Scale efficiency of China's regional R &amp; D value chain: A double frontier network DEA approach

Saeed Assani; Jianlin Jiang; Ahmad Assani; Feng Yang

doi:10.3934/jimo.2020025

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doi: 10.3934/jimo.2020025

Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach

Saeed Assani ^1,2,, , Jianlin Jiang ^1, , Ahmad Assani ^3, and Feng Yang ^4,

1.	Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2.	Department of Mathematical Statistics, Faculty of Science, Tishreen University, Latakia, Syria
3.	Faculty of Computer Science and Business Computer Systems, Karlsruhe University of Applied Science, Karlsruhe, 76133, Germany
4.	School of Management, University of Science and Technology of China, Hefei 230026, China

^* Corresponding author: Saeed Assani

Received December 2018 Revised October 2019 Published February 2020

Data envelopment analysis (DEA) is one of the vastly available literature on efficiency analysis. In general, the efficiency of decision making units (DMUs) can be measured from two perspectives, optimistic and pessimistic. Two different perspectives lead to two different conflicting and biased scale efficiency measurements. To deal with the problem, in this paper, we introduce a double frontier approach to integrate both optimistic and pessimistic scale efficiencies' viewpoints in one single scale efficiency term, which will be more realistic and has benchmarking preferences. We first investigate the scale efficiency concept from double frontier perspective in black-box DEA and then extend it to the two-stage DEA framework. Mathematical analysis proved that the double frontier scale efficiency of a two-stage system could be decomposed into the internal stages' double frontier scale efficiencies. Finally, we elaborate applicability and merits of the proposed approach using a case of China's regional R & D value chain in terms of its profitability and marketability.

Keywords: Data envelopment analysis, scale efficiency, optimistic-pessimistic efficiency, double frontier approach, R & D.

Mathematics Subject Classification: Primary: 90B10, 90B30; Secondary: 90B50.

Citation: Saeed Assani, Jianlin Jiang, Ahmad Assani, Feng Yang. Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020025

References:

[1]	Q. An, F. Meng, B. Xiong, Z. Wang and X. Chen, Assessing the relative efficiency of Chinese high-tech industries: A dynamic network data envelopment analysis approach, Annals of Operations Research, (2018), 1–23. doi: 10.1007/s10479-018-2883-2. Google Scholar
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[3]	S. Assani, J. Jiang, A. Assani and F. Yang, Most productive scale size of China's regional R & D value chain: A mixed structure network, preprint, arXiv: 1910.03805. Google Scholar
[4]	S. Assani, J. Jiang, R. Cao and F. Yang, Most productive scale size decomposition for multi-stage systems in data envelopment analysis, Computers and Industrial Engineering, 120 (2018), 279-287. doi: 10.1016/j.cie.2018.04.043. Google Scholar
[5]	H. Azizi, S. Kordrostami and A. Amirteimoori, Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers, Computers and Industrial Engineering, 79 (2015), 42-51. doi: 10.1016/j.cie.2014.10.019. Google Scholar
[6]	T. Badiezadeh, R. F. Saen and T. Samavati, Assessing sustainability of supply chains by double frontier network DEA: A big data approach, Computers and Operations Research, 98 (2018), 284-290. doi: 10.1016/j.cor.2017.06.003. Google Scholar
[7]	R. D. Banker, A. Charnes and W. W. Cooper, Some Models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30 (1984), 1078-1092. doi: 10.1287/mnsc.30.9.1078. Google Scholar
[8]	R. D. Banker and R. M. Thrall, Estimation of returns to scale using data envelopment analysis, European Journal of Operational Research, 62 (1992), 74-84. doi: 10.1016/0377-2217(92)90178-C. Google Scholar
[9]	N. Becheikh, R. Landry and N. Amara, Lessons from innovation empirical studies in the manufacturing sector: A systematic review of the literature from 1993-2003, Technovation, 26 (2006), 644-664. doi: 10.1016/j.technovation.2005.06.016. Google Scholar
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[11]	N. Capon, J. U. Farley and S. Hoenig, Determinants of financial performance, Management Science, 36 (2011), 1143-1159. doi: 10.1287/mnsc.36.10.1143. Google Scholar
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[21]	J. Guan and K. Chen, Measuring the innovation production process: A cross-region empirical study of China's high-tech innovations, Technovation, 30 (2010), 348-358. doi: 10.1016/j.technovation.2010.02.001. Google Scholar
[22]	B. H. Hall and R. H. Ziedonis, The patent paradox revisited: An empirical study of patenting in the U.S. semiconductor industry, 1979-1995, The RAND Journal of Economics, 32 (2001), 101-101. doi: 10.2307/2696400. Google Scholar
[23]	M. A. Hitt, R. E. Hoskisson and H. Kim, International diversification: Effects on innovation and firm performance in product-diversified firms, Academy of Management Journal, 40 (1997), 767-798. doi: 10.2307/256948. Google Scholar
[24]	K. Hosseini and A. Stefaniec, Efficiency assessment of Iran's petroleum refining industry in the presence of unprofitable output: A dynamic two-stage slacks-based measure, Energy, 189 (2019), 116112. doi: 10.1016/j.energy.2019.116112. Google Scholar
[25]	J. L. Jiang, E. P. Chew, L. H. Lee and Z. Sun, DEA based on strongly efficient and inefficient frontiers and its application on port efficiency measurement, OR Spectrum, 34 (2012), 943-969. doi: 10.1007/s00291-011-0263-2. Google Scholar
[26]	C. Kao and S. N. Hwang, Decomposition of technical and scale efficiencies in two-stage production systems, European Journal of Operational Research, 211 (2011), 515-519. doi: 10.1016/j.ejor.2011.01.010. Google Scholar
