Quantitative Relationship Model of Input and Output of Student Work in Colleges and Universities and Optimization of Management Strategies

Input-output efficiency refers to the proportional relationship between inputs, consumption and outputs and returns in the production process. Input-output efficiency of college students’ higher education is a rational view of college students’ higher education by considering education as a production process [1-4]. The main inputs for college students to receive higher education are money and time. Families from different classes and regions have different sensitivities to monetary inputs [5-7]. The output of higher education is characterized by comprehensiveness and lag. College students receiving higher education can not only improve their personal quality, such as improving their cultivation and taste, expanding the space of ability enhancement, but also help them find a satisfactory job and obtain economic resources [8-11].

The outputs of higher education are often not achieved overnight, but are continuously reflected in a long life course. For example, in the short term, higher education can help its recipients find a job [12-14]. In the medium term, higher education can provide its recipients with learning methods that will enable them to further their learning on the job and to take on more difficult and better-paying jobs. In the long term, higher education can even have a beneficial effect on the growth and learning of its recipient’s offspring [15-17].

This paper analyzes the specific content of the input level and output level of college student work, and constructs the input-output efficiency evaluation index system of college student work based on the fundamental principles of evaluation index system. Analyzing the advantages of the DEA method, the subdivided DEA models are CCR model, BCC model, and SE-DEA model.Combine the Malmquist index with the DEA method to obtain the DEA-Malmquist productivity index model. Select the DEA-BCC model combined with the DEA-Malmquist model to quantify the relationship between inputs and outputs of college student work. Recombine the indicators of students’ quantity, quality and efficiency at the output level of college student work, calculate the efficiency value of different combinations of indicators, and analyze the new management strategy of input and output of college student work.

2

Evaluation of student work performance in universities based on DEA

2.1

Principles for the construction of the evaluation indicator system

1)

Scientific principle

The selection of indicators should focus on its scientific nature, so that the selected indicators can comprehensively and reasonably reflect the reality of the input and output of university student work, but also to avoid the intersection and duplication between the indicators. Ensure that all types of input and output indicators are representative, reduce the coupling relationship between the indicators, and ensure the accuracy and scientificity of the results of the input and output efficiency analysis.

2)

Principle of Comparability

The principle of comparability requires that the calculation caliber and time range of each indicator in the indicator system should be consistent, and this study selects the indicator data of 2023 for measurement, so it is necessary to ensure that the indicators of each region are all the same cross-section of data in 2023.

3)

Principle of Operability

The principle of operability requires that the selected indicators have both accurate and reliable data sources, as well as accessibility. It is necessary to ensure that the indicators can be measured by scientific and effective methods, to avoid the existence of indicators that are difficult to obtain data or unquantifiable, etc., to ensure the effectiveness of the efficiency analysis.

4)

Systematic principle

When evaluating the input-output efficiency of university student work, the evaluation object should be viewed as a subsystem from the viewpoint of system theory. When evaluating the system, internal and external circumstances, as well as the specifics of inputs and outputs, are considered comprehensively. The evaluation index system should comprehensively consider the correlation between the indicators, and should not just select the indicators in a one-sided way, but should carry out an all-round and systematic evaluation and analysis of the research object with the most representative and core indicators.

2.2

Construction of evaluation index system for input-output efficiency of student work in colleges and universities

2.2.1

Input-output efficiency in higher education

From the perspective of input level, most studies believe that higher education input is the sum of human and material resources invested in the field of higher education for the purpose of training various types of specialists and improving people’s labor capacity.

According to the nature of the input resources of student work in higher education, most scholars divide the input of student work in higher education into three levels, i.e. human input, material input and financial input. And the utilization of input resources is characterized by non-profit, continuity, persistence, and long-term effects. To sum up, this paper defines “student work input in higher education” as the sum of human resources, material resources, financial resources and other resource inputs invested in higher education for the purpose of promoting the development of higher education and cultivating various specialists.

From the output level, in most empirical studies, due to the non-measurable nature of some output indicators in higher education, indicators that are easy to measure and relatively important are often chosen.Other non-measurable outputs can be analyzed by controlling variables that are assumed to be homogeneous. In summary, this paper defines “output of university student work” as the sum of resource outputs in the process of cultivating talents in higher education, which is expressed in talent cultivation, scientific research, social services and other aspects.

