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Finding strong defining hyperplanes of PPS using multiplier form

  • Jahanshahloo, G.R.
  • Shirzadi, A.
  • Mirdehghan, S.M.
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    The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In this paper, we deal with the problem of finding the strong defining hyperplanes of the PPS. These hyperplanes are equations that form efficient surfaces. It is well known that the optimal solutions of the envelopment formulation for extreme efficient units are often highly degenerate and, therefore, may have alternate optima for the multiplier form. Every optimal solution of the multiplier form yields a hyperplane which is supporting at the PPS. We will show that the hyperplane which corresponds to an extreme optimal solution of the multiplier form (in evaluating an efficient DMU), and whose components corresponding to inputs and outputs are non zero is a strong defining hyperplane of the PPS. This will be discussed in details in this paper. These hyperplanes are useful in sensitivity and stability analysis, the status of returns to scale of a DMU, incorporating performance into the efficient frontier analysis, and so on. Using numerical examples, we will demonstrate how to use the results.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 194 (2009)
    Issue (Month): 3 (May)
    Pages: 933-938

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    Handle: RePEc:eee:ejores:v:194:y:2009:i:3:p:933-938
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    2. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    3. P. Korhonen, 1997. "Searching the Efficient Frontier in Data Envelopment Analysis," Working Papers ir97079, International Institute for Applied Systems Analysis.
    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. Jahanshahloo, G.R. & Hosseinzadeh Lotfi, F. & Zhiani Rezai, H. & Rezai Balf, F., 2007. "Finding strong defining hyperplanes of Production Possibility Set," European Journal of Operational Research, Elsevier, vol. 177(1), pages 42-54, February.
    6. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, 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. Yu, Gang & Wei, Quanling & Brockett, Patrick & Zhou, Li, 1996. "Construction of all DEA efficient surfaces of the production possibility set under the Generalized Data Envelopment Analysis Model," European Journal of Operational Research, Elsevier, vol. 95(3), pages 491-510, December.
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