[27]	C. Kao and S. N. Hwang, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan, European Journal of Operational Research, 185 (2008), 418-429. doi: 10.1016/j.ejor.2006.11.041. Google Scholar
[28]	C. Kao and S. N. Hwang, Scale efficiency measurement in two-stage production systems, International Series in Operations Research and Management Science, 208 (2014), 119-135. doi: 10.1007/978-1-4899-8068-7_6. Google Scholar
[29]	P. Khoshnevis and P. Teirlinck, Performance evaluation of R & D active firms, Socio-Economic Planning Sciences, 61 (2018), 16-28. doi: 10.1016/j.seps.2017.01.005. Google Scholar
[30]	S. Lee and H. Lee, Measuring and comparing the R & D performance of government research institutes: A bottom-up data envelopment analysis approach, Journal of Informetrics, 9 (2015), 942-953. doi: 10.1016/j.joi.2015.10.001. Google Scholar
[31]	J. S. Liu, L. Y. Y. Lu, W. M. Lu and B. J. Y. Lin, A survey of DEA applications, Omega, 41 (2013), 893-902. doi: 10.1016/j.omega.2012.11.004. Google Scholar
[32]	J. S. Liu and W. M. Lu, DEA and ranking with the network-based approach: A case of R & D performance, Omega, 38 (2010), 453-464. doi: 10.1016/j.omega.2009.12.002. Google Scholar
[33]	K. Lv, D. Wang and Y. Cheng, Measuring the dynamic performances of innovation production process from the carry-over perspective: An empirical study of China's high-tech industry, Transformations in Business and Economics, 16 (2017), 345-361. Google Scholar
[34]	M. M. Mousavi, J. Ouenniche and K. Tone, A comparative analysis of two-stage distress prediction models, Expert Systems with Applications, 119 (2019), 322-341. doi: 10.1016/j.eswa.2018.10.053. Google Scholar
[35]	G. P$\acute{e}$rez-L$\acute{o}$pez, D. Prior and J. L. Zafra-G$\acute{o}$mez, Temporal scale efficiency in DEA panel data estimations. An application to the solid waste disposal service in Spain, Omega, 76 (2018), 18-27. doi: 10.1016/j.omega.2017.03.005. Google Scholar
[36]	$\ddot{U}$. Sa$\check{g}$lam, Assessment of the productive efficiency of large wind farms in the United States: An application of two-stage data envelopment analysis, Energy Conversion and Management, 153 (2017), 188-214. doi: 10.1016/j.enconman.2017.09.062. Google Scholar
[37]	B. K. Sahoo, J. Zhu, K. Tone and B. M. Klemen, Decomposing technical efficiency and scale elasticity in two-stage network DEA, European Journal of Operational Research, 233 (2014), 584-594. doi: 10.1016/j.ejor.2013.09.046. Google Scholar
[38]	L. M. Seiford and J. Zhu, Profitability and marketability of the top 55 U.S. commercial banks, Management Science, 45 (1999), 1270-1288. doi: 10.1287/mnsc.45.9.1270. Google Scholar
[39]	S. R. Seyedalizadeh Ganji, A. Rassafi and D. L. Xu, A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance, Measurement, 136 (2019), 668-688. doi: 10.1016/j.measurement.2018.12.098. Google Scholar
[40]	A. Sterlacchini, Do innovative activities matter to small firms in non R & D intensive industries? An application to export performance, Research Policy, 28 (1999), 819-832. doi: 10.1016/S0048-7333(99)00023-2. Google Scholar
[41]	T. Sueyoshi and D. Wang, Measuring scale efficiency and returns to scale on large commercial rooftop photovoltaic systems in California, Energy Economics, 65 (2017), 389-398. doi: 10.1016/j.eneco.2017.04.019. Google Scholar
[42]	S. Thornhill, Knowledge, innovation and firm performance in high and low technology regimes, Journal of Business Venturing, 21 (2006), 687-703. doi: 10.1016/j.jbusvent.2005.06.001. Google Scholar
[43]	B. Walheer, Scale efficiency for multi-output cost minimizing producers: The case of the US electricity plants, Energy Economics, 70 (2018), 26-36. doi: 10.1016/j.eneco.2017.12.017. Google Scholar
[44]	C. H. Wang, Y. H. Lu, C. W. Huang and J. Y. Lee, R & D, productivity, and market value: An empirical study from high-technology firms, Omega, 41 (2013), 143-155. doi: 10.1016/j.omega.2011.12.011. Google Scholar
[45]	Y. M. Wang, K. S. Chin and J. B. Yang, Measuring the performances of decision-making units using geometric average efficiency, Journal of the Operational Research Society, 58 (2007), 929-937. doi: 10.1057/palgrave.jors.2602205. Google Scholar
[46]	Y. M. Wang and Y. X. Lan, Estimating most productive scale size with double frontiers data envelopment analysis, Economic Modelling, 33 (2013), 182-186. doi: 10.1016/j.econmod.2013.04.021. Google Scholar
[47]	Y. M. Wang and J. B. Yang, Measuring the performances of decision-making units using interval efficiencies, Journal of Computational and Applied Mathematics, 198 (2007), 253-267. doi: 10.1016/j.cam.2005.12.025. Google Scholar
[48]	P. F. Wanke and C. P. Barros, Public-private partnerships and scale efficiency in Brazilian ports: Evidence from two-stage DEA analysis, Socio-Economic Planning Sciences, 51 (2015), 13-22. doi: 10.1016/j.seps.2015.06.002. Google Scholar
[49]	Z. G. Xin and W. Zhen, The technical efficiency of China's wind power list enterprises: An estimation based on DEA method and micro-data, Renewable Energy, 133 (2019), 470-479. doi: 10.1016/j.renene.2018.10.049. Google Scholar
[50]	V. Zelenyuk, Aggregation of scale efficiency, European Journal of Operational Research, 240 (2015), 269-277. doi: 10.1016/j.ejor.2014.06.038. Google Scholar
[51]	B. Zhang, Y. Luo and Y. H. Chiu, Efficiency evaluation of China's high-tech industry with a multi-activity network data envelopment analysis approach, Socio-Economic Planning Sciences, 66 (2019), 2-9. doi: 10.1016/j.seps.2018.07.013. Google Scholar
[52]	W. Zhong, W. Yuan, S. X. Li and Z. Huang, The performance evaluation of regional R & D investments in China: An application of DEA based on the first official China economic census data, Omega, 39 (2011), 447-455. doi: 10.1016/j.omega.2010.09.004. Google Scholar

