Input-Output Benefit Analysis of Green Building Incremental Cost Based on DEA-Entropy Weight Method

Abstract

Green buildings are an important carrier for the transformation of the construction industry to green, efficient and energy-saving, and an important part of the national sustainable development strategy. At present, the development of green building in China is still in the primary stage, the willingness of construction enterprises to develop green building is low, and the promotion of green building is facing the problem of insufficient power. The main reason is that the incremental cost of green building is too high. Therefore, this paper takes green building as the research object, and studies the quantification and evaluation of its incremental cost-benefit. Firstly, the incremental cost composition of green buildings is analysed from the perspective of the whole life cycle, and the incremental benefits are divided into economic benefits, environmental benefits and social benefits. Secondly, the green building incremental cost-benefit evaluation model is constructed by combining the entropy weight method and the data envelopment analysis (DEA) method. Finally, the feasibility of this evaluation method is verified through the analysis of practical engineering cases. By evaluating the input-output benefits of incremental costs, the projects with DEA effectiveness and DEA ineffectiveness are identified, and specific suggestions are put forward for them respectively. The research results not only provide theoretical support for the quantification and evaluation of incremental costs and benefits of green buildings, but also provide a reference for the formulation of corresponding cost control measures, and lay a foundation for the realization of the cost minimization and benefit maximization of green buildings.

1. Introduction

In September 2020, China proposed at the general debate of the 75th United Nations General Assembly that China’s carbon dioxide emissions will reach a carbon peak in 2030 and achieve carbon integration in 2060. At that time, China has actively explored energy conservation and emission reduction in various fields. In March 2021, in the “14th Five-Year Plan for National Economic and Social Development of the People’s Republic of China and the Outline of Vision 2035”, it was proposed to actively respond to climate change, promote clean, low-carbon, safe and efficient use of energy, and further promote the low-carbon transformation of industry, construction, transportation and other fields. In China, the real estate architecture industry is known as the “great energy consumer” jointly with the industrial engineering and transportation industry [1]. The energy consumption of the construction industry accounts for 45% of China’s total energy consumption. With the acceleration of China’s urbanization process, it is estimated that China’s urbanization level will reach 70% in 2030, and the demand for urban housing will continue to increase, which will lead to an increase in building energy consumption [2]. In this context, China has successively issued supporting policies to vigorously develop green buildings. As early as 2006, Ministry of Housing and Urban-Rural Development issued Green Building Assessing Standard to encourage and advocate the development of green building, and provide preferential policy support and fiscal subsidiary. China started to implement the green building assessment and labeling system in April 2013. Up to the end of 2021, China has totally assessed over 4000 green building labeling projects. In July 2020, the Ministry of Housing and Urban-Rural Development issued the Action Plan for the Creation of Green Buildings, proposing that by 2022, the proportion of green buildings in new urban buildings nationwide will reach 70% [3]. Although green buildings have achieved rapid development in China driven by policies, many builders are still cautious about green buildings due to the complexity and difficulty of incremental cost control of green buildings. The incremental cost-effectiveness of green buildings has become an obstacle to the promotion and development of green buildings. Therefore, it is vital to quantify and evaluate the incremental cost effectiveness of green buildings and to improve the input-output effectiveness of incremental green building costs to promote the development of the green building industry.

Incremental cost is the most important factor for investors to consider before planning green buildings, and it is also a key factor affecting the success of the project [4,5]. Therefore, scholars have conducted a great deal of research on incremental cost effectiveness. In terms of factors influencing green building cost-effectiveness. Greg et al. (2003) analyzed the cost constitution of green buildings, as well as its energy consumption and conservation, and quantified the energy saved by green buildings with currencies [6]. Zhang et al. (2011) analyzed the influence of green technology increment cost to the architectural structure, and they mentioned factors hindering the popularization of the green technology [7]. Hwang et al. (2017) collected data related to 242 traditional and 121 green building projects from 30 different companies. The incremental cost and cost performance of green building projects are investigated. The results show that the incremental cost of green building is between 5% and 10%, with project type and size being important factors in the cost increase [8]. Samari et al. (2013) conducted research through field research and found that high input cost, low demand rate and limited credit resources have become the main factors hindering the promotion of green buildings in Malaysia [9]. Peter (2014) studied green buildings from the perspective of the whole life cycle and found that green buildings have a positive impact on human health while reducing energy consumption and improving efficiency. And this goal can be achieved through the environmental impact of green products [10]. Some scholars divide economic efficiency into direct efficiency and indirect efficiency. The former mainly represents the proportion of value added at the economic level of buildings and the reduction of building energy consumption costs, while the latter mainly represents the improvement of living comfort in green buildings [11,12,13]. Liu (2021) used structural equation model and AMOS software to build a structural model of green building development, and explored the key influencing paths and key influencing factors driving the development of green buildings, thereby revealing the driving mechanism of green building development and proposing corresponding driving countermeasures [14]. These researches provide helpful thoughts and methods for studying the increment cost benefits of green buildings.

