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A new gradient computational formula for optimal control problems with time-delay
CCR model-based evaluation on the effectiveness and maturity of technological innovation
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 |
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.
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. Google Scholar |
[3] |
M. Idi and B. M. Aliyu, Cyber security capability maturity model for network system, International Journal of Development Research, 6 (2019), 37-41. Google Scholar |
[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. Google Scholar |
[5] |
J-C. Lu and G- W Han, Osculating value method of business technology innovation capacity evaluation, Science Research Management, 1 (2002), 54-57. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[8] |
L. Nils and S. Alexander, Modeling time-dependent randomness in stochastic dual dynamic programming, European Journal of Operational Research, 2 (2019), 650-661. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[14] |
Y-P. Zhou, Neural network experience analysis on enterprise technological innovation ability, Science and Technology Progress and Policy, 17 (2000), 62-63. Google Scholar |
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. Google Scholar |
[3] |
M. Idi and B. M. Aliyu, Cyber security capability maturity model for network system, International Journal of Development Research, 6 (2019), 37-41. Google Scholar |
[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. Google Scholar |
[5] |
J-C. Lu and G- W Han, Osculating value method of business technology innovation capacity evaluation, Science Research Management, 1 (2002), 54-57. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[8] |
L. Nils and S. Alexander, Modeling time-dependent randomness in stochastic dual dynamic programming, European Journal of Operational Research, 2 (2019), 650-661. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[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. Google Scholar |
[14] |
Y-P. Zhou, Neural network experience analysis on enterprise technological innovation ability, Science and Technology Progress and Policy, 17 (2000), 62-63. Google Scholar |
No. | Weight | Decision-making unit | ||||||
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No. | Weight | Decision-making unit | ||||||
1 | 2 | ... | j | ... | n | |||
Input data | 1 | ... | ... | |||||
2 | ... | ... | ||||||
... | ... | ... | ... | |||||
... | ... | |||||||
Output data | 1 | ... | ... | |||||
2 | ... | ... | ||||||
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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 |
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 |
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 | % |
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 | % |
Enterprises | Year | ||||||||||||
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 |
Enterprises | Year | ||||||||||||
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 |
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 |
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 |
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 |
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 |
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. |
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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