show all references

References:

[1]	Q. An, F. Meng, B. Xiong, Z. Wang and X. Chen, Assessing the relative efficiency of Chinese high-tech industries: A dynamic network data envelopment analysis approach, Annals of Operations Research, (2018), 1–23. doi: 10.1007/s10479-018-2883-2. Google Scholar
[2]	S. Assani, J. Jiang, A. Assani and F. Yang, Estimating and decomposing most productive scale size in parallel DEA networks with shared inputs: A case of China's Five-Year Plans, preprint, arXiv: 1910.03421. Google Scholar
[3]	S. Assani, J. Jiang, A. Assani and F. Yang, Most productive scale size of China's regional R & D value chain: A mixed structure network, preprint, arXiv: 1910.03805. Google Scholar
[4]	S. Assani, J. Jiang, R. Cao and F. Yang, Most productive scale size decomposition for multi-stage systems in data envelopment analysis, Computers and Industrial Engineering, 120 (2018), 279-287. doi: 10.1016/j.cie.2018.04.043. Google Scholar
[5]	H. Azizi, S. Kordrostami and A. Amirteimoori, Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers, Computers and Industrial Engineering, 79 (2015), 42-51. doi: 10.1016/j.cie.2014.10.019. Google Scholar
[6]	T. Badiezadeh, R. F. Saen and T. Samavati, Assessing sustainability of supply chains by double frontier network DEA: A big data approach, Computers and Operations Research, 98 (2018), 284-290. doi: 10.1016/j.cor.2017.06.003. Google Scholar
[7]	R. D. Banker, A. Charnes and W. W. Cooper, Some Models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30 (1984), 1078-1092. doi: 10.1287/mnsc.30.9.1078. Google Scholar
[8]	R. D. Banker and R. M. Thrall, Estimation of returns to scale using data envelopment analysis, European Journal of Operational Research, 62 (1992), 74-84. doi: 10.1016/0377-2217(92)90178-C. Google Scholar
[9]	N. Becheikh, R. Landry and N. Amara, Lessons from innovation empirical studies in the manufacturing sector: A systematic review of the literature from 1993-2003, Technovation, 26 (2006), 644-664. doi: 10.1016/j.technovation.2005.06.016. Google Scholar
[10]	R. Blundell, R. Griffith and J. V. Reenen, Market share, market value and innovation in a panel of British manufacturing firms, Review of Economic Studies, 66 (1999), 529-554. doi: 10.1111/1467-937X.00097. Google Scholar
[11]	N. Capon, J. U. Farley and S. Hoenig, Determinants of financial performance, Management Science, 36 (2011), 1143-1159. doi: 10.1287/mnsc.36.10.1143. Google Scholar
[12]	A. Charnes and W. W. Cooper, The non-archimedean CCR ratio for efficiency analysis: A rejoinder to Boyd and F$\ddot{a}$re, European Journal of Operational Research, 15 (1984), 333-334. doi: 10.1016/0377-2217(84)90102-4. Google Scholar
[13]	A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European Journal of Operational Research, 2 (1978), 429-444. doi: 10.1016/0377-2217(78)90138-8. Google Scholar
[14]	K. Chen, M. Kou and X. Fu, Evaluation of multi-period regional R & D efficiency: An application of dynamic DEA to China's regional R & D systems, Omega, 74 (2018), 103-114. doi: 10.1016/j.omega.2017.01.010. Google Scholar
[15]	X. Chen, Z. Liu and Q. Zhu, Performance evaluation of China's high-tech innovation process: Analysis based on the innovation value chain, Technovation, 74-75 (2018), 42-53. doi: 10.1016/j.technovation.2018.02.009. Google Scholar
[16]	W. W. Cooper, L. M. Seiford and K. Tone, Introduction to Data Envelopment Analysis and Its Uses. In Introduction to Data Envelopment Analysis and Its Uses: With DEA-Solver Software and References, Springer, Boston, 2006. doi: 10.1007/0-387-29122-9. Google Scholar
[17]	P. Coto-Millán, V. Inglada, X. L. Fernández, L. Inglada-Pérez and M. Á. Pesquera, The "effect procargo" on technical and scale efficiency at airports: The case of Spanish airports (2009-2011), Utilities Policy, 39 (2016), 29-35. doi: 10.1016/j.jup.2016.01.004. Google Scholar
[18]	D. M. Decarolis and D. L. Deeds, The impact of stocks and flows of organizational knowledge on firm performance: An empirical investigation of the biotechnology industry, Strategic Management Journal, 20 (1999), 953-968. doi: 10.1002/(SICI)1097-0266(199910)20:10<953::AID-SMJ59>3.0.CO;2-3. Google Scholar
[19]	A. Emrouznejad and G. Yang, A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016, Socio-Economic Planning Sciences, 61 (2018), 4-8. doi: 10.1016/j.seps.2017.01.008. Google Scholar
[20]	S. B. Graves and N. S. Langowitz, R & D productivity: A global multi-industry comparison, Technological Forecasting and Social Change, 53 (1996), 125-137. doi: 10.1016/S0040-1625(96)00068-6. Google Scholar
[21]	J. Guan and K. Chen, Measuring the innovation production process: A cross-region empirical study of China's high-tech innovations, Technovation, 30 (2010), 348-358. doi: 10.1016/j.technovation.2010.02.001. Google Scholar
[22]	B. H. Hall and R. H. Ziedonis, The patent paradox revisited: An empirical study of patenting in the U.S. semiconductor industry, 1979-1995, The RAND Journal of Economics, 32 (2001), 101-101. doi: 10.2307/2696400. Google Scholar
[23]	M. A. Hitt, R. E. Hoskisson and H. Kim, International diversification: Effects on innovation and firm performance in product-diversified firms, Academy of Management Journal, 40 (1997), 767-798. doi: 10.2307/256948. Google Scholar
[24]	K. Hosseini and A. Stefaniec, Efficiency assessment of Iran's petroleum refining industry in the presence of unprofitable output: A dynamic two-stage slacks-based measure, Energy, 189 (2019), 116112. doi: 10.1016/j.energy.2019.116112. Google Scholar
[25]	J. L. Jiang, E. P. Chew, L. H. Lee and Z. Sun, DEA based on strongly efficient and inefficient frontiers and its application on port efficiency measurement, OR Spectrum, 34 (2012), 943-969. doi: 10.1007/s00291-011-0263-2. Google Scholar
[26]	C. Kao and S. N. Hwang, Decomposition of technical and scale efficiencies in two-stage production systems, European Journal of Operational Research, 211 (2011), 515-519. doi: 10.1016/j.ejor.2011.01.010. Google Scholar
