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Data envelopment analysis with nonlinear virtual inputs and outputs

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  • Despotis, Dimitris K.
  • Stamati, Lamprini V.
  • Smirlis, Yiannis G.

Abstract

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.

Suggested Citation

  • Despotis, Dimitris K. & Stamati, Lamprini V. & Smirlis, Yiannis G., 2010. "Data envelopment analysis with nonlinear virtual inputs and outputs," European Journal of Operational Research, Elsevier, vol. 202(2), pages 604-613, April.
    • Handle: RePEc:eee:ejores:v:202:y:2010:i:2:p:604-613
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    Cited by:

    1. Mousavi-Avval, Seyed Hashem & Rafiee, Shahin & Jafari, Ali & Mohammadi, Ali, 2011. "Improving energy use efficiency of canola production using data envelopment analysis (DEA) approach," Energy, Elsevier, vol. 36(5), pages 2765-2772.
    2. Alexander Cotte, Poveda, 2011. "Economic development and growth in Colombia: An empirical analysis with super-efficiency DEA and panel data models," Socio-Economic Planning Sciences, Elsevier, vol. 45(4), pages 154-164, December.
    3. Giménez, Víctor & Ayvar-Campos, Francisco Javier & Navarro-Chávez, José César Lenin, 2017. "Efficiency in the generation of social welfare in Mexico: A proposal in the presence of bad outputs," Omega, Elsevier, vol. 69(C), pages 43-52.
    4. Mariano, Enzo Barberio & Sobreiro, Vinicius Amorim & Rebelatto, Daisy Aparecida do Nascimento, 2015. "Human development and data envelopment analysis: A structured literature review," Omega, Elsevier, vol. 54(C), pages 33-49.
    5. Enzo Barberio Mariano & Diogo Ferraz & Simone Cristina Oliveira Gobbo, 2021. "The Human Development Index with Multiple Data Envelopment Analysis Approaches: A Comparative Evaluation Using Social Network Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 443-500, September.
    6. Hung, Shiu-Wan & Wang, An-Pang, 2012. "Entrepreneurs with glamour? DEA performance characterization of high-tech and older-established industries," Economic Modelling, Elsevier, vol. 29(4), pages 1146-1153.

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