From the perspective of efficiency, “input-output efficiency” in economics refers to the comparative relationship between inputs and outputs. The “input-output efficiency of university student work” is the comparative relationship between inputs and outputs in the field of university student work. It allows for a comprehensive assessment of the performance of university student work in each region, thus providing guidance for improving the efficiency of the utilization of existing educational resources.

2.2.2

Selection of Input-Output Indicators for Student Work in Colleges and Universities

This paper explores the efficiency of educational inputs and outputs of colleges and universities directly under the Ministry of Education using the DEA method. Following the above principle, for the selected sample number of 72 colleges and universities directly under the Ministry of Education from 2020 to 2023, the indicators of student work input and educational output of colleges and universities are selected respectively.

The evaluation indexes for input and output efficiency of student work in colleges and universities are shown in Table 1.

Table 1.

Evaluation index of student work input and output efficiency of college students

Input index (X)	Financial investment	Education expenditure (X1)
	Human resource input	Special teacher (X2)
	Human resource input	Other faculty (X3)
	Basic investment	School building area (X4)
		Fixed assets (X5)
		Teaching and scientific instrument equipment (X6)
		Book (X7)
Output indicators (Y)	Talent culture	Student quantity (Y1)
	Scientific achievement	Thesis number (Y2)
		Monographs (Y3)
		Knowledge of the number of property rights (Y4)
	Social services	Scientific income (Y5)
	Social services	Operating income (Y6)

1)

Input indicators of student work in colleges and universities

(1)

Financial input

Fiscal inputs are expressed through the expenditure data of higher education institutions. Expenditures of higher education institutions include career expenses, operating expenses, self-financed capital expenditures, and subsidized expenditures to affiliated units.

(2)

Human Resource Input

If students are the products produced in the operation of colleges and universities, the processor of these students as quasi-public products is teachers. Full-time teachers at all levels and in all categories are the main part of human resource inputs, in addition to which human resource inputs also include college counselors, administrative staff, support staff, laborers, research institution staff, school-run enterprises, and personnel of affiliated organizations. Full-time teachers at all levels and in all categories refer to teachers who work full-time at the senior, deputy senior, intermediate, junior, and unspecified levels.

(3)

Capital investment

Capital investment refers to the actual campus area, value of fixed assets, value of teaching and research instruments and equipments, and number of books put into use in the year for the purpose of cultivating qualified undergraduates and postgraduates and doctoral students with innovative thinking and practical ability. The area of school buildings includes classrooms, libraries, laboratories, internship spaces, specialized research rooms, gymnasiums, halls, and administrative offices.

2)

Output Indicators of Student Work in Higher Education

(1) Talent cultivation is the main duty of higher education, and is the most direct product of higher education institutions for production output. It mainly refers to the qualified college students, postgraduates, and doctoral students with innovative thinking and practical ability that colleges and universities supply to society every year.

(2) Research output is reflected by the number of scientific and technical monographs published by colleges and universities, the number of academic papers published, and the number of intellectual property rights authorized.

(3) The sum of income from scientific research and business is used as indicator data for social services. Scientific research income, including income obtained through undertaking scientific and technological projects, carrying out scientific research collaboration, transferring scientific and technological achievements, and conducting scientific and technological consultation.

2.3

Selection of Input-Output Efficiency Evaluation Models for Higher Education Student Work

2.3.1

Data Envelopment Analysis Methods

Data Envelopment Analysis (DEA) can be considered as a mainstream research method in educational efficiency research. Compared with other methods, the advantage of DEA is that the DEA model can not only realize the overall efficiency measurement of multiple inputs and multiple outputs, but also accurately and quantitatively analyze the complex relationship between multiple independent variables and dependent variables. Moreover, DEA does not need to determine the functional expression of the relationship between inputs and outputs in advance, which makes its operation more concise and convenient as well [18-19].

Among the DEA models, the most basic and commonly used are the CCR model, the BCC model and the SE-DEA model (i.e., super-efficient DEA). And this section will focus on these three models.

