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March  2022, 18(2): 1425-1437. doi: 10.3934/jimo.2021026

CCR model-based evaluation on the effectiveness and maturity of technological innovation

Liling Lin 1,, and  Linfeng Zhao 2,,

1. 

The Department of Finance, School of Business, China University of Political Science and Law, Beijing, 100088, China
2. 

The Physics Department, School of Arts and Sciences, Boston University, Boston, MA 02215, USA

* Corresponding author: Liling Lin and Linfeng Zhao

Received  June 2020 Revised  December 2020 Published  March 2022 Early access  February 2021

As there are many indexes for evaluating technological innovation in enterprises, it is hard to quantify all those indexes. Therefore, common evaluation methods cannot be applied to solve the absolute value of the evaluation indexes. Therefore, this study used the nonparametric CCR model based on input-output to estimate the relative value of evaluation index, and took dual programming tool to obtain the judgment basis for the most effective and optimal solution. Based on the software evaluation criteria, this paper proposed the concept of "maturity in technological innovation, " its four levels, and an evaluation standard for maturity. Based on the homogeneity, the paper selected four Beijing enterprises as evaluation samples. After comparing and analyzing the efficiency, scale return, production surface projection and maturity, we found that the evaluation results conform to the reality of sampling enterprises. CCR model was used to evaluate decision-making units with multiple inputs and outputs. The results show that this method can help accurately obtain the relative order and the enterprises' ability to make technological innovation. Thus, CCR model is able to help enterprises formulate policies on technological innovation.

Keywords: Technological innovation, DEA model, CCR model, maturity, evaluation.
Mathematics Subject Classification: Primary 91B06, 91B38; Secondary 90B50, 90B30.
Citation: Liling Lin, Linfeng Zhao. CCR model-based evaluation on the effectiveness and maturity of technological innovation. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1425-1437. doi: 10.3934/jimo.2021026
References:
[1]

F. T. Akyildiz and K. Vajravelu, Galerkin-chebyshev pseudo spectral method and a split step new approach for a class of two dimensional semi-linear parabolic equations of second order, Applied Mathematics and Nonlinear Sciences, 3 (2018), 255-264.  doi: 10.21042/AMNS.2018.1.00019.

[2]

E. Bohlool and T. Mehdi, Efficiency bounds and efficiency classifications in imprecise DEA: An extension, Journal of the Operational Research Society, 7 (2019), 30-35. 

[3]

M. Idi and B. M. Aliyu, Cyber security capability maturity model for network system, International Journal of Development Research, 6 (2019), 37-41. 

[4]

X. Liu, C-W. Ni and L-Y. Zhang, Durability assessment of lightweight cellular concrete in sub-grade by the method of analytic hierarchy process combined with fuzzy comprehensive evaluation, Mathematical Problems in Engineering, 2019 (2019), 1-10. 

[5]

J-C. Lu and G- W Han, Osculating value method of business technology innovation capacity evaluation, Science Research Management, 1 (2002), 54-57. 

[6]

T. Madjid, K-D. Kaveh, S. A. J. Francisco and H. Amineh, A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries, Computers and Industrial Engineering, 9 (2019), 143-155. 

[7]

R. T. Md, N. Rasmus and K. A. Md, Efficiency and production environmental heterogeneity in aquaculture: A meta-frontier DEA approach, Aquaculture, 6 (2019), 140-148. 

[8]

L. Nils and S. Alexander, Modeling time-dependent randomness in stochastic dual dynamic programming, European Journal of Operational Research, 2 (2019), 650-661. 

[9]

L. L. Pan and L. X. Sun, Modeling time-dependent randomness in stochastic dual dynamic programming, Science and Technology Management Research, 7 (2019), 32-37. 

[10]

C. Rojas and J. Belmonte-Beitia, Optimal control problems for differential equations applied to tumor growth: State of the art, Applied Mathematicsand Nonlinear Sciences, 3 (2018), 375-402.  doi: 10.21042/AMNS.2018.2.00029.

[11]

Y-Z. Tang and S-G. Zhou, Grey synthetic evaluation of enterprise' technological innovation capacity, Science and Technology Progress and Policy, 5 (1999), 46-81. 

