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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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. George J. Stigler, 1945. "The Cost of Subsistence," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 27(2), pages 303-314.
    6. 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.
    7. Färe, Rolf & Karagiannis, Giannis, 2014. "Benefit-of-the-doubt aggregation and the diet problem," Omega, Elsevier, vol. 47(C), pages 33-35.
    8. 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.
    9. 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.
    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.
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    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.

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