First, there is the CCR model, which is described as follows:

Suppose: There is n research subject (j = 1,2,3…,n), each of which has the same m inputs and s outputs. Accordingly, a vector of inputs and outputs can be obtained as shown below: $x_{j} = {(x_{1 j}, x_{2 j}, x_{3 j}, ..., x_{m j})}^{T} > 0, j = 1, 2..., n$ $y_{j} = {(y_{1 j}, y_{2 j}, y_{3 j}, ..., y_{m j})}^{T} > 0, j = 1, 2..., n$ where x_ij and y_ij represent the amount of inputs and outputs of the jrd research subject for the ith type, respectively. Further the inputs and outputs are assigned. After the assignment is completed, the weight vector of inputs and outputs can be obtained: $v = {(v_{1}, v_{2}, v_{3}, ..., v_{m})}^{T}$ $u = {(u_{1}, u_{2}, u_{3}, ..., u_{s})}^{T}$ where v_i and u_r represent the input weights of type i and the output weights of type r, respectively.

Define the efficiency evaluation index for each research object DMU_j: $h_{j} = \sum_{r = 1}^{s} u_{r} y_{r j} / \sum_{i = 1}^{m} v_{i} x_{i j}, j = 1, 2, 3 \dots, n$

Where $Σ_{r = 1}^{s} u_{r} y_{r j}$ represents the composite value of outputs and Σi = 1^mv_ix_ij represents the composite value of inputs. Now, the key is to determine a set of optimal weight vectors v and u. Obviously, h_j ≤ 1. This means that if the efficiency evaluation index (h) of a decision unit is 1, then this decision unit is the most efficient and effective relative to other decision units. If it is less than 1, it means that the efficiency leaves something to be desired, relatively speaking.

The following relative efficiency optimization model can be constructed for the j₀ th DMU (decision unit): $\begin{array}{l} \max h_{j_{0}} = \sum_{r = 1}^{s} u_{r} y_{r j_{0}} / \sum_{i = 1}^{m} v_{i} x_{i j_{0}} \\ s . t . {\begin{array}{l} \sum_{r = 1}^{s} u_{r} y_{r j} / \sum_{i = 1}^{m} v_{i} x_{i j} \leq 1, j = 1, 2, 3 \dots, n \\ v = {(v_{1}, v_{2}, v_{3}, \dots, v_{m})}^{T} \geq 0 \\ u = {(u_{1}, u_{2}, u_{3}, \dots, u_{s})}^{T} \geq 0 \end{array} \end{array}$

If there are v^* > 0 and u^* > 0 that satisfy h_j₀ = 1, then DMU_j₀ is DEA valid, otherwise it is invalid.

The dyadic model is further developed by introducing the slack variable s⁺ and the residual variable s⁻. To form an equationally constrained form: $s . t . {\begin{array}{l} m i n θ \\ \sum_{j = 1}^{n} λ_{j} x_{j} + s^{+} = θ x_{0} \\ \sum_{j = 1}^{n} λ_{j} y_{j} - s^{-} = y_{0} \\ λ_{j} \geq 0, j = 1, 2, 3 \dots, n \end{array}$ where θ is unconstrained, s ≥ 0 and s ≥ 0. Assuming that the optimal solution is $θ^{*}, λ^{*}, s_{-}^{*}, s_{+}^{*}$ the following conclusions follow for the CCR model:

If there are θ^* = 1, and $s_{-}^{*}, s_{+}^{*}$ are both 0, decision cell DMU_j₀ is DEA valid, i.e., technologically efficient and scale efficient.

If there is θ^* = 1, and $s_{-}^{*}, s_{+}^{*}$ are both greater than 0, decision cell DMU_j₀ is DEA weakly effective, i.e., technologically effective and scale effective are not simultaneous.

If there is θ^* < 1, decision cell DMU_j₀ is DEA invalid, i.e., neither technical efficiency nor scale efficiency is optimal.

λ^* represents the value of scale efficiency.

$Σ λ_{j}^{*} = 1$ , Decision unit DMU_j₀ Constant economies of scale.

$Σ λ_{j}^{*} = 1$ , Decision unit DMU_j₀ Increasing economies of scale.

$Σ λ_{j}^{*} = 1$ , Decision unit DMU_j₀ decreasing economies of scale.

