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

Liling Lin; Linfeng Zhao

doi:10.3934/jimo.2021026

Article Contents

2022, Volume 18, Issue 2: 1425-1437. Doi: 10.3934/jimo.2021026

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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
^* Corresponding author: Liling Lin and Linfeng Zhao

Received: June 2020

Revised: December 2020

Early access: February 26, 2021

Published online: February 26, 2021

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Abstract

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:

Mathematics Subject Classification: Primary 91B06, 91B38; Secondary 90B50, 90B30.

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Table 1. Input and output of evaluation departments

	No.	Weight	Decision-making unit
	No.	Weight	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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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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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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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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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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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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Table 7. Variable adjustment of enterprise 1

Enterprise	Year	Value	X										Y
Enterprise	Year	Value	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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