[12]

A. Yokus and Gülbahar, Numerical solutions with linearization techniques of the fractional harry dym equation, Applied Mathematicsand Nonlinear Sciences, 4 (2018), 35-42.  doi: 10.2478/AMNS.2019.1.00004.

[13]

L-F. Zhao, X. Zhou, Y. Du and L-D. Tan, DEA comprehensive evaluation on enterprise's technology innovation capacity, China Science Forum, 6 (2007), 49-52. 

[14]

Y-P. Zhou, Neural network experience analysis on enterprise technological innovation ability, Science and Technology Progress and Policy, 17 (2000), 62-63. 

show all references

References:
[1]

F. T. Akyildiz and K. Vajravelu, Galerkin-chebyshev pseudo spectral method and a split step new approach for a class of two dimensional semi-linear parabolic equations of second order, Applied Mathematics and Nonlinear Sciences, 3 (2018), 255-264.  doi: 10.21042/AMNS.2018.1.00019.

[2]

E. Bohlool and T. Mehdi, Efficiency bounds and efficiency classifications in imprecise DEA: An extension, Journal of the Operational Research Society, 7 (2019), 30-35. 

[3]

M. Idi and B. M. Aliyu, Cyber security capability maturity model for network system, International Journal of Development Research, 6 (2019), 37-41. 

[4]

X. Liu, C-W. Ni and L-Y. Zhang, Durability assessment of lightweight cellular concrete in sub-grade by the method of analytic hierarchy process combined with fuzzy comprehensive evaluation, Mathematical Problems in Engineering, 2019 (2019), 1-10. 

[5]

J-C. Lu and G- W Han, Osculating value method of business technology innovation capacity evaluation, Science Research Management, 1 (2002), 54-57. 

[6]

T. Madjid, K-D. Kaveh, S. A. J. Francisco and H. Amineh, A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries, Computers and Industrial Engineering, 9 (2019), 143-155. 

[7]

R. T. Md, N. Rasmus and K. A. Md, Efficiency and production environmental heterogeneity in aquaculture: A meta-frontier DEA approach, Aquaculture, 6 (2019), 140-148. 

[8]

L. Nils and S. Alexander, Modeling time-dependent randomness in stochastic dual dynamic programming, European Journal of Operational Research, 2 (2019), 650-661. 

[9]

L. L. Pan and L. X. Sun, Modeling time-dependent randomness in stochastic dual dynamic programming, Science and Technology Management Research, 7 (2019), 32-37. 

[10]

C. Rojas and J. Belmonte-Beitia, Optimal control problems for differential equations applied to tumor growth: State of the art, Applied Mathematicsand Nonlinear Sciences, 3 (2018), 375-402.  doi: 10.21042/AMNS.2018.2.00029.

[11]

Y-Z. Tang and S-G. Zhou, Grey synthetic evaluation of enterprise' technological innovation capacity, Science and Technology Progress and Policy, 5 (1999), 46-81. 

[12]

A. Yokus and Gülbahar, Numerical solutions with linearization techniques of the fractional harry dym equation, Applied Mathematicsand Nonlinear Sciences, 4 (2018), 35-42.  doi: 10.2478/AMNS.2019.1.00004.

[13]

L-F. Zhao, X. Zhou, Y. Du and L-D. Tan, DEA comprehensive evaluation on enterprise's technology innovation capacity, China Science Forum, 6 (2007), 49-52. 

[14]

Y-P. Zhou, Neural network experience analysis on enterprise technological innovation ability, Science and Technology Progress and Policy, 17 (2000), 62-63. 

