Cross-inefficiency with the Variable Returns to Scale in ‎DEA

Subject Areas : International Journal of Industrial Mathematics

بهداد اسدی ¹ , هادی ناصری ² , فرهاد حسین زاده لطفی ³

1 - Department of Mathematics, University of Mazandaran, Babolsar, Iran
2 - Department of Mathematics, University of Mazandaran, Babolsar, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2019-12-17 Accepted : 2020-06-07 Published : 2020-08-01

Keywords: Negative cross-efficiency, Data Envelopment Analysis, VRS production possibility set, Cross-inefficiency, Variable returns to scale,

Abstract :

The cross-efficiency ranking method is a well-known method in DEA which is frequently used under the constant returns to scale assumption; while various applications exist based on the variable returns to scale (VRS). This is due to the presence of negative input-oriented VRS cross-efficiencies. In this paper, each cross-efficiency is replaced by an equivalent distance measure as inefficiency measure. Then, the cross-inefficiency method is developed under the VRS assumption.

References:

[1] L. Angulo-Meza, J. C. C. B. Soares deMello, E. G. Gomes, L. Biondi Neto, Eficiencias negativas em modelos DEA-BCC: como surgem e como evita-las, VII Simposio de Pesquisa Operacional e Logistica da Marinha-SPOLM (2004).
[2] R. D. Banker, Estimating most productive scale size using data envelopment analysis, European Journal of Operational Research 17 (1984) 35-44.
[3] R. D. Banker, A. Charnes, W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science 30 (1984) 1078-1092.
[4] M. Carrillo, J. M. Jorge, An alternative neutral approach for cross-efficiency evaluation, Computers & Industrial Engineering 120 (2018) 137-145.
[5] A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, European journal of operational research 2 (1978) 429-444.
[6] A. Charnes, W. W. Cooper, A. Y. Lewin, L. M. Seiford, Data envelopment analysis: Theory, methodology, and applications, Springer Science & Business Media (2013).
[7] L. Chen, Y. M. Wang, DEA target setting approach within the cross efficiency framework, Omega (2019) 10-20.
[8] W. Chen, K. Zhou, S. Yang, Evaluation of Chinas electric energy efficiency under environmental constraints: A DEA cross efficiency model based on game relationship. Journal of Cleaner Production 164 (2017) 38-44.
[9] W. W. Cooper, L. M. Seiford, K. A. Tone, A comprehensive text with models, applications, references and DEA-solver software, Springer Science+ Business Media (2007).
[10] J. C. C. S. de Mello, L. A. Meza, J. Q. da Silveira, E. G. Gomes, About negative efficiencies in cross evaluation BCC input oriented models European Journal of Operational Research 229 (2013) 732-737.
[11] J. C. C. B. S. de Mello, M. P. E. Lins, E. G. Gomes, Contruction of a smoothed DEA frontier, Pesquisa operacional 22 (2002) 183-201.
[12] S. S. Ganji, A. Rassafi, D. L. A. Xu, A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance, Measurement 136 (2019) 668-688.
[13] X. Huang, H. Jin, H. Bai, Vulnerability assessment of China’s coastal cities based on DEA cross-efficiency model, International Journal of Disaster Risk Reduction 36 (2019) 101-109.
[14] G. R. Jahanshahloo, M. SoleimaniDamaneh, A note on simulating weights restrictions in DEA: an improvement of Thanassoulis and Allen’s method, Computers & operations research 32 (2005) 1037-1044.
[15] S. Lim, J. Zhu, DEA cross-efficiency evaluation under variable returns to scale, Journal of the Operational Research Society 66 (2015) 476-487.
[16] H. H. Liu, Y. Y. Song, X. X. Liu, G. L. Yang, Aggregating the DEA prospect crossefficiency with an application to state key laboratories in China, Socio-Economic Planning Sciences (2020) 100-109.
[17] M. Oral, O. Kettani, P. Lang, A methodology for collective evaluation and selection of industrial R& D projects, Management science 37 (1991) 871-885.
[18] V. V. Podinovski, T. Bouzdine-Chameeva, Weight restrictions and free production in data envelopment analysis, Operations Research 61 (2013) 426-437.
[19] T. R. Sexton, R. H. Silkman, A. J. Hogan, Data envelopment analysis: Critique and extensions, New Directions for Program Evaluation 11 (1986) 73-105.
[20] H. Shi, Y. Wang, L. Chen, Neutral crossefficiency evaluation regarding an ideal frontier and anti-ideal frontier as evaluation criteria, Computers & Industrial Engineering 132 (2019) 385-394.
[21] E. Thanassoulis, M. Kortelainen, R. Allen, Improving envelopment in data envelopment analysis under variable returns to scale, European journal of operational research 218 (2012) 175-185.
[22] J. Wu, J. Chu, J. Sun, Q. Zhu, DEA crossefficiency evaluation based on Pareto improvement, European Journal of Operational Research 248 (2016) 571-579.
[23] J. Wu, L. Liang, Y. Chen, DEA game cross-efficiency approach to Olympic rankings, Omega 37 (2009) 909-918.
[24] Z. Yang, X. Wei, The measurement and influences of China’s urban total factor energy efficiency under environmental pollution: Based on the game cross-efficiency DEA, Journal of cleaner production 209 (2019) 439-450
[25] Y. Zhou, W. Liu, X. Lv, X. Chen, M. Shen, Investigating interior driving factors and cross-industrial linkages of carbon emission efficiency in China’s construction industry: Based on Super-SBM DEA and GVAR model, Journal of Cleaner Production 241
(2019)118-122.