Secondly, there is the BCC model. This model is actually a further optimization and improvement of the CCR model, which assumes that the scale benefit of the research object is constant, but in real life, this assumption is difficult to meet. Compared with the CCR model, the BCC model actually adds a constraint, i.e., ∑λ_j = 1, to its original dyadic model, so that the BCC model can satisfy the assumption of variable returns to scale.

The linear programming equation model of the BCC model is given below: $\begin{array}{l} m a x \sum_{r = 1}^{s} u_{r} y_{r k} - u_{0} \\ s . t . {\begin{array}{l} \sum_{r = 1}^{s} u_{r} y_{r k} - \sum_{r = 1}^{m} v_{i} x_{i j} - u_{0} \leq 0 \\ \sum_{r = 1}^{m} v_{i} x_{i j} = 1 \\ v \geq 0; u \geq 0; u_{0} f r e e \end{array} \end{array}$

The dyadic model of the BCC model continues to be given below: $\begin{array}{l} \min θ \\ s . t . {\begin{array}{l} \sum_{j = 1}^{n} λ_{j} x_{j} \leq θ x_{0} \\ \sum_{j = 1}^{n} λ_{j} y_{j} \geq y_{0} \\ \sum_{j = 1}^{n} λ_{j} = 1, λ \geq 0 \end{array} \end{array}$

The BCC model is interpreted similarly to the CCR and will not be repeated here.

Finally, there is the SE-DEA model (also called the Super-Efficiency DEA). The introduction of the CCR model and the BCC model has already occurred. However, both models have a common disadvantage, which is the inability to re-rank the efficiency of decision units with efficiency value of 1. To solve this problem, the SE-DEA model is proposed. This model can further compare the decision units with an efficiency value of 1, thus obtaining the situation where the efficiency value is greater than 1, from which the term “super-efficiency” is derived.

The SE-DEA model is more similar to the CCR model as a whole. The only difference is that the inputs and outputs of the jrd DMU are expressed as inputs and outputs using the other DMU inputs and outputs first, when the effectiveness of the jst DMU is calculated. The jth DMU is excluded from the calculation process and the model removes the constraint that the value of the efficiency metric in the CCR model is less than or equal to 1, so that an efficiency value greater than 1 can be obtained.

The super-efficiency DEA model for the input-oriented CRS is: $\begin{array}{l} \min θ \\ s . t . {\begin{matrix} \sum_{j = 1}^{n} λ_{j} x_{i j} \leq θ x_{i k} \\ \sum_{j = 1}^{n} λ_{j} y_{r j} \geq y_{r k} \\ \sum_{j = 1}^{n} λ_{j} = 1, λ \geq 0 \end{matrix} \end{array}$ where λ ≥ 0.

The VRS super-efficiency model is obtained by adding the following constraints to the above model: $\sum_{j = 1, j \neq k}^{n} λ_{j} = 1$

There is no superiority or inferiority of these categorized models mentioned above; they all have strengths and weaknesses. The models can be selected according to the object of research. Combined with the specific situation of student work in colleges and universities, this paper mainly uses the input-oriented scale return variable correlation model (Input-BCC) as its research model. BCC model and CCR model, compared with its “perfection” is higher, although the CCR model has a certain advantage in the calculation of comprehensive efficiency value. The CCR model has some advantages in the calculation of comprehensive efficiency value, but it is insufficient in the calculation of pure technical efficiency value, which is the advantage of the BCC model. In addition, the model also has some advantages in the calculation of scale efficiency values.

At the same time, combining Malmquist index with DEA method to get DEA-Malmquist productivity index model can make it optimized in time and space. After comprehensive consideration, this paper chooses the DEA-BCC model combined with the DEA-Malmquist model as it is more scientific and adaptable. It can understand and analyze multiple aspects of student work in colleges and universities, which provides a basis for subsequent problem solving.

2.3.2

Malmquist Index

The Malmquist index model is used to analyze changes in the quantity of input consumption.The Malmquist productivity index, which is based on DEA, has been found to be a useful tool for assessing the productivity of decision-making units. The index consists of two elements. One measures the change in the technological frontier while the other measures the change in technological efficiency. Using periods s and t as the technological reference, if the Malmquist index is greater than 1, it means that total factor productivity is on an increasing trend during this period. Equal to one means no change, while less than one indicates a decline in efficiency.