[27]	C. Kao and S. N. Hwang, Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan, European Journal of Operational Research, 185 (2008), 418-429. doi: 10.1016/j.ejor.2006.11.041. Google Scholar
[28]	C. Kao and S. N. Hwang, Scale efficiency measurement in two-stage production systems, International Series in Operations Research and Management Science, 208 (2014), 119-135. doi: 10.1007/978-1-4899-8068-7_6. Google Scholar
[29]	P. Khoshnevis and P. Teirlinck, Performance evaluation of R & D active firms, Socio-Economic Planning Sciences, 61 (2018), 16-28. doi: 10.1016/j.seps.2017.01.005. Google Scholar
[30]	S. Lee and H. Lee, Measuring and comparing the R & D performance of government research institutes: A bottom-up data envelopment analysis approach, Journal of Informetrics, 9 (2015), 942-953. doi: 10.1016/j.joi.2015.10.001. Google Scholar
[31]	J. S. Liu, L. Y. Y. Lu, W. M. Lu and B. J. Y. Lin, A survey of DEA applications, Omega, 41 (2013), 893-902. doi: 10.1016/j.omega.2012.11.004. Google Scholar
[32]	J. S. Liu and W. M. Lu, DEA and ranking with the network-based approach: A case of R & D performance, Omega, 38 (2010), 453-464. doi: 10.1016/j.omega.2009.12.002. Google Scholar
[33]	K. Lv, D. Wang and Y. Cheng, Measuring the dynamic performances of innovation production process from the carry-over perspective: An empirical study of China's high-tech industry, Transformations in Business and Economics, 16 (2017), 345-361. Google Scholar
[34]	M. M. Mousavi, J. Ouenniche and K. Tone, A comparative analysis of two-stage distress prediction models, Expert Systems with Applications, 119 (2019), 322-341. doi: 10.1016/j.eswa.2018.10.053. Google Scholar
[35]	G. P$\acute{e}$rez-L$\acute{o}$pez, D. Prior and J. L. Zafra-G$\acute{o}$mez, Temporal scale efficiency in DEA panel data estimations. An application to the solid waste disposal service in Spain, Omega, 76 (2018), 18-27. doi: 10.1016/j.omega.2017.03.005. Google Scholar
[36]	$\ddot{U}$. Sa$\check{g}$lam, Assessment of the productive efficiency of large wind farms in the United States: An application of two-stage data envelopment analysis, Energy Conversion and Management, 153 (2017), 188-214. doi: 10.1016/j.enconman.2017.09.062. Google Scholar
[37]	B. K. Sahoo, J. Zhu, K. Tone and B. M. Klemen, Decomposing technical efficiency and scale elasticity in two-stage network DEA, European Journal of Operational Research, 233 (2014), 584-594. doi: 10.1016/j.ejor.2013.09.046. Google Scholar
[38]	L. M. Seiford and J. Zhu, Profitability and marketability of the top 55 U.S. commercial banks, Management Science, 45 (1999), 1270-1288. doi: 10.1287/mnsc.45.9.1270. Google Scholar
[39]	S. R. Seyedalizadeh Ganji, A. Rassafi and D. L. Xu, A double frontier DEA cross efficiency method aggregated by evidential reasoning approach for measuring road safety performance, Measurement, 136 (2019), 668-688. doi: 10.1016/j.measurement.2018.12.098. Google Scholar
[40]	A. Sterlacchini, Do innovative activities matter to small firms in non R & D intensive industries? An application to export performance, Research Policy, 28 (1999), 819-832. doi: 10.1016/S0048-7333(99)00023-2. Google Scholar
[41]	T. Sueyoshi and D. Wang, Measuring scale efficiency and returns to scale on large commercial rooftop photovoltaic systems in California, Energy Economics, 65 (2017), 389-398. doi: 10.1016/j.eneco.2017.04.019. Google Scholar
[42]	S. Thornhill, Knowledge, innovation and firm performance in high and low technology regimes, Journal of Business Venturing, 21 (2006), 687-703. doi: 10.1016/j.jbusvent.2005.06.001. Google Scholar
[43]	B. Walheer, Scale efficiency for multi-output cost minimizing producers: The case of the US electricity plants, Energy Economics, 70 (2018), 26-36. doi: 10.1016/j.eneco.2017.12.017. Google Scholar
[44]	C. H. Wang, Y. H. Lu, C. W. Huang and J. Y. Lee, R & D, productivity, and market value: An empirical study from high-technology firms, Omega, 41 (2013), 143-155. doi: 10.1016/j.omega.2011.12.011. Google Scholar
[45]	Y. M. Wang, K. S. Chin and J. B. Yang, Measuring the performances of decision-making units using geometric average efficiency, Journal of the Operational Research Society, 58 (2007), 929-937. doi: 10.1057/palgrave.jors.2602205. Google Scholar
[46]	Y. M. Wang and Y. X. Lan, Estimating most productive scale size with double frontiers data envelopment analysis, Economic Modelling, 33 (2013), 182-186. doi: 10.1016/j.econmod.2013.04.021. Google Scholar
[47]	Y. M. Wang and J. B. Yang, Measuring the performances of decision-making units using interval efficiencies, Journal of Computational and Applied Mathematics, 198 (2007), 253-267. doi: 10.1016/j.cam.2005.12.025. Google Scholar
[48]	P. F. Wanke and C. P. Barros, Public-private partnerships and scale efficiency in Brazilian ports: Evidence from two-stage DEA analysis, Socio-Economic Planning Sciences, 51 (2015), 13-22. doi: 10.1016/j.seps.2015.06.002. Google Scholar
[49]	Z. G. Xin and W. Zhen, The technical efficiency of China's wind power list enterprises: An estimation based on DEA method and micro-data, Renewable Energy, 133 (2019), 470-479. doi: 10.1016/j.renene.2018.10.049. Google Scholar
[50]	V. Zelenyuk, Aggregation of scale efficiency, European Journal of Operational Research, 240 (2015), 269-277. doi: 10.1016/j.ejor.2014.06.038. Google Scholar
[51]	B. Zhang, Y. Luo and Y. H. Chiu, Efficiency evaluation of China's high-tech industry with a multi-activity network data envelopment analysis approach, Socio-Economic Planning Sciences, 66 (2019), 2-9. doi: 10.1016/j.seps.2018.07.013. Google Scholar
[52]	W. Zhong, W. Yuan, S. X. Li and Z. Huang, The performance evaluation of regional R & D investments in China: An application of DEA based on the first official China economic census data, Omega, 39 (2011), 447-455. doi: 10.1016/j.omega.2010.09.004. Google Scholar