Table 1.  Input and output of evaluation departments
No. Weight Decision-making unit
1 2 ... j ... n
Input data 1 $ v_{1} $ $ x_{11} $ $ x_{12} $ ... $ x_{1j} $ ... $ x_{1n} $
2 $ v_{2} $ $ x_{21} $ $ x_{22} $ ... $ x_{2j} $ ... $ x_{2n} $
... ... ... ...
$ m $ $ v_{m} $ $ x_{m1} $ $ x_{m2} $ ... $ x_{mj} $ ... $ x_{mn} $
Output data 1 $ u_{1} $ $ y_{11} $ $ y_{12} $ ... $ y_{1j} $ ... $ y_{1n} $
2 $ u_{2} $ $ y_{21} $ $ y_{22} $ ... $ y_{2j} $ ... $ y_{2n} $
... ... ... ...
$ s $ $ u_{s} $ $ y_{s1} $ $ y_{s2} $ ... $ y_{sj} $ ... $ y_{sn} $
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No. Weight Decision-making unit
1 2 ... j ... n
Input data 1 $ v_{1} $ $ x_{11} $ $ x_{12} $ ... $ x_{1j} $ ... $ x_{1n} $
2 $ v_{2} $ $ x_{21} $ $ x_{22} $ ... $ x_{2j} $ ... $ x_{2n} $
... ... ... ...
$ m $ $ v_{m} $ $ x_{m1} $ $ x_{m2} $ ... $ x_{mj} $ ... $ x_{mn} $
Output data 1 $ u_{1} $ $ y_{11} $ $ y_{12} $ ... $ y_{1j} $ ... $ y_{1n} $
2 $ u_{2} $ $ y_{21} $ $ y_{22} $ ... $ y_{2j} $ ... $ y_{2n} $
... ... ... ...
$ s $ $ u_{s} $ $ y_{s1} $ $ y_{s2} $ ... $ y_{sj} $ ... $ y_{sn} $
Table 2.  Data of sample enterprises
Enter-prises Years R & D funds/product sales revenue (A13) (%)x1 Number of full-time R&D personnel /number of employees (A22) (%)x2 Technology introduction and transformation cost/ product sales revenue (A31) (%)x3 Annual per capita income of R&D personnel /annual per capita income of enterprises (B21) X4 Innovation strategy (B11) X5 Technical level (C11) x6 Number of patents and proprietary technology (C41) x7 Equipment level (D11) x8 Marketing costs for new products /new product sales revenue (E32) (%) x9 Number of full -time sales personnel/ number of employees (E42) x10 New product sales revenue /total product sales revenue (F12) (%) Y1
Enterprise I 01 3.14 13.85 5.38 1.01 75 1 15 0.8 3.81 0.24 24.94
02 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
03 3.65 15.98 6.43 1.11 80 1 15 0.8 6.34 0.26 35.51
04 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
05 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
Enterprise II 01 3.47 14.33 19.69 1.21 70 0.4 9 0.6 20 0.19 7.3
02 4.24 14.51 26.63 1.32 70 0.4 9 0.6 27.91 0.2 8.12
03 4.55 14.63 35.06 1.05 70 0.4 9 0.6 34.12 0.22 11.17
04 3.37 15.66 4.84 1.12 70 0.4 10 0.6 32.12 0.22 13.36
05 3.13 16.05 3.2 1.19 70 0.6 10 0.6 29.66 0.22 13
Enterprise III 01 9.1 7.11 3.17 1.51 80 0.6 6 0.4 13.55 0.1 2.16
02 10.94 7.23 4.66 1.62 80 0.6 6 0.4 14.21 0.1 2.22
03 29.66 7.39 2.65 1.68 80 0.6 6 0.4 15.33 0.1 3.27
04 20.91 7.43 3.05 1.65 80 0.6 6 0.4 17.17 0.1 4.68
05 15.66 7.51 0.74 1.69 80 0.6 6 0.4 15.61 0.1 4.95
Enterprise III 01 2.96 22 21.45 1.22 70 0.4 5 0.4 13.23 0.3 8.085
02 3.36 25 0.48 1.52 70 0.4 5 0.4 8.07 0.3 10.01
03 3.52 21 0.76 1.4 75 0.4 5 0.4 7.13 0.3 15.575
04 4.36 29 3.35 1.29 80 0.4 5 0.4 3.9 0.3 22.14
05 7.47 27 2.35 1.06 80 0.4 5 0.4 2.38 0.3 25.69
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Enter-prises Years R & D funds/product sales revenue (A13) (%)x1 Number of full-time R&D personnel /number of employees (A22) (%)x2 Technology introduction and transformation cost/ product sales revenue (A31) (%)x3 Annual per capita income of R&D personnel /annual per capita income of enterprises (B21) X4 Innovation strategy (B11) X5 Technical level (C11) x6 Number of patents and proprietary technology (C41) x7 Equipment level (D11) x8 Marketing costs for new products /new product sales revenue (E32) (%) x9 Number of full -time sales personnel/ number of employees (E42) x10 New product sales revenue /total product sales revenue (F12) (%) Y1
