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The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs

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  • Khalili, M.
  • Camanho, A.S.
  • Portela, M.C.A.S.
  • Alirezaee, M.R.

Abstract

The most popular weight restrictions are assurance regions (ARs), which impose ratios between weights to be within certain ranges. ARs can be categorized into two types: ARs type I (ARI) and ARs type II (ARII). ARI specify bounds on ratios between input weights or between output weights, whilst ARII specify bounds on ratios that link input to output weights. DEA models with ARI successfully maximize relative efficiency, but in the presence of ARII the DEA models may under-estimate relative efficiency or may become infeasible. In this paper we discuss the problems that can occur in the presence of ARII and propose a new nonlinear model that overcomes the limitations discussed. Also, the dual model is described, which enables the assessment of relative efficiency when trade-offs between inputs and outputs are specified. The application of the model developed is illustrated in the efficiency assessment of Portuguese secondary schools.

Suggested Citation

  • Khalili, M. & Camanho, A.S. & Portela, M.C.A.S. & Alirezaee, M.R., 2010. "The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs," European Journal of Operational Research, Elsevier, vol. 203(3), pages 761-770, June.
  • Handle: RePEc:eee:ejores:v:203:y:2010:i:3:p:761-770
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    Cited by:

    1. Kristof de Witte & Laura López-Torres, 2015. "Efficiency in Education. A Review of Literature and a Way Forward," Working Papers 1501, Departament Empresa, Universitat Autònoma de Barcelona, revised Apr 2015.
    2. Podinovski, Victor V., 2016. "Optimal weights in DEA models with weight restrictions," European Journal of Operational Research, Elsevier, vol. 254(3), pages 916-924.
    3. Kristof De Witte & Laura López-Torres, 2017. "Efficiency in education: a review of literature and a way forward," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 339-363, April.
    4. Minegishi, Kota, 2014. "Integrating Efficiency Concepts in Technology Approximation: A Weighted DEA Approach," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170277, Agricultural and Applied Economics Association.
    5. Victor V. Podinovski & Wan Rohaida Wan Husain, 2017. "The hybrid returns-to-scale model and its extension by production trade-offs: an application to the efficiency assessment of public universities in Malaysia," Annals of Operations Research, Springer, vol. 250(1), pages 65-84, March.
    6. Ströhl, Florian & Borsch, Erik & Souren, Rainer, 2018. "Integration von Gewichtsrestriktionen in das DEA-Modell nach Charnes, Cooper und Rhodes: Exemplarische Optionen und Auswirkungen," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 3, number 32018.
    7. Ghasemi, M.-R. & Ignatius, Joshua & Emrouznejad, Ali, 2014. "A bi-objective weighted model for improving the discrimination power in MCDEA," European Journal of Operational Research, Elsevier, vol. 233(3), pages 640-650.
    8. Vitezslav Titl & Kristof De Witte & Benny Geys, 2019. "Political donations, public procurement and government efficiency," CESifo Working Paper Series 7591, CESifo.
    9. Podinovski, Victor V. & Bouzdine-Chameeva, Tatiana, 2015. "Consistent weight restrictions in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 244(1), pages 201-209.
    10. Rezaeiani, M.J. & Foroughi, A.A., 2018. "Ranking efficient decision making units in data envelopment analysis based on reference frontier share," European Journal of Operational Research, Elsevier, vol. 264(2), pages 665-674.
    11. Kanematsu, Simon Y. & Carvalho, Ney P. & Martinhon, Carlos A. & Almeida, Mariana R., 2020. "Ranking using η-efficiency and relative size measures based on DEA," Omega, Elsevier, vol. 90(C).
    12. Samoilenko, Sergey & Osei-Bryson, Kweku-Muata, 2010. "Determining sources of relative inefficiency in heterogeneous samples: Methodology using Cluster Analysis, DEA and Neural Networks," European Journal of Operational Research, Elsevier, vol. 206(2), pages 479-487, October.
    13. Ahn, Heinz & Neumann, Ludmila & Vazquez Novoa, Nadia, 2012. "Measuring the relative balance of DMUs," European Journal of Operational Research, Elsevier, vol. 221(2), pages 417-423.

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