Figure 1. Two-stage DEA system

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Figure 2. Two-stage R & D value chain

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Figure 3. Efficiency evaluation from an optimistic perspective by area

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Figure 4. Efficiency evaluation from a pessimistic perspective by area

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Figure 5. Efficiency evaluation from double frontier perspective by area

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Table 1. Dataset

DMU	Inputs		Output
DMU	$ X_1 $	$ X_2 $	$ Y $
A	40	7	210
B	32	12	105
C	52	20	304
D	35	13	200
E	32	8	150

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DMU	Inputs		Output
DMU	$ X_1 $	$ X_2 $	$ Y $
A	40	7	210
B	32	12	105
C	52	20	304
D	35	13	200
E	32	8	150

Table 2. Scale efficiencies and DMUs rankings under optimistic, pessimistic, and double frontier

DMU	Optimistic perspective				Pessimistic perspective				Double frontier
DMU	$ E_{opt}^{\ast} $	$ T_{opt}^{\ast} $	$ SE_{opt} $	$ R $	$ E_{pess}^{\ast} $	$ T_{pess}^{\ast} $	$ SE_{pess} $	$ R $	$ SE_{df} $	$ R $
A	1.0000	1.0000	1.0000	1	1.6000	1.0638	1.5040	2	1.2264	2
B	0.5639	1.0000	0.5639	5	1.0000	1.0000	1.0000	5	0.7509	5
C	1.0000	1.0000	1.0000	1	1.7371	1.0000	1.7371	1	1.3180	1
D	0.9838	1.0000	0.9838	3	1.7415	1.1871	1.4670	3	1.2013	3
E	0.8580	1.0000	0.8580	4	1.4286	1.1413	1.2517	4	1.0363	4

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DMU	Optimistic perspective				Pessimistic perspective				Double frontier
DMU	$ E_{opt}^{\ast} $	$ T_{opt}^{\ast} $	$ SE_{opt} $	$ R $	$ E_{pess}^{\ast} $	$ T_{pess}^{\ast} $	$ SE_{pess} $	$ R $	$ SE_{df} $	$ R $
A	1.0000	1.0000	1.0000	1	1.6000	1.0638	1.5040	2	1.2264	2
B	0.5639	1.0000	0.5639	5	1.0000	1.0000	1.0000	5	0.7509	5
C	1.0000	1.0000	1.0000	1	1.7371	1.0000	1.7371	1	1.3180	1
D	0.9838	1.0000	0.9838	3	1.7415	1.1871	1.4670	3	1.2013	3
E	0.8580	1.0000	0.8580	4	1.4286	1.1413	1.2517	4	1.0363	4

Table 3. Summary of inputs and outputs descriptive statistics of China's regional R & D activities

	Mean	S.D.	Minimum	Mximum
Employees	1356.5	1111.2	141	5980
Investment in fixed assets (100 million Yuan)	14014.7	16100.7	688	69113
R & D personnel	88048.3	111505.4	2068	424872
R & D projects	11415.9	13971.5	156	53117
R & D expenditure (10000 Yuan)	3084654.9	3771958.6	92528	13765378
Sales volumes (100 million Yuan)	36403	36819.4	1901	141194
Number of patents	26320.2	32272.3	660	146660
Market value (100 million Yuan)	26911.2	57669.3	65	313719