Enterprise I 01 3.14 13.85 5.38 1.01 75 1 15 0.8 3.81 0.24 24.94
02 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
03 3.65 15.98 6.43 1.11 80 1 15 0.8 6.34 0.26 35.51
04 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
05 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
Enterprise II 01 3.47 14.33 19.69 1.21 70 0.4 9 0.6 20 0.19 7.3
02 4.24 14.51 26.63 1.32 70 0.4 9 0.6 27.91 0.2 8.12
03 4.55 14.63 35.06 1.05 70 0.4 9 0.6 34.12 0.22 11.17
04 3.37 15.66 4.84 1.12 70 0.4 10 0.6 32.12 0.22 13.36
05 3.13 16.05 3.2 1.19 70 0.6 10 0.6 29.66 0.22 13
Enterprise III 01 9.1 7.11 3.17 1.51 80 0.6 6 0.4 13.55 0.1 2.16
02 10.94 7.23 4.66 1.62 80 0.6 6 0.4 14.21 0.1 2.22
03 29.66 7.39 2.65 1.68 80 0.6 6 0.4 15.33 0.1 3.27
04 20.91 7.43 3.05 1.65 80 0.6 6 0.4 17.17 0.1 4.68
05 15.66 7.51 0.74 1.69 80 0.6 6 0.4 15.61 0.1 4.95
Enterprise III 01 2.96 22 21.45 1.22 70 0.4 5 0.4 13.23 0.3 8.085
02 3.36 25 0.48 1.52 70 0.4 5 0.4 8.07 0.3 10.01
03 3.52 21 0.76 1.4 75 0.4 5 0.4 7.13 0.3 15.575
04 4.36 29 3.35 1.29 80 0.4 5 0.4 3.9 0.3 22.14
05 7.47 27 2.35 1.06 80 0.4 5 0.4 2.38 0.3 25.69
Table 3.  Definition of input and output indicators
Types Names Code Definition Unit
Enterprise III X1 A13 R & D funds / product sales revenue %
X2 A22 Number of full-time R & D personnel / number of employees %
X3 A31 Technology introduction and transformation cost / product sales revenue %
X4 B21 Annual per capita income of R & D personnel/ annual per capita income of enterprises %
X5 B11 Innovation strategy Point
X6 C11 Technical level= 1 × international level + 0.6 × domestic level + 0.3 × enterprise level
X7 C41 Number of patents and proprietary technology Piece
X8 D11 Equipment level = 1 × international advanced level (%) + 0.8 × international general level (%) + 0.6 × domestic advanced level (%) + 0.4 × domestic general level (%) + 0.2 × others
X9 E32 Marketing costs for new products/new product sales revenue %
X10 E42 Number of full-time sales personnel/ number of employees
Output variable Y1 F12 New product sales revenue/total product sales revenue %
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Types Names Code Definition Unit
Enterprise III X1 A13 R & D funds / product sales revenue %
X2 A22 Number of full-time R & D personnel / number of employees %
X3 A31 Technology introduction and transformation cost / product sales revenue %
X4 B21 Annual per capita income of R & D personnel/ annual per capita income of enterprises %
X5 B11 Innovation strategy Point
X6 C11 Technical level= 1 × international level + 0.6 × domestic level + 0.3 × enterprise level
X7 C41 Number of patents and proprietary technology Piece
X8 D11 Equipment level = 1 × international advanced level (%) + 0.8 × international general level (%) + 0.6 × domestic advanced level (%) + 0.4 × domestic general level (%) + 0.2 × others
X9 E32 Marketing costs for new products/new product sales revenue %
X10 E42 Number of full-time sales personnel/ number of employees
