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Scale efficiency of China's regional R & D value chain: A double frontier network DEA approach
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 |
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.
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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[50] |
V. Zelenyuk,
Aggregation of scale efficiency, European Journal of Operational Research, 240 (2015), 269-277.
doi: 10.1016/j.ejor.2014.06.038. |
[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. |
[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. |
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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[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. |
[49] |
Z. G. Xin and W. Zhen,
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DMU | Inputs | Output | |
A | 40 | 7 | 210 |
B | 32 | 12 | 105 |
C | 52 | 20 | 304 |
D | 35 | 13 | 200 |
E | 32 | 8 | 150 |
DMU | Inputs | Output | |
A | 40 | 7 | 210 |
B | 32 | 12 | 105 |
C | 52 | 20 | 304 |
D | 35 | 13 | 200 |
E | 32 | 8 | 150 |
DMU | Optimistic perspective | Pessimistic perspective | Double frontier | |||||||||
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 |
DMU | Optimistic perspective | Pessimistic perspective | Double frontier | |||||||||
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 |
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 |
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 |
Region | |||||||||
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 |
|
Region | |||||||||
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 |
|
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 |
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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