As to the calculation of building cost-benefit, scholars have made a lot of beneficial work. In terms of incremental cost-effectiveness, Li (2020) constructed a green building incremental cost-benefit estimation model based on the perspective of system dynamics, and estimated the incremental cost-benefit of green building projects in the whole life cycle [15]. Chen (2021) sorted out the components of green building operating costs, and through the analysis of the influencing factors of each component cost, constructed a green building operating cost calculation model, and proposed a calculation method based on BIM technology [16]. Bee (2016) developed a model analysis method for estimating the whole life cycle cost of buildings based on the parameter information related to LCC, and can simulate the cost-effectiveness of green buildings [17]. Liu et al. (2014) uses the energy efficiency technology method to discuss the cost-benefit of green buildings in China. The results show that green buildings only consider economic benefits, which is not conducive to the green building market, and energy prices, energy-saving technologies, and life cycle length will affect the cost of green buildings, thereby affecting the green building market and economic benefits of green buildings [18]. Dwaikata (2018) analyzed the whole life cycle cost of green buildings, identified the cost variables, and established the cost budget model. The research results show that reduced energy consumption in the green building is the most influential factor to reduce its total life cycle cost [19]. Saurabh (2020) studied the secondary data and vertical operating costs of green building certification in developing countries, compared the stock market performance of non-green building competitors with similar scale industries, and estimated the financial benefits of investing in green buildings [20]. Gabay (2014) established a cost-benefit model in line with green building standards and concluded that the incremental cost of green building can be controlled between 4–12% through reasonable investment and cost allocation [21]. Khoshbakht (2017) provides a cost-benefit prediction method combined with SWOT analysis. The survey results show that the methods used in green building cost-effectiveness studies can be divided into different categories according to data collection and analysis methods. It also points out that green building costs can be divided into two categories: pre-construction cost and post-construction cost [22]. Some scholars focus on the environmental benefits brought by green building. In the process of their research, they pointed out that the degree of impact on the environment can be used to measure the degree of green development. The commonly used indicators generally include various pollution factors such as total industrial output value and wastewater discharge. They constructed a DEA analysis model and pointed out that the development of green degree [23,24]. Zhong (2017) used the data envelopment analysis (DEA) method and the Malmquist index measurement to measure and evaluate the inter-provincial green development welfare in his own country [25]. Sattary (2016) and Chel (2017) compared the economic and environmental impacts of energy use on the construction projects before, during and after construction, and took corresponding energy-saving measures [26,27]. Some scholars have investigated the energy efficiency and carbon emission efficiency of buildings in different countries or regions to improve the low-carbon development of building projects and achieve green development goals [28,29,30]. Some scholars analyzed the application effects of green building energy-saving technologies from different positions, and revealed the energy-saving rate and comprehensive benefits of improving energy-saving technologies [31,32,33].