Output variable Y1 F12 New product sales revenue/total product sales revenue %
Table 4.  Optimal solution and relaxation variables
Enterprises Year $ \theta $ $ S1^{-} $ $ S2^{-} $ $ S3^{-} $ $ S4^{-} $ $ S5^{-} $ $ S6^{-} $ $ S7^{-} $ $ S8^{-} $ $ S9^{-} $ $ S10^{-} $ $ S1^{+} $
Enterprise 1 01 0.8696334 0 1.06315 2.51657 0.16280 7.44845 0.17362 2.60427 0.13889 0 0.02634 0
02 1.000000 0 0 0 0 0 0 0 0 0 0 0
03 0.9852941 0.27588 1.64544 2.55191 0.09853 0 0 0 0 0.85721 0.00985 0
04 1.000000 0 0 0 0 0 0 0 0 0 0 0
05 1.000000 0 0 0 0 0 0 0 0 0 0 0
Enterprise 2 01 0.3938900 0 0 6.98602 0.20658 7.49104 0 1.33744 0.09783 6.92850 0.00430 0
02 0.4257631 0.15493 0 10.54098 0.27466 7.73962 0 1.45311 0.10515 10.91772 0.00741 0
03 0.5837402 0.37323 0 19.37040 0.21680 10.45333 0 1.99557 0.14390 18.59308 0.02118 0
04 0.7169654 0 0 1.94594 0.26629 11.90772 0 3.18738 0.17519 21.15136 0.02213 0
05 0.5354496 0 0 0.18736 0.16405 3.44490 0 0.70910 0.05036 13.86115 0.00275 0
Enterprise 3 01 0.1498335 1.16151 0.20767 0.24483 0.16572 7.19201 0.02997 0 0.01199 1.70241 0 0
02 0.1539956 1.47713 0.23192 0.48108 0.18726 7.39179 0.03080 0 0.01232 1.85134 0 0
03 0.2268313 6.42205 0.37790 0.25269 0.28944 10.88790 0.04537 0 0.01815 2.98102 0 0
04 0.3246393 6.35059 0.55383 0.49150 0.40450 15.58269 0.06493 0 0.02597 4.86375 0 0
05 0.3677099 5.12719 0.46604 0 0.47199 17.78455 0.08123 0.11527 0.03556 5.09078 0 0
Enterprise 4 01 0.4552423 0 1.58449 8.64749 0.15586 5.94956 0.01313 0 0.02625 4.65633 0.04266 0
02 0.7785724 0.89338 11.53132 0 0.66614 21.97158 0.03695 0 0.07390 3.89102 0.11639 0
03 1.000000 0 0 0 0 0 0 0 0 0 0 0
04 1.000000 0 0 0 0 0 0 0 0 0 0 0
05 1.000000 0 0 0 0 0 0 0 0 0 0 0
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Enterprises Year $ \theta $ $ S1^{-} $ $ S2^{-} $ $ S3^{-} $ $ S4^{-} $ $ S5^{-} $ $ S6^{-} $ $ S7^{-} $ $ S8^{-} $ $ S9^{-} $ $ S10^{-} $ $ S1^{+} $
Enterprise 1 01 0.8696334 0 1.06315 2.51657 0.16280 7.44845 0.17362 2.60427 0.13889 0 0.02634 0
02 1.000000 0 0 0 0 0 0 0 0 0 0 0
03 0.9852941 0.27588 1.64544 2.55191 0.09853 0 0 0 0 0.85721 0.00985 0
04 1.000000 0 0 0 0 0 0 0 0 0 0 0
05 1.000000 0 0 0 0 0 0 0 0 0 0 0
Enterprise 2 01 0.3938900 0 0 6.98602 0.20658 7.49104 0 1.33744 0.09783 6.92850 0.00430 0
02 0.4257631 0.15493 0 10.54098 0.27466 7.73962 0 1.45311 0.10515 10.91772 0.00741 0
03 0.5837402 0.37323 0 19.37040 0.21680 10.45333 0 1.99557 0.14390 18.59308 0.02118 0
04 0.7169654 0 0 1.94594 0.26629 11.90772 0 3.18738 0.17519 21.15136 0.02213 0
05 0.5354496 0 0 0.18736 0.16405 3.44490 0 0.70910 0.05036 13.86115 0.00275 0
Enterprise 3 01 0.1498335 1.16151 0.20767 0.24483 0.16572 7.19201 0.02997 0 0.01199 1.70241 0 0
02 0.1539956 1.47713 0.23192 0.48108 0.18726 7.39179 0.03080 0 0.01232 1.85134 0 0
03 0.2268313 6.42205 0.37790 0.25269 0.28944 10.88790 0.04537 0 0.01815 2.98102 0 0
04 0.3246393 6.35059 0.55383 0.49150 0.40450 15.58269 0.06493 0 0.02597 4.86375 0 0
05 0.3677099 5.12719 0.46604 0 0.47199 17.78455 0.08123 0.11527 0.03556 5.09078 0 0
Enterprise 4 01 0.4552423 0 1.58449 8.64749 0.15586 5.94956 0.01313 0 0.02625 4.65633 0.04266 0
02 0.7785724 0.89338 11.53132 0 0.66614 21.97158 0.03695 0 0.07390 3.89102 0.11639 0
03 1.000000 0 0 0 0 0 0 0 0 0 0 0
04 1.000000 0 0 0 0 0 0 0 0 0 0 0
05 1.000000 0 0 0 0 0 0 0 0 0 0 0
