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In the determination of weight sets to compute cross-efficiency ratios in DEA

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  • K F Lam

    (City University of Hong Kong)

Abstract

Data envelopment analysis (DEA) measures the production performance of decision-making units (DMUs) which consume multiple inputs and produce multiple outputs. Although DEA has become a very popular method of performance measure, it still suffers from some shortcomings. For instance, one of its drawbacks is that multiple solutions exist in the linear programming solutions of efficient DMUs. The obtained weight set is just one of the many optimal weight sets that are available. Then why use this weight set instead of the others especially when this weight set is used for cross-evaluation? Another weakness of DEA is that extremely diverse or unusual values of some input or output weights might be obtained for DMUs under assessment. Zero input and output weights are not uncommon in DEA. The main objective of this paper is to develop a new methodology which applies discriminant analysis, super-efficiency DEA model and mixed-integer linear programming to choose suitable weight sets to be used in computing cross-evaluation. An advantage of this new method is that each obtained weight set can reflect the relative strengths of the efficient DMU under consideration. Moreover, the method also attempts to preserve the original classificatory result of DEA, and in addition this method produces much less zero weights than DEA in our computational results.

Suggested Citation

  • K F Lam, 2010. "In the determination of weight sets to compute cross-efficiency ratios in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 134-143, January.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:1:d:10.1057_jors.2008.138
    DOI: 10.1057/jors.2008.138
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    References listed on IDEAS

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    Cited by:

    1. Paola Cappanera & Filippo Visintin & Carlo Banditori, 2018. "Addressing conflicting stakeholders’ priorities in surgical scheduling by goal programming," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 252-271, June.
    2. Ramón, Nuria & Ruiz, José L. & Sirvent, Inmaculada, 2011. "Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation," Omega, Elsevier, vol. 39(6), pages 634-641, December.
    3. Hashem Omrani & Khatereh Shafaat & Arash Alizadeh, 2019. "Integrated data envelopment analysis and cooperative game for evaluating energy efficiency of transportation sector: a case of Iran," Annals of Operations Research, Springer, vol. 274(1), pages 471-499, March.
    4. Shiang-Tai Liu, 2018. "A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio," Annals of Operations Research, Springer, vol. 261(1), pages 207-232, February.
    5. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    6. Shiang-Tai Liu & Yueh-Chiang Lee, 2021. "Fuzzy measures for fuzzy cross efficiency in data envelopment analysis," Annals of Operations Research, Springer, vol. 300(2), pages 369-398, May.
    7. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    8. H. Örkcü & Mehmet Ünsal & Hasan Bal, 2015. "A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity," Annals of Operations Research, Springer, vol. 235(1), pages 599-623, December.
    9. Ruiz, José L. & Sirvent, Inmaculada, 2012. "On the DEA total weight flexibility and the aggregation in cross-efficiency evaluations," European Journal of Operational Research, Elsevier, vol. 223(3), pages 732-738.
    10. Hamid Kiaei & Reza Farzipoor Saen & Reza Kazemi Matin, 2023. "Cross-efficiency evaluation and improvement in two-stage network data envelopment analysis," Annals of Operations Research, Springer, vol. 321(1), pages 281-309, February.

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