Specifically, the Malmquist index analysis method mainly expresses the efficiency of inputs and outputs through the ratio between the distance functions of different period stages. Measuring the Malmquist index first needs to construct a production frontier surface to find out the distance function, which requires the use of DEA or stochastic frontier production function to obtain help.The traditional DEA model is limited to comparing efficiency situations at the same point in time and cross-sectionally.It is not very applicable to panel data, and it is difficult to identify the dynamic changes and development trends in efficiency.

Malmquist index can better overcome this shortcoming, can compare the efficiency of the same decision-making unit in different periods, better analyze the panel data, and realize dynamic analysis of decision-making units.Malmquist index formula is shown in equation (12): $M (x^{t + 1}, y^{t + 1}, x^{t}, y^{t}) = E C \times T E C = \frac{D_{v}^{l + 1} (x^{l - 1}, y^{l + 1})}{D_{v}^{l} (x^{l + 1}, y^{l + 1})} \times {[\frac{D_{v}^{l} (x^{l + 1}, y^{l + 1})}{D_{v}^{l + 1} (x^{l + 1}, y^{l + 1})} \times \frac{D_{v}^{l} (x^{l}, y^{l})}{D_{v}^{l + 1} (x^{l}, y^{l})}]}^{\frac{1}{2}}$

Where (x^t,y^t) is the input vector in period t. (x^t*1,y^t*1) is the output vector for period t + 1, and $D_{0}^{1} and D_{0}^{t}^{* 1}$ are the distance functions for the above periods. M₀ = 1, M₀ < 1 denotes the performance improvement, no change, and decrease in the neighboring 2 periods, respectively.

3

Evaluation and analysis of the input and output performance of university student work

3.1

Evaluation and Analysis of Student Work Performance in Colleges and Universities Based on DEA

In this paper, several second-level colleges of a university in Sichuan are used as decision-making units (DMUs), and the DEA-BCC model is applied to evaluate the work of university students. Next, a series of analyses will be conducted to compare the comprehensive efficiency value, pure technical efficiency value, scale efficiency value, and total factor productivity change among each second-level college.

In this study, the student work performance of several second-level colleges of a university with a total of 24 decision-making units for three consecutive academic years is measured by the collected data, which are input-oriented and assuming the conditions of fixed returns to scale (CRS) and variable returns to scale (VRS).

The three efficiency values obtained were analyzed and compared across colleges and academic years. The measured values of student work efficiency are shown in Table 2. Where the DMU is said to be DEA effective when PTE=1 and SE=1. According to the display, 18 out of 24 DMUs are relatively DEA effective and 6 DMUs are non-DEA effective. It should be noted that in the table below, in the column of Return to Scale, “IRS” stands for Increasing Return to Scale, “DRS” stands for Decreasing Return to Scale, and “-” stands for Constant Return to Scale.

Table 2.

Student productivity measurement

College	Year	TE	PTE	SE	Scale compensation
Software college	2020-2021	1	1	1	-
	2021-2022	1	1	1	-
	2022-2023	1	1	1	-
Management institute	2020-2021	1	1	1	-
	2021-2022	1	1	1	-
	2022-2023	1	1	1	-
Accounting institute	2020-2021	1	1	1	-
	2021-2022	0.912	1	0.899	DRS
	2022-2023	1	1	1	-
Mechanical and electrical college	2020-2021	1	1	1	-
	2021-2022	1	1	1	-
	2022-2023	1	1	1	-
School of transportation	2020-2021	0.675	0.842	0.724	IRS
	2021-2022	1	1	1	-
	2022-2023	1	1	1	-
Civil college	2020-2021	0.924	0.972	0.941	IRS
	2021-2022	0.936	0.955	0.992	IRS
	2022-2023	1	1	1	-
Informatics institute	2020-2021	1	1	1	-
	2021-2022	1	1	1	-
	2022-2023	1	1	1	-
Art school	2020-2021	1	1	1	-
	2021-2022	0.907	0.946	0.975	IRS
	2022-2023	0.892	0.911	0.953	IRS
Mean value		0.969	0.984	0.979	/

School of Software, School of Management, School of Electrical and Mechanical Engineering, and School of Information Technology have achieved DEA efficiency for three consecutive academic years, and all the three efficiency values are 1. This indicates that the student management work in their colleges has been rationally allocated in terms of the input resources to maximize the outputs, and it should be continued.