At the same time, there are also many researches on the evaluation of green building benefits. Michael et al. (2014) established a comprehensive evaluation model of buildings under different climates, technical conditions, and socio-economic conditions [34]. Zhu et al. (2018) constructed an econometric model, analyzed the incremental cost and incremental benefit of the green building’s entire life cycle, and made a comprehensive evaluation of building energy efficiency analysis based on the theory of value engineering [35]. Cao (2012) conducted a cost-benefit evaluation of the water-saving benefits of a residential area by establishing a green building cost-benefit evaluation system, and found that effective control of costs and improvement of saving efficiency are conducive to shortening the payback period of incremental costs [36]. Sun (2015) established a green building evaluation system based on LCC, explored the economics of specific projects, represented incremental benefits through cost savings, and obtained the evaluation results of project economic benefits [37]. Some scholars have established a green building carbon emission measurement model from the perspective of carbon emissions, measured incremental environmental benefits, and proposed cost-benefit evaluation methods [38,39,40]. Data Envelopment analysis (DEA) is widely used because of its objective evaluation of project cost effectiveness. Ashuri (2019) applied DEA evaluation model to evaluate the energy efficiency of 124 residential projects from the perspectives of comprehensive efficiency, technical efficiency and scale efficiency, and found that the energy efficiency of green technology residential projects was higher [41]. Wu introduced the production efficiency of manufacturing industry into the incremental cost-benefit evaluation of green buildings, and quantitatively evaluated the production efficiency of green buildings by constructing the DEA evaluation model [42]. In addition, DEA model has shown advantages in evaluating the social benefits of green buildings and the efficiency of green innovation technology [43,44]. These studies provide reference for the determination of research methods in this paper.

To sum up, green building is an important carrier to realize the green development of cities and towns, and it is a new requirement for buildings to break through the bottleneck of resource and environmental constraints. It can be seen from the existing research results that most of the current research on green building benefits focuses on the single incremental cost benefit, economic benefit and environmental benefit research, while the research on economic, social and environmental benefits less considered in combination. The research methods mostly use fuzzy comprehensive evaluation, system dynamics, cost-benefit analysis, etc., which are greatly influenced by subjective factors. However, the DEA-entropy weight method can effectively solve inconsistent statistical units, simplify complex data, and perform dimensionless calculations. At the same time, this method can objectively calculate variable weights, scientifically avoid the influence of subjectivity on calculation results, and ensure the objectivity of the results. Therefore, based on the existing research and literature, this paper establishes a green building incremental cost-benefit evaluation index system from the perspective of inputs and outputs, combined with the whole life cycle theory. The DEA-entropy method is used to construct a green building incremental cost-benefit evaluation model, analyse the relationship between incremental costs and benefits, determine whether the project has redundant inputs or insufficient outputs by conducting DEA validity on them, and propose targeted policy recommendations accordingly. The research results provide a reference for the rational control of the incremental cost and benefit of green buildings, and have important theoretical and practical significance for promoting the development of green buildings.

2. Green Building Input-Output Measurement Index System

The green building concept is an expression of the eco-efficiency concept in the field of sustainable building. While, ecological efficiency was proposed by German economist Schaltegger in 1990 and defined as the extent to which ecological resources meet the needs of economic development [45]. Its essential idea is to describe the ability of a certain industry to obtain more high-quality output with less resource input, and effectively reduce the negative impact on the environment, and strive to achieve the goal of win-win or multi-win. There, this paper applies the concept of eco-efficiency to green buildings, examining the incremental costs and benefits of green buildings to maximise value and minimise impact. “Value” refers to the incremental cost of green building, namely, the cost change brought by using the green technology than using the ordinary architectural technology. It belongs to the scope of economy. “Influence” refers to the incremental benefit of green building, namely, the reduced ecological influence brought by using the green technology than using the ordinary architectural technology, which is manifested in economic, environmental and social aspects.

2.1. Incremental Cost of Green Building

Incremental cost refers to the additional cost increase caused by increasing the output of a specific product or service under the existing production technology level [46]. According to the research of relevant scholars and the cost structure of construction projects, it can be seen that the incremental cost of green building is mainly composed of three parts: the incremental cost of consultation, construction technology and certification. [47,48]. While, some scholars believe that incremental cost exists in the whole life cycle of green buildings, defined it as the cost increase caused by the introduction of advanced technology and advanced management in the design, construction and operation of green buildings [49].

Summarize the research results of related scholars, this paper takes green buildings as the research object, and defines the incremental cost of green buildings from the perspective of the whole life cycle. In order to facilitate the analysis of the cost-effectiveness of green buildings, the incremental costs of green buildings are divided into incremental costs in the early stage, incremental cost in the construction stage, incremental cost in the operation stage, and incremental cost in the demolition and recovery stage. The specific incremental cost indicators are shown in the

Table 1. Incremental Cost of Green Building.

