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Linear programming solutions and distance functions under a constant returns to scale technology

Author

Listed:
  • J-P Boussemart

    (University of Lille and LEM-IESEG)

  • W Briec

    (University of Perpignan)

  • H Leleu

    (CNRS-LEM-Catholic University of Lille)

Abstract

In this paper, we investigate the various relationships among the linear programming solutions of data envelopment analysis (DEA) models under a constant returns to scale technology. We derive the analytical relationships among the efficiency measures and the activity variables for four separate models: the input-based, the output-based, the hyperbolic, and the proportional distance functions. We apply our results in order to derive a test of consistency that can be used in assessing the returns to scale among differing DEA models.

Suggested Citation

  • J-P Boussemart & W Briec & H Leleu, 2009. "Linear programming solutions and distance functions under a constant returns to scale technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 72-78, January.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_palgrave.jors.2602519
    DOI: 10.1057/palgrave.jors.2602519
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    References listed on IDEAS

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    1. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    2. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    3. J-P Boussemart & W Briec & H Leleu, 2009. "Linear programming solutions and distance functions under a constant returns to scale technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 72-78, January.
    4. Boussemart, Jean-Philippe & Briec, Walter & Peypoch, Nicolas & Tavéra, Christophe, 2009. "[alpha]-Returns to scale and multi-output production technologies," European Journal of Operational Research, Elsevier, vol. 197(1), pages 332-339, August.
    5. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    6. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    7. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    8. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
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    Cited by:

    1. J-P Boussemart & W Briec & H Leleu, 2010. "Linear programming solutions and distance functions under α-returns to scale," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(8), pages 1297-1301, August.
    2. J-P Boussemart & W Briec & H Leleu, 2009. "Linear programming solutions and distance functions under a constant returns to scale technology," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 72-78, January.
    3. Leleu, Hervé & Moises, James & Valdmanis, Vivian, 2012. "Optimal productive size of hospital's intensive care units," International Journal of Production Economics, Elsevier, vol. 136(2), pages 297-305.
    4. Carlos P. Barros & Qi Bin Liang & Nicolas Peypoch, 2014. "Technical Efficiency in the Angolan Banking Sector with the B-convexity Model," South African Journal of Economics, Economic Society of South Africa, vol. 82(3), pages 443-454, September.

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    More about this item

    Keywords

    data envelopment analysis; methodology; linear programming; production;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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