Table 5.  Maturity of technological innovation of sample enterprises
Enterprises Year DEA optimal solution Technological innovation maturity
Enterprise 1 2014 0.8696334 Less maturity
2015 1.000000 Full maturity
2016 0.9852941 Less maturity
2017 1.000000 Full maturity
2018 1.000000 Full maturity
Enterprise 2 2014 0.39389 Immaturity
2015 0.425763 Immaturity
2016 0.58374 Less maturity
2017 0.716965 Less maturity
2018 0.53545 Less maturity
Enterprise 3 2014 0.149834 Immaturity
2015 0.153996 Immaturity
2016 0.226831 Immaturity
2017 0.324639 Immaturity
2018 0.36771 Immaturity
Enterprise 4 2014 0.455242 Immaturity
2015 0.778572 Less maturity
2016 1.000000 Full maturity
2017 1.000000 Full maturity
2018 1.000000 Full maturity
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Enterprises Year DEA optimal solution Technological innovation maturity
Enterprise 1 2014 0.8696334 Less maturity
2015 1.000000 Full maturity
2016 0.9852941 Less maturity
2017 1.000000 Full maturity
2018 1.000000 Full maturity
Enterprise 2 2014 0.39389 Immaturity
2015 0.425763 Immaturity
2016 0.58374 Less maturity
2017 0.716965 Less maturity
2018 0.53545 Less maturity
Enterprise 3 2014 0.149834 Immaturity
2015 0.153996 Immaturity
2016 0.226831 Immaturity
2017 0.324639 Immaturity
2018 0.36771 Immaturity
Enterprise 4 2014 0.455242 Immaturity
2015 0.778572 Less maturity
2016 1.000000 Full maturity
2017 1.000000 Full maturity
2018 1.000000 Full maturity
Table 6.  Adjustment range of evaluation indexes of enterprise 1
Types Names Definition Change in value (unit) Adjusted values (unit)
Input variables X1 R & D funds/product sales revenue -0.409351124 (%) 2.730648876 (%)
X2 Number of full-time R & D personnel/ number of employees -2.86872741 (%) 10.98127259 (%)
X3 Technology introduction and transformation cost / product sales revenue -3.217942308 (%) 2.162057692 (%)
X4 Annual per capita income of R & D personnel / annual per capita income of enterprises -0.294470266 (%) 0.715529734 (%)
X5 Innovation strategy -17.225945 (Score) 57.774055 (Score)
X6 Technical level -0.3039866 0.6960134
X7 Number of patents and proprietary technology -4.559769 10.440231
X8 Equipment level -0.24318328 0.55681672
X9 Marketing costs for new products / new product sales revenue -0.496696746 (%) 3.313303254 (%)
X10 Number of full-time sales personnel / number of employees -0.057627984 0.182372016
Output variable Y1 New product sales revenue / total product sales revenue 0 (%) 24.94
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Types Names Definition Change in value (unit) Adjusted values (unit)
Input variables X1 R & D funds/product sales revenue -0.409351124 (%) 2.730648876 (%)
X2 Number of full-time R & D personnel/ number of employees -2.86872741 (%) 10.98127259 (%)
X3 Technology introduction and transformation cost / product sales revenue -3.217942308 (%) 2.162057692 (%)
X4 Annual per capita income of R & D personnel / annual per capita income of enterprises -0.294470266 (%) 0.715529734 (%)
X5 Innovation strategy -17.225945 (Score) 57.774055 (Score)
X6 Technical level -0.3039866 0.6960134
X7 Number of patents and proprietary technology -4.559769 10.440231
X8 Equipment level -0.24318328 0.55681672
X9 Marketing costs for new products / new product sales revenue -0.496696746 (%) 3.313303254 (%)