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	Mean	S.D.	Minimum	Mximum
Employees	1356.5	1111.2	141	5980
Investment in fixed assets (100 million Yuan)	14014.7	16100.7	688	69113
R & D personnel	88048.3	111505.4	2068	424872
R & D projects	11415.9	13971.5	156	53117
R & D expenditure (10000 Yuan)	3084654.9	3771958.6	92528	13765378
Sales volumes (100 million Yuan)	36403	36819.4	1901	141194
Number of patents	26320.2	32272.3	660	146660
Market value (100 million Yuan)	26911.2	57669.3	65	313719

Table Appendix.1. Data of R&D activities of 30 provincial-level regions in mainland China for 2014

	Region	$ X_1 $	$ X_2 $	$ X_3 $	$ X_4 $	$ X_5 $	$ Z_1 $	$ Z_2 $	$ Y $
1	Beijing	5980	11582	57761	2335010	9010	18228	78129	313719
2	Tianjin	1069	16877	79014	3228057	15055	27391	23391	38856
3	Hebei	1448	20762	75142	2606711	8714	46685	8332	2922
4	Shanxi	733	4581	35775	1247027	2726	15214	6107	4846
5	Inner Mongolia	622	14709	27068	1080287	2265	19517	1924	1394
6	Liaoning	1690	26103	63374	3242303	8608	48764	18417	21746
7	Jilin	788	12383	24395	789431	2264	22964	5288	2858
8	Heilongjiang	1154	9229	37509	955820	4324	13139	13468	12028
9	Shanghai	2254	5467	93868	4492192	13821	32458	39133	59245
10	Jiangsu	2151	60663	422865	13765378	53117	141194	146660	54316
11	Zhejiang	1610	9149	290339	7681473	45679	64914	52406	8725
12	Anhui	958	21948	95287	2847303	14648	36505	49960	16983
13	Fujian	848	5269	110892	3153831	10949	37373	12529	3919
14	Jiangxi	554	5440	28803	1284642	4385	28727	4688	5076
15	Shandong	1842	69113	230800	11755482	34353	139627	77298	24929
16	Henan	1639	13262	134256	3372310	12635	67149	19646	4079
17	Hubei	1517	9427	91456	3629506	9955	42012	22536	58068
18	Hunan	1292	20605	77428	3100446	9393	34394	14474	9793
19	Guangdong	3193	16477	424872	13752869	42941	116336	75147	41325
20	Guangxi	977	7054	22793	848808	3260	19629	22237	1158
21	Hainan	219	1184	3484	111010	934	1901	969	65
22	Chongqing	766	2975	43797	1664720	7879	18439	19418	15620
23	Sichuan	2106	8311	62145	1960112	11027	37400	29926	19905
24	Guizhou	766	1515	15659	410132	1682	9053	8203	2004
25	Yunnan	1011	3215	12980	516572	2102	10022	4732	4792
26	Shaanxi	1777	33830	50753	1606946	6668	19947	24399	64002
27	Gansu	704	6623	14380	464410	1894	7886	4986	11452
28	Qinghai	229	688	2068	92528	156	2475	660	2910
29	Ningxia	141	702	5799	186518	1136	3584	2183	318
30	Xinjiang	657	1297	6688	357812	897	9161	2360	282
$X_1$:Employees, $X_2$:Investment in fixed assets (100 million Yuan) $X_3$:R&D personnel, $X_4$:R&D projects, $X_5$:R&D expenditure (10000 Yuan), $Z_1$:Sales volumes (100 million Yuan, ) $Z_2$:Number of patents, $Y$: Market value (100 million Yuan)

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	Region	$ X_1 $	$ X_2 $	$ X_3 $	$ X_4 $	$ X_5 $	$ Z_1 $	$ Z_2 $	$ Y $
1	Beijing	5980	11582	57761	2335010	9010	18228	78129	313719
2	Tianjin	1069	16877	79014	3228057	15055	27391	23391	38856
3	Hebei	1448	20762	75142	2606711	8714	46685	8332	2922
4	Shanxi	733	4581	35775	1247027	2726	15214	6107	4846
5	Inner Mongolia	622	14709	27068	1080287	2265	19517	1924	1394
6	Liaoning	1690	26103	63374	3242303	8608	48764	18417	21746
7	Jilin	788	12383	24395	789431	2264	22964	5288	2858
8	Heilongjiang	1154	9229	37509	955820	4324	13139	13468	12028
9	Shanghai	2254	5467	93868	4492192	13821	32458	39133	59245
10	Jiangsu	2151	60663	422865	13765378	53117	141194	146660	54316
11	Zhejiang	1610	9149	290339	7681473	45679	64914	52406	8725
12	Anhui	958	21948	95287	2847303	14648	36505	49960	16983
13	Fujian	848	5269	110892	3153831	10949	37373	12529	3919
14	Jiangxi	554	5440	28803	1284642	4385	28727	4688	5076
15	Shandong	1842	69113	230800	11755482	34353	139627	77298	24929
16	Henan	1639	13262	134256	3372310	12635	67149	19646	4079
17	Hubei	1517	9427	91456	3629506	9955	42012	22536	58068
18	Hunan	1292	20605	77428	3100446	9393	34394	14474	9793
19	Guangdong	3193	16477	424872	13752869	42941	116336	75147	41325
20	Guangxi	977	7054	22793	848808	3260	19629	22237	1158
21	Hainan	219	1184	3484	111010	934	1901	969	65
22	Chongqing	766	2975	43797	1664720	7879	18439	19418	15620
23	Sichuan	2106	8311	62145	1960112	11027	37400	29926	19905
24	Guizhou	766	1515	15659	410132	1682	9053	8203	2004
25	Yunnan	1011	3215	12980	516572	2102	10022	4732	4792
26	Shaanxi	1777	33830	50753	1606946	6668	19947	24399	64002
27	Gansu	704	6623	14380	464410	1894	7886	4986	11452
28	Qinghai	229	688	2068	92528	156	2475	660	2910
29	Ningxia	141	702	5799	186518	1136	3584	2183	318
30	Xinjiang	657	1297	6688	357812	897	9161	2360	282
$X_1$:Employees, $X_2$:Investment in fixed assets (100 million Yuan) $X_3$:R&D personnel, $X_4$:R&D projects, $X_5$:R&D expenditure (10000 Yuan), $Z_1$:Sales volumes (100 million Yuan, ) $Z_2$:Number of patents, $Y$: Market value (100 million Yuan)

Table Appendix.2. Optimistic, pessimistic, and double frontier's CCR, BCC, and scale efficiencies of the two-stage China's R&D value chain

