinkovics, Rudolf R. & Pishchulov, Grigory, 2015. "Towards a consolidation of worldwide journal rankings – A classification using random forests and aggregate rating via data envelopment analysis," Omega, Elsevier, vol. 51(C), pages 11-23.
    16. Mohammad Pakkar, 2015. "An integrated approach based on DEA and AHP," Computational Management Science, Springer, vol. 12(1), pages 153-169, January.
    17. Vincent Charles & Guillermo Díaz, 2017. "A Non-radial DEA Index for Peruvian Regional Competitiveness," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 134(2), pages 747-770, November.
    18. R Färe & S Grosskopf & D Margaritis, 2011. "The diet problem and DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1420-1422, July.
    19. Juan Aparicio & Magdalena Kapelko, 2019. "Enhancing the Measurement of Composite Indicators of Corporate Social Performance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 807-826, July.
    20. Martin Bod’a & Martin Dlouhý & Emília Zimková, 2018. "Unobservable or omitted production variables in data envelopment analysis through unit-specific production trade-offs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(4), pages 813-846, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:250:y:2017:i:1:d:10.1007_s10479-015-2042-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.