X10 Number of full-time sales personnel / number of employees -0.057627984 0.182372016
Output variable Y1 New product sales revenue / total product sales revenue 0 (%) 24.94
Table 7.  Variable adjustment of enterprise 1
Enterprise Year Value X Y
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 Y1
I 01 S 0 1.06315 2.51657 0.1628 7.44845 0.17362 2.60427 0.13889 0 0.02634 0
T1 3.14 13.85 5.38 1.01 75 1 15 0.8 3.81 0.24 24.94
T2 2.730648876 10.98127259 2.162057692 0.715529734 57.774055 0.6960134 10.440231 0.55681672 3.313303254 0.182372016 24.94
C 0.409351124 2.86872741 3.217942308 0.294470266 17.225945 0.3039866 4.559769 0.24318328 0.496696746 0.057627984 0
02 S 0 0 0 0 0 0 0 0 0 0 0
T1 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
T2 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
C 0 0 0 0 0 0 0 0 0 0 0
03 S 0.27588 1.64544 2.55191 0.09853 0 0 0 0 0.85721 0.00985 0
T1 3.65 15.98 6.43 1.11 80 1 15 0.8 6.34 0.26 35.51
T2 3.320443465 14.09955972 3.783531063 0.995146451 78.823528 0.9852941 14.7794115 0.78823528 5.389554594 0.246326466 35.51
C 0.329556535 1.880440282 2.646468937 0.114853549 1.176472 0.0147059 0.2205885 0.01176472 0.950445406 0.013673534 0
04 S 0 0 0 0 0 0 0 0 0 0 0
T1 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
T2 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
C 0 0 0 0 0 0 0 0 0 0 0
05 S 0 0 0 0 0 0 0 0 0 0 0
T1 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
T2 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
C 0 0 0 0 0 0 0 0 0 0 0
Note: in the table, S represents slack variable; T1 refers to variable value before adjustment; T2 means variable value after adjustment; and C represents difference.
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Enterprise Year Value X Y
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 Y1
I 01 S 0 1.06315 2.51657 0.1628 7.44845 0.17362 2.60427 0.13889 0 0.02634 0
T1 3.14 13.85 5.38 1.01 75 1 15 0.8 3.81 0.24 24.94
T2 2.730648876 10.98127259 2.162057692 0.715529734 57.774055 0.6960134 10.440231 0.55681672 3.313303254 0.182372016 24.94
C 0.409351124 2.86872741 3.217942308 0.294470266 17.225945 0.3039866 4.559769 0.24318328 0.496696746 0.057627984 0
02 S 0 0 0 0 0 0 0 0 0 0 0
T1 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
T2 3.37 14.31 3.84 1.01 80 1 15 0.8 5.47 0.25 36.04
C 0 0 0 0 0 0 0 0 0 0 0
03 S 0.27588 1.64544 2.55191 0.09853 0 0 0 0 0.85721 0.00985 0
T1 3.65 15.98 6.43 1.11 80 1 15 0.8 6.34 0.26 35.51
T2 3.320443465 14.09955972 3.783531063 0.995146451 78.823528 0.9852941 14.7794115 0.78823528 5.389554594 0.246326466 35.51
C 0.329556535 1.880440282 2.646468937 0.114853549 1.176472 0.0147059 0.2205885 0.01176472 0.950445406 0.013673534 0
04 S 0 0 0 0 0 0 0 0 0 0 0
T1 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
T2 5.05 17.44 1.1 1.1 85 1 15 0.8 4.29 0.27 35.27
C 0 0 0 0 0 0 0 0 0 0 0
05 S 0 0 0 0 0 0 0 0 0 0 0
T1 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
T2 5.21 19.19 1.4 1.07 90 1 15 0.8 3.11 0.29 35.35
C 0 0 0 0 0 0 0 0 0 0 0
Note: in the table, S represents slack variable; T1 refers to variable value before adjustment; T2 means variable value after adjustment; and C represents difference.
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