		Profitability stage				Marketability stage				R&D value chain
No	Model	CCR	BCC	SE	R	CCR	BCC	SE	R	CCR	BCC	SE	R
1	Opt	1.000	1.000	1.000	7	1.000	1.000	1.000	1	1.000	1.000	1.000	1
	Pess	1.000	1.000	1.000	26	176.7	1.000	176.7	1	176.7	1.000	176.7	1
	DF	1.000	1.000	1.000	10	13.29	1.000	13.29	1	13.29	1.000	13.29	1
2	Opt	0.547	0.620	0.883	11	0.403	0.412	0.976	10	0.220	0.256	0.862	9
	Pess	1.000	1.000	1.000	28	32.14	20.82	1.544	20	32.14	20.82	1.544	20
	DF	0.739	0.787	0.939	14	3.600	2.932	1.227	20	2.663	2.308	1.153	12
3	Opt	0.221	0.946	0.234	29	0.076	0.086	0.875	24	0.016	0.082	0.205	28
	Pess	1.181	1.000	1.181	8	2.335	1.000	2.335	12	2.758	1.000	2.758	13
	DF	0.511	0.972	0.526	29	0.421	0.294	1.430	13	0.215	0.286	0.752	27
4	Opt	0.400	0.711	0.562	21	0.185	0.195	0.950	18	0.074	0.139	0.534	19
	Pess	1.000	1.000	1.000	22	10.31	6.918	1.491	21	10.31	6.918	1.491	22
	DF	0.632	0.843	0.750	23	1.385	1.163	1.190	21	0.876	0.981	0.893	23
5	Opt	0.165	0.924	0.178	30	0.141	0.174	0.809	26	0.023	0.161	0.144	29
	Pess	1.000	1.000	1.000	21	2.721	1.000	2.721	11	2.721	1.000	2.721	14
	DF	0.406	0.961	0.422	30	0.620	0.417	1.484	11	0.252	0.401	0.627	29
6	Opt	0.422	0.781	0.540	22	0.275	0.293	0.939	20	0.116	0.229	0.508	21
	Pess	1.239	1.000	1.239	6	13.95	7.438	1.876	18	17.29	7.438	2.325	16
	DF	0.723	0.883	0.818	19	1.960	1.476	1.327	18	1.418	1.305	1.087	17
7	Opt	0.362	1.000	0.362	26	0.120	0.133	0.907	23	0.043	0.133	0.329	25
	Pess	1.441	1.000	1.441	1	4.535	2.328	1.948	15	6.539	2.328	2.808	11
	DF	0.723	1.000	0.723	26	0.740	0.556	1.329	17	0.535	0.556	0.961	21
8	Opt	0.533	0.584	0.912	10	0.217	0.221	0.983	7	0.116	0.129	0.897	8
	Pess	1.134	1.000	1.134	10	19.62	16.54	1.186	23	22.26	16.54	1.345	25
	DF	0.778	0.764	1.017	7	2.068	1.914	1.080	23	1.609	1.464	1.099	14
9	Opt	1.000	1.000	1.000	4	0.370	0.376	0.984	5	0.370	0.376	0.984	4
	Pess	1.082	1.000	1.082	16	33.52	6.038	5.552	5	36.28	6.038	6.009	5
	DF	1.040	1.000	1.040	6	3.526	1.508	2.338	4	3.668	1.508	2.432	4
10	Opt	1.000	1.000	1.000	2	0.090	0.173	0.522	28	0.090	0.173	0.522	20
	Pess	1.349	1.000	1.349	2	8.236	1.000	8.236	3	11.11	1.000	11.11	3
	DF	1.161	1.000	1.161	1	0.862	0.416	2.073	7	1.002	0.416	2.408	5
11	Opt	1.000	1.000	1.000	3	0.040	0.041	0.973	13	0.040	0.041	0.973	7
	Pess	1.000	1.000	1.000	30	2.919	1.000	2.919	9	2.919	1.000	2.919	10
	DF	1.000	1.000	1.000	9	0.343	0.203	1.685	9	0.343	0.203	1.685	9
12	Opt	1.000	1.000	1.000	5	0.083	0.084	0.986	3	0.083	0.084	0.986	2
	Pess	1.657	1.280	1.294	4	8.224	1.000	8.224	4	13.63	1.280	10.65	4
	DF	1.287	1.131	1.138	2	0.828	0.290	2.848	3	1.066	0.329	3.241	3
13	Opt	0.523	1.000	0.523	23	0.072	0.077	0.932	21	0.037	0.077	0.488	22
	Pess	1.000	1.000	1.000	25	3.542	1.823	1.942	16	3.542	1.823	1.942	17
	DF	0.723	1.000	0.723	25	0.506	0.376	1.346	15	0.366	0.376	0.974	20
14	Opt	0.321	1.000	0.321	27	0.231	0.266	0.870	25	0.074	0.266	0.279	27
	Pess	1.433	1.327	1.080	17	7.806	2.815	2.773	10	11.19	3.737	2.994	9
	DF	0.679	1.152	0.589	27	1.344	0.865	1.553	10	0.912	0.997	0.915	22
15	Opt	0.764	1.000	0.764	15	0.076	0.0803	0.958	17	0.058	0.080	0.732	13
	Pess	1.178	1.000	1.178	9	5.093	1.000	5.093	6	6.004	1.000	6.004	6
	DF	0.949	1.000	0.949	12	0.626	0.283	2.208	5	0.594	0.283	2.096	6
16	Opt	0.458	1.000	0.458	25	0.047	0.051	0.920	22	0.021	0.051	0.421	24
	Pess	1.294	1.000	1.294	5	2.159	1.000	2.159	14	2.794	1.000	2.794	12
	DF	0.770	1.000	0.770	21	0.320	0.227	1.410	14	0.246	0.227	1.085	18
17	Opt	0.619	0.868	0.713	16	0.613	0.640	0.958	16	0.380	0.555	0.683	15
	Pess	1.153	1.135	1.016	18	39.52	21.06	1.876	17	45.60	23.91	1.907	18
	DF	0.845	0.992	0.851	17	4.925	3.672	1.341	16	4.163	3.646	1.141	13
18	Opt	0.360	0.629	0.572	20	0.159	0.167	0.947	19	0.057	0.105	0.541	17
	Pess	1.000	1.000	1.000	23	8.711	4.929	1.767	19	8.711	4.929	1.767	19
	DF	0.600	0.793	0.756	22	1.176	0.909	1.293	19	0.706	0.722	0.978	19
19	Opt	0.848	1.000	0.848	12	0.132	0.136	0.964	14	0.112	0.136	0.818	10
	Pess	1.000	1.000	1.000	20	9.085	1.857	4.890	7	9.085	1.857	4.890	7
	DF	0.920	1.000	0.920	15	1.095	0.504	2.172	6	1.008	0.504	2.000	8
20	Opt	1.000	1.000	1.000	8	0.012	0.012	0.984	6	0.012	0.012	0.984	5
	Pess	2.240	2.033	1.102	12	1.306	1.000	1.306	22	2.928	2.033	1.440	23
	DF	1.497	1.426	1.049	4	0.129	0.113	1.134	22	0.193	0.162	1.190	11
21	Opt	0.298	0.981	0.304	28	0.015	1.000	0.015	30	0.004	0.981	0.004	30
	Pess	1.000	1.000	1.000	29	1.000	1.000	1.000	30	1.000	1.000	1.000	30
	DF	0.546	0.990	0.551	28	0.126	1.000	0.126	30	0.069	0.990	0.069	30
22	Opt	1.000	1.000	1.000	6	0.196	0.199	0.982	9	0.196	0.199	0.982	6
	Pess	1.535	1.372	1.118	11	16.23	14.84	1.093	28	24.92	20.38	1.222	28
	DF	1.239	1.171	1.057	3	1.785	1.722	1.036	27	2.212	2.018	1.096	16
23	Opt	0.771	0.958	0.805	14	0.161	0.165	0.973	12	0.124	0.158	0.784	12
	Pess	1.832	1.664	1.100	14	12.24	5.656	2.164	13	22.43	9.414	2.383	15
	DF	1.189	1.263	0.941	13	1.404	0.967	1.451	12	1.670	1.221	1.366	10
24	Opt	0.815	1.000	0.815	13	0.059	0.060	0.983	8	0.048	0.060	0.801	11
	Pess	1.597	1.197	1.333	3	4.875	4.323	1.127	26	7.786	5.177	1.503	21
	DF	1.140	1.094	1.042	5	0.538	0.511	1.053	24	0.614	0.559	1.097	15
25	Opt	0.319	0.640	0.499	24	0.239	0.249	0.962	15	0.076	0.159	0.480	23
	Pess	1.101	1.000	1.101	13	14.44	12.70	1.137	25	15.90	12.70	1.252	26
	DF	0.593	0.800	0.741	24	1.860	1.778	1.046	26	1.103	1.423	0.775	26
26	Opt	0.589	0.590	0.998	9	0.642	0.652	0.985	4	0.378	0.384	0.984	3
	Pess	1.000	1.000	1.000	27	59.28	13.62	4.352	8	59.28	13.62	4.352	8
	DF	0.767	0.768	0.999	11	6.173	2.980	2.071	8	4.739	2.289	2.070	7
27	Opt	0.391	0.646	0.606	19	0.551	0.565	0.975	11	0.216	0.365	0.591	16
	Pess	1.085	1.000	1.085	15	38.60	34.25	1.127	27	41.92	34.25	1.224	27
	DF	0.652	0.804	0.811	20	4.613	4.399	1.048	25	3.009	3.537	0.850	25
28	Opt	1.000	1.000	1.000	1	0.535	1.000	0.535	27	0.535	1.000	0.535	18
	Pess	1.000	1.000	1.000	19	42.81	1.000	42.81	2	42.81	1.000	42.81	2
	DF	1.000	1.000	1.000	8	4.789	1.000	4.789	2	4.789	1.000	4.789	2
29	Opt	0.712	1.000	0.712	17	0.034	0.035	0.990	2	0.024	0.035	0.705	14
	Pess	1.695	1.695	1.000	24	2.325	2.217	1.048	29	3.944	3.760	1.048	29
	DF	1.099	1.302	0.843	18	0.284	0.279	1.019	28	0.313	0.364	0.860	24
30	Opt	0.633	0.956	0.662	18	0.014	0.029	0.491	29	0.009	0.027	0.325	26
	Pess	1.217	1.000	1.217	7	1.146	1.000	1.146	24	1.395	1.000	1.395	24
	DF	0.878	0.978	0.898	16	0.127	0.170	0.750	29	0.112	0.166	0.674	28
	Opt	0.636	0.894	0.709		0.226	0.286	0.878		0.152	0.248	0.636
	Pess	1.248	1.123	1.111		19.51	6.406	9.787		21.53	6.965	10.14
	DF	0.869	0.996	0.867		2.049	1.131	1.938		1.792	1.041	1.789