Comprehensive Technical Efficiency (TE) reflects the level of DMU’s full utilization and output of available input resources. When TE is greater than or equal to 1, it indicates that the human, material, and financial input resources of the college have been fully tapped and utilized in that academic year, indicating that the DEA is effective.And when TE is less than 1, it indicates that the college’s human, material and financial resources are underutilized and considered as DEA ineffective.The higher the value of TE, the higher the utilization of input resources.

The comprehensive efficiency of inputs and outputs of student work in each secondary college of a university in the academic year 2020-2023 is shown in Table 3.In the academic year 2020-2021, only the College of Transportation and the College of Civil Engineering have a comprehensive efficiency value of less than 1, and all of them have ineffective DEA.In the academic year 2021-2022, the College of Accounting, the College of Civil Engineering and the College of Arts have comprehensive efficiency values of less than 1, and their non-DEA is effective. The College of Art has the lowest efficiency value with an efficiency value of 0.907. In the academic year 2022-2023, only the College of Art does not have a composite efficiency value of 1. The remaining seven colleges have a composite efficiency value of 1 and are all DEA-effective. Among them, the comprehensive efficiency of the two colleges, like the College of Civil Engineering and the College of Arts, is not high in the three academic years, with low input and output levels, and the trend of efficiency changes is large, indicating that these two colleges have certain problems in the utilization of resources, and need to reflect on the root causes of the problems in time, and take effective measures to promote the maximization of the output of resources.

Table 3.

2020-2023 annual investment output integrated efficiency

College	2020-2021	2021-2022	2022-2023
Software college	1	1	1
Management institute	1	1	1
Accounting institute	1	0.912	1
Mechanical and electrical college	1	1	1
School of transportation	0.675	1	1
Civil college	0.924	0.936	1
Informatics institute	1	1	1
Art school	1	0.907	0.892
Mean value	0.950	0.969	0.987

3.2

Dynamic Analysis of Input-Output Performance of Student Work in Higher Education Institutions

In order to further analyze the changes in the input-output performance of student work in universities directly under the Ministry of Education in Sichuan Province, this study is based on the Malmquist index method and uses DEAP software to dynamically analyze the performance of student work in five universities directly under the Ministry of Education in Sichuan Province from 2013 to 2023.

Malmquist index is mainly used to measure the change of total factor productivity (Tfpch) of decision-making units during the sample period, mainly refers to the fact that the Malmquist index can be decomposed into the index of change in technical efficiency (Effch) and the index of technological progress (Techch), which is also called the index of external change, under the constant scale of compensation. The technical efficiency change index (Effch) can be decomposed into a pure technical efficiency index (Pech) and a scale efficiency index (Sech).

3.2.1

Quantitative performance of outputs

The dynamic analysis can help to understand the trend of the input-output-quantity performance of student work in colleges and universities from 2013-2023, and measure the overall Malmquist productivity index of colleges and universities and its decomposition index.

The analysis of the overall total factor productivity of output quantity performance from 2013-2023 is shown in Figure 1.

The average annual growth of total factor productivity of the five universities in Sichuan Province from 2013 to 2023 is 7.975%, and the analysis of the various influencing factors reveals that the index of change in technological progress (techch), also known as the index of external change, grows by an average of 7.407% per year. It can be seen that the increase in total factor productivity of student work in colleges and universities directly under the Ministry of Education in Sichuan Province mainly stems from the technological progress index.

3.2.2

Output quality performance

The dynamic analysis can help to understand the trend of the input and output quality performance of student work in universities from 2013-2023, and measure the overall Malmquist productivity index and its decomposition index of universities.

The analysis of the overall total factor productivity of output quality performance from 2013-2023 is shown in Figure 2. The average annual growth of total factor productivity of the five universities in Sichuan Province is 0.991% from 2013 to 2023. The mean values of the index of change in technical efficiency (effch) and the index of change in technical progress (techch) are 1.0113 and 1.04323, respectively.It shows that the scientific and technological innovation capacity and technical progress level of the universities directly under the Ministry of Education in Sichuan Province have increased from 2013 to 2023, while the resource allocation is in a dragging state and is not able to increase the level of performance with the original level of science and technology.