Incremental Costs in the Construction Cycle Phase	Incremental Cost Notes
Upfront incremental cost	Incremental cost of planning, design, certification, etc. in the early stage of engineering projects
Construction Incremental Cost	Incremental costs incurred in the construction phase due to green technology, water saving, land saving, material saving, indoor and outdoor environment improvement, etc.
Incremental cost of operations	Incremental costs in maintenance of energy-saving equipment, post-operation star certification fees, etc.
Demolition recovery incremental cost	Incremental cost of adopting advanced environmental protection demolition measures, incremental cost of restoring the original ecology and incremental cost of recycling waste building materials

.

2.2. Incremental Benefits of Green Building

By analogy with the definition of incremental cost of green buildings, combined with the theory of ecological efficiency, the incremental benefits of green buildings can be defined as the additional economic benefits brought by green buildings reducing environmental pollution and energy consumption compared to traditional buildings [36]. Based on the existing research results, combined with the characteristics of green buildings and related cases, the incremental benefits of green buildings can be divided into direct incremental benefits and indirect incremental benefits. The direct incremental benefit refers to the direct economic benefits brought by the adoption of green building standards, and the indirect incremental benefit refers to the environmental and social benefits that cannot be measured in monetary terms brought about by green buildings. The specific green building incremental benefit composition is shown in

Table 2. Index Constitution of Green Building Incremental Benefit.

Incremental Benefit Indicators	Interpretation of Indicators	Type of Benefit
Economic benefit	Save energy, water, land and material	Explicit benefit
	Save maintenance cost in operation, and prolong the building service life
Environmental benefit	Reduce pollution benefit	Implicit benefit
	Improve the ecological environment
Social benefit	Micro-level: inhabitant health
	Regional level: save public utilities
	Macro level: promote sustainable development

.

(1)

Economic benefit: Economic benefit refers to the reduction of environmental influence brought by green building compared with ordinary building in the operation stage. The reduced influence of this aspect will usually bring economic benefits, namely, the saved using cost.

(2)

Environmental benefit: Environmental benefit of green building is demonstrated in the energy, water, material, land resource conservation, improvement of the air, noise, light conditions in the ambient environment, as well as the creation of ecological environment. Environmental benefit of green building is firstly and primarily manifested by the reduction of the pollutant emissions, including CO₂ and SO₂, the generated emission reduction, as well as the creation and improvement of the ecological environment by using the green technology. The life cycle process of green building includes the common energy consumption, common building material consumption and common plant using. Its CO₂ emission factors are indicated in

Table 3. CO₂ emission factor.

Energy Type	CO2 Emission Factor	Material Type	CO2 Emission Factor	Plant Type	CO2 Fixed Amount (kg/m3 × Year)
Coal	2.49 kg CO2/kg	Cement	1.45	Ecological multilayer	1200
Gasoline	2.99 kg CO2/kg	Steel	4.47	Arbor	600
Diesel	3.16 kg CO2/kg	Concrete	0.95	Bush	300
Nature gas	2.19 kg CO2/kg	Concrete block	0.44	Cirrus	100
Electricity	0.997 kg CO2/kwh	Solid clay brick	0.73	Natural weeds, aquatic plants	20
-	-	Glass	5.13	-	-
-	-	Lime	2.75	-	-

.

(3)

Social benefit: Social benefit can be divided into micro social benefit, regional social benefit and macro social benefit. Micro social benefit means that green building emphasizes on providing healthy, comfortable and safe habitation activity space for human beings, reducing the suffering opportunity cost, improving the people’s living quality and habitation comfort. Regional social benefit means that green building can improve the community image and spiritual appearance, reduce the contributions of the city in pollution treatment and ecological maintenance. Macro social benefit means: On one hand, green building can enhance the “environmental awareness” of the whole society, improve people’s living and consumption philosophies; On the other hand, green building has great and positive influence to the establishment of a harmonious society, and it promotes the stable development of the whole society.

