Cross-inefficiency with the Variable Returns to Scale in ‎DEA

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

B. Asadi ¹ , H. Nasseri ² , Farhad Hosseinzade Lotfi 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

تاریخ دریافت : 1398/09/26 تاریخ پذیرش : 1399/03/18 تاریخ انتشار : 1399/05/11

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

چکیده مقاله :

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.

چکیده انگلیسی:

روش رتبه‌بندی کارایی متقاطع یکی از روش‌های شناخته شده در تحلیل پوششی داده‌هاست که اغلب تحت فرض بازده به مقیاس ثابت به کار گرفته می‌شود. این در حالی است که کاربردهای فراوانی تحت فرض بازده به مقیاس متغیر موجود هستند. دلیل اصلی این امر، حضور مقادیر کارایی متقاطع منفی در فرض بازده به مقیاس متغیر با ماهیت ورودی است. در این مقاله، هر کارایی متقاطع با یک معیار فاصله‌ی معادل به عنوان شاخصی از ناکارایی جایگزین می‌شود. سپس، بر اساس معیار فاصله مذکور، روش ناکارایی متقاطع تحت فرض بازده به مقیاس متغیر توسعه داده می‌شود.

منابع و مأخذ:

[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.