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		Profitability stage				Marketability stage				R&D value chain
No	Model	CCR	BCC	SE	R	CCR	BCC	SE	R	CCR	BCC	SE	R
1	Opt	1.000	1.000	1.000	7	1.000	1.000	1.000	1	1.000	1.000	1.000	1
	Pess	1.000	1.000	1.000	26	176.7	1.000	176.7	1	176.7	1.000	176.7	1
	DF	1.000	1.000	1.000	10	13.29	1.000	13.29	1	13.29	1.000	13.29	1
2	Opt	0.547	0.620	0.883	11	0.403	0.412	0.976	10	0.220	0.256	0.862	9
	Pess	1.000	1.000	1.000	28	32.14	20.82	1.544	20	32.14	20.82	1.544	20
	DF	0.739	0.787	0.939	14	3.600	2.932	1.227	20	2.663	2.308	1.153	12
3	Opt	0.221	0.946	0.234	29	0.076	0.086	0.875	24	0.016	0.082	0.205	28
	Pess	1.181	1.000	1.181	8	2.335	1.000	2.335	12	2.758	1.000	2.758	13
	DF	0.511	0.972	0.526	29	0.421	0.294	1.430	13	0.215	0.286	0.752	27
4	Opt	0.400	0.711	0.562	21	0.185	0.195	0.950	18	0.074	0.139	0.534	19
	Pess	1.000	1.000	1.000	22	10.31	6.918	1.491	21	10.31	6.918	1.491	22
	DF	0.632	0.843	0.750	23	1.385	1.163	1.190	21	0.876	0.981	0.893	23
5	Opt	0.165	0.924	0.178	30	0.141	0.174	0.809	26	0.023	0.161	0.144	29
	Pess	1.000	1.000	1.000	21	2.721	1.000	2.721	11	2.721	1.000	2.721	14
	DF	0.406	0.961	0.422	30	0.620	0.417	1.484	11	0.252	0.401	0.627	29
6	Opt	0.422	0.781	0.540	22	0.275	0.293	0.939	20	0.116	0.229	0.508	21
	Pess	1.239	1.000	1.239	6	13.95	7.438	1.876	18	17.29	7.438	2.325	16
	DF	0.723	0.883	0.818	19	1.960	1.476	1.327	18	1.418	1.305	1.087	17
7	Opt	0.362	1.000	0.362	26	0.120	0.133	0.907	23	0.043	0.133	0.329	25
	Pess	1.441	1.000	1.441	1	4.535	2.328	1.948	15	6.539	2.328	2.808	11
	DF	0.723	1.000	0.723	26	0.740	0.556	1.329	17	0.535	0.556	0.961	21
8	Opt	0.533	0.584	0.912	10	0.217	0.221	0.983	7	0.116	0.129	0.897	8
	Pess	1.134	1.000	1.134	10	19.62	16.54	1.186	23	22.26	16.54	1.345	25
	DF	0.778	0.764	1.017	7	2.068	1.914	1.080	23	1.609	1.464	1.099	14
9	Opt	1.000	1.000	1.000	4	0.370	0.376	0.984	5	0.370	0.376	0.984	4
	Pess	1.082	1.000	1.082	16	33.52	6.038	5.552	5	36.28	6.038	6.009	5
	DF	1.040	1.000	1.040	6	3.526	1.508	2.338	4	3.668	1.508	2.432	4
10	Opt	1.000	1.000	1.000	2	0.090	0.173	0.522	28	0.090	0.173	0.522	20
	Pess	1.349	1.000	1.349	2	8.236	1.000	8.236	3	11.11	1.000	11.11	3
	DF	1.161	1.000	1.161	1	0.862	0.416	2.073	7	1.002	0.416	2.408	5
11	Opt	1.000	1.000	1.000	3	0.040	0.041	0.973	13	0.040	0.041	0.973	7
	Pess	1.000	1.000	1.000	30	2.919	1.000	2.919	9	2.919	1.000	2.919	10
	DF	1.000	1.000	1.000	9	0.343	0.203	1.685	9	0.343	0.203	1.685	9
12	Opt	1.000	1.000	1.000	5	0.083	0.084	0.986	3	0.083	0.084	0.986	2
	Pess	1.657	1.280	1.294	4	8.224	1.000	8.224	4	13.63	1.280	10.65	4
	DF	1.287	1.131	1.138	2	0.828	0.290	2.848	3	1.066	0.329	3.241	3
13	Opt	0.523	1.000	0.523	23	0.072	0.077	0.932	21	0.037	0.077	0.488	22
	Pess	1.000	1.000	1.000	25	3.542	1.823	1.942	16	3.542	1.823	1.942	17
	DF	0.723	1.000	0.723	25	0.506	0.376	1.346	15	0.366	0.376	0.974	20
14	Opt	0.321	1.000	0.321	27	0.231	0.266	0.870	25	0.074	0.266	0.279	27
	Pess	1.433	1.327	1.080	17	7.806	2.815	2.773	10	11.19	3.737	2.994	9
	DF	0.679	1.152	0.589	27	1.344	0.865	1.553	10	0.912	0.997	0.915	22
15	Opt	0.764	1.000	0.764	15	0.076	0.0803	0.958	17	0.058	0.080	0.732	13
	Pess	1.178	1.000	1.178	9	5.093	1.000	5.093	6	6.004	1.000	6.004	6
	DF	0.949	1.000	0.949	12	0.626	0.283	2.208	5	0.594	0.283	2.096	6
16	Opt	0.458	1.000	0.458	25	0.047	0.051	0.920	22	0.021	0.051	0.421	24
	Pess	1.294	1.000	1.294	5	2.159	1.000	2.159	14	2.794	1.000	2.794	12
	DF	0.770	1.000	0.770	21	0.320	0.227	1.410	14	0.246	0.227	1.085	18
17	Opt	0.619	0.868	0.713	16	0.613	0.640	0.958	16	0.380	0.555	0.683	15
	Pess	1.153	1.135	1.016	18	39.52	21.06	1.876	17	45.60	23.91	1.907	18
	DF	0.845	0.992	0.851	17	4.925	3.672	1.341	16	4.163	3.646	1.141	13
18	Opt	0.360	0.629	0.572	20	0.159	0.167	0.947	19	0.057	0.105	0.541	17
	Pess	1.000	1.000	1.000	23	8.711	4.929	1.767	19	8.711	4.929	1.767	19
	DF	0.600	0.793	0.756	22	1.176	0.909	1.293	19	0.706	0.722	0.978	19
19	Opt	0.848	1.000	0.848	12	0.132	0.136	0.964	14	0.112	0.136	0.818	10
	Pess	1.000	1.000	1.000	20	9.085	1.857	4.890	7	9.085	1.857	4.890	7
	DF	0.920	1.000	0.920	15	1.095	0.504	2.172	6	1.008	0.504	2.000	8
20	Opt	1.000	1.000	1.000	8	0.012	0.012	0.984	6	0.012	0.012	0.984	5
	Pess	2.240	2.033	1.102	12	1.306	1.000	1.306	22	2.928	2.033	1.440	23
	DF	1.497	1.426	1.049	4	0.129	0.113	1.134	22	0.193	0.162	1.190	11
21	Opt	0.298	0.981	0.304	28	0.015	1.000	0.015	30	0.004	0.981	0.004	30
	Pess	1.000	1.000	1.000	29	1.000	1.000	1.000	30	1.000	1.000	1.000	30
	DF	0.546	0.990	0.551	28	0.126	1.000	0.126	30	0.069	0.990	0.069	30
22	Opt	1.000	1.000	1.000	6	0.196	0.199	0.982	9	0.196	0.199	0.982	6
	Pess	1.535	1.372	1.118	11	16.23	14.84	1.093	28	24.92	20.38	1.222	28
	DF	1.239	1.171	1.057	3	1.785	1.722	1.036	27	2.212	2.018	1.096	16
23	Opt	0.771	0.958	0.805	14	0.161	0.165	0.973	12	0.124	0.158	0.784	12
	Pess	1.832	1.664	1.100	14	12.24	5.656	2.164	13	22.43	9.414	2.383	15
	DF	1.189	1.263	0.941	13	1.404	0.967	1.451	12	1.670	1.221	1.366	10
24	Opt	0.815	1.000	0.815	13	0.059	0.060	0.983	8	0.048	0.060	0.801	11
	Pess	1.597	1.197	1.333	3	4.875	4.323	1.127	26	7.786	5.177	1.503	21
	DF	1.140	1.094	1.042	5	0.538	0.511	1.053	24	0.614	0.559	1.097	15
25	Opt	0.319	0.640	0.499	24	0.239	0.249	0.962	15	0.076	0.159	0.480	23
	Pess	1.101	1.000	1.101	13	14.44	12.70	1.137	25	15.90	12.70	1.252	26
	DF	0.593	0.800	0.741	24	1.860	1.778	1.046	26	1.103	1.423	0.775	26
26	Opt	0.589	0.590	0.998	9	0.642	0.652	0.985	4	0.378	0.384	0.984	3
	Pess	1.000	1.000	1.000	27	59.28	13.62	4.352	8	59.28	13.62	4.352	8
	DF	0.767	0.768	0.999	11	6.173	2.980	2.071	8	4.739	2.289	2.070	7
27	Opt	0.391	0.646	0.606	19	0.551	0.565	0.975	11	0.216	0.365	0.591	16
	Pess	1.085	1.000	1.085	15	38.60	34.25	1.127	27	41.92	34.25	1.224	27
	DF	0.652	0.804	0.811	20	4.613	4.399	1.048	25	3.009	3.537	0.850	25
28	Opt	1.000	1.000	1.000	1	0.535	1.000	0.535	27	0.535	1.000	0.535	18
	Pess	1.000	1.000	1.000	19	42.81	1.000	42.81	2	42.81	1.000	42.81	2
	DF	1.000	1.000	1.000	8	4.789	1.000	4.789	2	4.789	1.000	4.789	2
29	Opt	0.712	1.000	0.712	17	0.034	0.035	0.990	2	0.024	0.035	0.705	14
	Pess	1.695	1.695	1.000	24	2.325	2.217	1.048	29	3.944	3.760	1.048	29
	DF	1.099	1.302	0.843	18	0.284	0.279	1.019	28	0.313	0.364	0.860	24
30	Opt	0.633	0.956	0.662	18	0.014	0.029	0.491	29	0.009	0.027	0.325	26
	Pess	1.217	1.000	1.217	7	1.146	1.000	1.146	24	1.395	1.000	1.395	24
	DF	0.878	0.978	0.898	16	0.127	0.170	0.750	29	0.112	0.166	0.674	28
	Opt	0.636	0.894	0.709		0.226	0.286	0.878		0.152	0.248	0.636
	Pess	1.248	1.123	1.111		19.51	6.406	9.787		21.53	6.965	10.14
	DF	0.869	0.996	0.867		2.049	1.131	1.938		1.792	1.041	1.789

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2019 Impact Factor: 1.366

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2019 Impact Factor: 1.366

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2019 Impact Factor: 1.366

American Institute of Mathematical Sciences

Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach

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American Institute of Mathematical Sciences

Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach

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