2.2.1. Calculation Rules of Economic Benefit

According to the above analysis, the incremental benefits of green buildings are composed of economic benefits, environmental benefits and social benefits. Now, if the incremental benefit of green building is IB, the economic benefit is BE, the environmental benefit is BF, and the social benefit is BS, the calculation formula of the incremental benefit of green building can be listed:

$$IB=BE+BF+BS$$

(1)

Calculated from the green building put into use, the economic benefits (BE) in future years can be expressed as:

$$B{E}_{mi}=L_i+E_i+W_i+M_i+I_i+O_i$$

(2)

$$BE={\displaystyle \sum _{n=1}^n}{\displaystyle \sum _{i=1}^n}B{E}_{mi}$$

(3)

BE: economic benefit;

L: annual income of saving land;

E: annual benefit of saving energy;

W: annual benefit of saving water resources;

M: annual benefit of saving materials;

I: annual benefit brought by architecture;

O: annual income during operation period.

2.2.2. Calculation Rules of Environmental Benefit

In full life cycle of green building, CO₂ exists everywhere. The environmental benefit of green building is reflected by the reduction of the CO₂ emission compared with the reference building in the construction and operation processes on one hand, and ecological environment improvement in the research scope on the other hand. The green plants play the role of CO₂ fixation. This paper mirrors the philosophy of carbon emission transaction. The carbon emission calculation and value calculation are introduced into the environmental benefit assessment of green building, so as to value the implicit benefit of green building, and calculate the investment efficiency, thus making the environmental benefit brought by building energy conservation to become more clear and definite. To sum up, the environmental benefit BF is composed of the carbon emission reduction benefit and the benefit brought by the improvement of the ecological environment.

(1)

CO₂ emission reduction

$$F_{1n}={\displaystyle \sum _{i=1}^n}(\Delta Q_{1ni}\times l\times {\lambda }_l)$$

(4)

F_1n: The emission reduction brought because the nth green technology uses the local construction materials and reduces the transportation;

$\Delta Q_{1ni}$: The quantity of the nth green technology using the ith local construction material;

$l$: Non-local material transportation mileage;

${\lambda }_l$: CO₂ emission factor of unit mileage.

$$F_{2n}={\displaystyle \sum _{i=1}^n}\Delta Q_{ni}\times {\lambda }_i$$

(5)

$F_{2n}$: Emission reduction brought by nth green technology saving material;

$\Delta Q_{1ni}$: Saving amount of ith material of nth green technology;

${\lambda }_i$: CO₂ emission factor of ith material.

$$F=F^{\prime }+F^{″}$$

(6)

$F^{\prime }$: construction emission reduction;

$F^{″}$: Operation emission reduction.

$$F^{″}={\displaystyle \sum _{n=1}^n}{\displaystyle \sum _{i=1}^n}(\Delta Q_{ni}\times \lambda )$$

(7)

$\Delta Q_{ni}$: Reduced consumption amount of nth energy per year.

(2)

Ecological improvement

$$\mathrm{F}={\displaystyle \sum _{n=1}^n}(S_{Gn}\times K_{Gn}\times T_n\times l)$$

(8)

$S_{Gn}$: The area of the nth green plant more than the reference building (m²);

$K_{Gn}$: Average ability of green vegetation absorbing CO₂ when the nth plant is in effective photosynthesis;

$T_n$: Days of effective photosynthesis of the nth plant in the whole year;

$l$: Life cycle of the green building.

Afterwards, the total environmental benefit realized by green building can be known. In some circumstances, in considering the environmental benefit of green building, the CO₂ reduction amount is used as the calculation and analysis unit, having problems of not frequently used, not easily to be compared with other benefits. Therefore, the environmental benefit of green building can be monetized. After considering the monetization of the environmental benefit, the monetization environment benefit of green building can be calculated by the following formula:

$$B{F}_{currency}=BF\times P$$

(9)

where P is the monetization factor.

2.2.3. Calculation Rules of Social Benefit

The social benefit of green building is a vague implicit benefit. It is hard to realize complete and accurate quantification. In considering the relevant quantification method, this paper concludes the social benefit of green building BS into the benefits brought to the physical health of the inhabitants, the corresponding saved benefits brought to the municipal public utilities by savings of the green building, and the improvement of the entire social benefits by promoting the whole society to advance to the sustainable target for calculation and analysis. The social benefit is hard to be quantified. Therefore, the aspiration investigation approach is relied for the quantification, so as to investigate how much excessive amount the habitats are willing to pay for the green building project. The excessive part is exactly the quantified expression of the benefit obtained by the habitats inhabiting in green building, so that the required social incremental benefit can be further concluded.

