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Finding strong defining hyperplanes of PPS using multiplier form

Author

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  • Jahanshahloo, G.R.
  • Shirzadi, A.
  • Mirdehghan, S.M.
Abstract
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.

Suggested Citation

  • Jahanshahloo, G.R. & Shirzadi, A. & Mirdehghan, S.M., 2009. "Finding strong defining hyperplanes of PPS using multiplier form," European Journal of Operational Research, Elsevier, vol. 194(3), pages 933-938, May.
    • Handle: RePEc:eee:ejores:v:194:y:2009:i:3:p:933-938
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    References listed on IDEAS

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    1. 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.
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    7. G R Jahanshahloo & F Hosseinzadeh & N Shoja & M Sanei & G Tohidi, 2005. "Sensitivity and stability analysis in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 342-345, March.
    8. 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.
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    3. Amineh Ghazi & Farhad Hosseinzadeh Lotfı & Masoud Sanei, 2022. "Finding the strong efficient frontier and strong defining hyperplanes of production possibility set using multiple objective linear programming," Operational Research, Springer, vol. 22(1), pages 165-198, March.
    4. Andreas Dellnitz & Elmar Reucher & Andreas Kleine, 2021. "Efficiency evaluation in data envelopment analysis using strong defining hyperplanes," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 441-465, June.
    5. Alirezaee, Mohammadreza & Hajinezhad, Ensie & Paradi, Joseph C., 2018. "Objective identification of technological returns to scale for data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 266(2), pages 678-688.

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