3.2.3

Output effectiveness performance

The dynamic analysis can help to understand the trend of the university’s science and technology input output performance from 2013-2023, and measure the overall Malmquist productivity index and its decomposition index of the university.

The overall total factor productivity of output benefit performance from 2013-2023 is analyzed as shown in Table 4. The average annual growth of total factor productivity of the five universities in Sichuan Province is 4.011% from 2013 to 2023. The technical efficiency change index and the technical progress change index have increased by 4.586% and 0.163% annually.The index of change in technical efficiency (effch) has increased by 4.586%, and the index of change in technological progress (techch) has increased by 0.163% annually. It shows that the level of technological innovation and progress in the work of students in higher education has not changed much, and the allocation of resources is good in terms of being able to improve the level of performance with the original level of technology.

Table 4.

Overall productivity productivity overall

	Effch	Techch	Pech	Sech	Tfpch
2013-2014	0.9985	1.1243	0.8354	1.2146	1.0286
2014-2015	1.3421	0.9354	1.1243	1.0377	1.1634
2013-2016	1.1001	0.9993	0.8186	1.4532	1.1243
2013-2017	0.9686	1.0065	0.8857	1.1339	0.9675
2013-2018	1.1252	0.9687	1.1346	1.0541	1.1421
2013-2019	0.9986	1.0146	0.9864	1.0032	1.0331
2013-2020	0.9341	1.1559	1.1249	0.0866	1.1042
2013-2021	1.1245	0.9365	0.9864	1.1234	1.0893
2013-2022	0.8697	1.0057	0.8585	1.0607	0.8917
2013-2023	0.9972	0.8694	1.1003	0.9568	0.8569

4

Analysis of the efficiency of the combination of indicators for evaluating the inputs and outputs of university student work

4.1

Constructing a portfolio of different evaluation indicators

When evaluating the efficiency of a decision-making unit, the selection of different evaluation indicators will have different effects on its efficiency value. In this paper, the selected evaluation indicators are combined to examine the input-output efficiency of university student work from three different perspectives, namely, student scale, student cultivation quality and scientific research achievements.

The different combinations of indicators of input-output efficiency of university student work are shown in Table 5. The output indicators of the three combinations are, respectively, the number of students graduated, the number of students graduated, the number of national excellent papers, the number of scientific and technological patents, and the number of papers published in foreign and national journals.

Table 5.

The different indicators of the efficiency of the students’ work

	Input index	Output indicator
Combination 1: Student scale efficiency	Guide number	Student graduation
	Research funding
	Library collection
	The value of the cost of scientific research
Combination 2: Student quality efficiency	Guide number	Student graduation
	Research funding	Student graduation
	Library collection	The number of outstanding papers in the country
	The value of the cost of scientific research	The number of outstanding papers in the country
Combination 3: Scientific efficiency	Guide number	Number of technology patents
	Research funding	Number of technology patents
	Library collection	The number of papers published abroad and national publications
	The value of the cost of scientific research

4.2

Analysis of efficiency values for different combinations of indicators

According to the three different combinations of indicators in the above table, the efficiency values of student work in 20 universities are calculated separately. The input-output efficiency of student work in colleges and universities under different combinations of indicators is shown in Table 6.

Table 6.

Different combinations of university students work in output efficiency

Serial number	Decision unit	Efficiency value
Serial number	Decision unit	Combination 1	Combination 2	Combination 3
1	Tsinghua university	1	1	1
2	Peking University	0.625	1	0.986
3	Xiamen university	0.717	0.763	0.702
4	Nanjing university	0.762	0.822	0.595
5	Fudan university	0.896	0.824	1
6	Tianjin university	1	1	1
7	Zhejiang university	1	1	1
8	Nankai university	0.936	0.972	0.803
9	Xi ‘an jiaotong university	0.624	0.663	0.525
10	Central China university of science and technology	0.799	0.811	0.577
11	Southeast university	0.621	0.654	0.825
12	Wuhan university	0.921	0.942	1
13	Shanghai jiaotong university	1	0.935	1
14	China sea university	1	1	1
15	Shandong university	0.785	0.726	0.882
16	Hunan university	0.829	0.915	1
17	Renmin university of China	1	1	1
18	Jilin university	1	0.986	0.456
19	Chongqing university	0.725	0.824	0.782
20	University of electronic science and technology	1	0.818	0.733

The evaluation indicators have a significant impact on the model’s efficiency value.There are five universities with efficiency values of 1 for all three combinations, namely Tsinghua University, Tianjin University, Zhejiang University, Ocean University of China, and Renmin University of China. Specifically:

There are 10 universities with efficiency values >0.9 in combination 1, including Nankai University (0.936) and Wuhan University (0.921).

There are 11 universities with efficiency values >0.9 in Combination 2, accounting for 55% of the total. 7 universities (35%) with 0.7< efficiency value <0.9. Xi’an Jiaotong University and Southeast University have student work efficiency values of 0.663 and 0.654, respectively.

Combination 1 and combination 2 have similar efficiency values, indicating that there is a significant relationship between the scale and quality of student work training in universities.Combination 3 has a significant difference from combinations 1 and 2, suggesting that some universities have a lower scale and quality of student work training, but higher research efficiency. Taking Southeast University as an example, the student regularity efficiency and student quality efficiency are 0.621 and 0.654 respectively, which are relatively low, but the scientific research efficiency reaches 0.825.This on the one hand indicates that the student scientific research output efficiency of these colleges and universities is higher, and on the other hand, it may be that student work in these colleges and universities does not pay enough attention to the quality and scale of the cultivation of students. Therefore, these colleges and universities should appropriately expand the scale and quality of their student management.

5

Conclusion

In this paper, based on the principle of screening the evaluation index system, the input and output efficiency indexes of students’ work in colleges and universities are determined. The DEA method establishes the evaluation model for the relationship between input and output of college student work. Combine the input and output performance evaluations of college student work, combine different indicators, and calculate the efficiency value of each combination of indicators.

1) The sample college uses its second-level colleges as decision-making units to analyze the combined efficiency value of each second-level college. Among the 24 decision-making units in this university, 1/4 of them are non-DEA effective. School of Software, School of Management, School of Mechanical and Electrical Engineering, and School of Information Technology have achieved DEA effective for three consecutive academic years, and all three efficiency values are 1. This college’s student management work has been rationally allocated in terms of input resources and maximized output, and it should continue.

2) The dynamic evaluation of student work performance in colleges and universities based on Malmquist index shows that the average annual growth of output quantitative performance, qualitative performance, and efficiency performance from 2013 to 2023 are 7.975%, 0.991%, and 4.011%, respectively. It can be seen that the growth of total factor productivity of student work in colleges and universities directly under the Ministry of Education in Sichuan Province mainly stems from the index of technological progress change. The level of scientific and technological innovation capacity and technological progress has increased, but there is still a need to improve the allocation of resources.

3) Considering the quantity, quality and benefit of output of student work in colleges and universities, combining the specific indexes of student scale, student cultivation quality and scientific research achievements. The efficiency value of university student work with the combination of student scale and quality is higher than the efficiency value of scientific research.

Not only should colleges and universities study the input-output evaluation index of student work, but they should also come up with a way to think about things in a way that lets them explore a new way of teaching based on teaching reform, student work, and combining different scenes. This way of thinking can really help to promote education and teaching reform, help students grow, give new ideas for digital education reform, and use new technology to make the service quality, education system, and efficiency of student work in colleges and universities better.

Langue:: Anglais

Périodicité:: 1 fois par an
Sujets de la revue:: Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres

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Quantitative Relationship Model of Input and Output of Student Work in Colleges and Universities and Optimization of Management Strategies

Huayan Li

Publié en ligne: 17 mars 2025

Reçu: 12 oct. 2024

Accepté: 02 févr. 2025

DOI: https://doi.org/10.2478/amns-2025-0260

Mots clésDEA model, Malmquist index, Input-output efficiency, College student work

© 2025 Huayan Li, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
DEA model, Malmquist index, Input-output efficiency, College student work