3. Measurement Comparison Model of Green Building

3.1. DEA Model of Green Building Input-Output Benefit Measurement

Data Envelopment analysis (DEA) is a non-parametric analysis tool to evaluate the relative effectiveness of multiple input and output decision making units (DMU) by establishing a linear programming model, and to judge whether DMU is located on the leading edge of production possibility set [50]. The green building input-output items are shown in Figure 1.

The commonly used analytical models for DEA methods are CCR and BCC [51]. Assuming there are n decision making units, the CCR model with non-Archimedes infinitesimals to evaluate the relative effectiveness of each decision making unit is as follows:

$$\{\begin{array}{c}\begin{array}{c}\min \left[\theta -\epsilon \left({\mathrm{ê}}^T{S}^{-}+{\mathrm{ê}}^T{S}^{+}\right)\right]\\ {\displaystyle \sum _{j=1}^n}{X}_j{\lambda }_j+S^{-}=\theta X_0\end{array}\\ {\displaystyle \sum _{j=1}^n}{Y}_j{\lambda }_j-S^{+}=Y_0\\ {\lambda }_j\ge 0,S^{-}\ge 0,S^{+}\ge 0,j=1,2,\dots n\end{array}$$

(10)

where $X_j={\left(X_{1j},X_{2j},\dots ,X_{mj}\right)}^T$ and $Y_j={\left(Y_{1j},Y_{2j},\dots ,Y_{sj}\right)}^T$ are input vector and output vector of ${\mathrm{DMU}}_j$, ${\lambda }_j$ is the proportion of the jth decision making unit in the hypothetical effective decision making unit combination constructed for ${\mathrm{DMU}}_{j0}$; $S^{-}={\left(s_1^{-}, s_2^{-},\dots s_m^{-}\right)}^T$ is the slack variable. Adding the constraint ${\sum }_{j=1}^n{\lambda }_j=1$ to the above model, an input-oriented BCC model assuming changes in returns to scale is obtained, as follows:

$$\{\begin{array}{c}\begin{array}{c}\min \left[\theta -\epsilon \left({\mathrm{ê}}^T{S}^{-}+{\mathrm{ê}}^T{S}^{+}\right)\right]\\ {\displaystyle \sum _{j=1}^n}{X}_j{\lambda }_j+S^{-}=\theta X_0\end{array}\\ \begin{array}{c}{\displaystyle \sum _{j=1}^n}{Y}_j{\lambda }_j-S^{+}=Y_0\\ {\displaystyle \sum _{j=1}^n}{\lambda }_j=1\end{array}\\ {\lambda }_j\ge 0,S^{-}\ge 0S^{+}\ge 0j=1,2,\dots n\end{array}$$

(11)

The efficiency $\theta \left(0\le \theta \le 1\right)$ calculated under the CCR model is the overall efficiency. This evaluation efficiency represents both technical efficiency and scale efficiency. The evaluation efficiency ${\theta }_T\left(0\le {\theta }_T\le 1\right)$ under the BCC model only represents the technical efficiency. The ratio of the comprehensive technical efficiency $\theta$ to the technical efficiency ${\theta }_T$ is the scale efficiency ${\theta }_S$.

Green building projects with $\theta =1$, indicating that the technology is effective and scale is effective. Effective technology indicates that the input and output of the project has reached the best, and there is no redundancy in input and insufficient output; effective scale indicates that the project is in a production mode with constant returns to scale, and the proportion of input increase is consistent with the increase in output. If θ < 1, the project is relatively ineffective. The reason for the ineffectiveness may not only come from the unreasonable input-output ratio, but also the scale factor.

3.2. Efficiency Evaluation Model Based on DEA-Entropy Weight Method

In the DEA evaluation model, $h_j=\frac{u^T{Y}_j}{v^T{X}_j},j=1,2,\dots ,n$ is the evaluation efficiency index, while, the corresponding input index and output index weight coefficients, $v={\left(v_1,v_2,\dots ,v_n\right)}^T$ and $u={\left(u_1,u_2,\dots ,u_n\right)}^T$ are subjective, which will lead to the lack of scientific and accuracy of the results to a certain extent. The introduction of the entropy weight method can solve this problem very well. Entropy weight method is a relatively rational weighting method, which gives objective weight according to the degree of index variability. The function of the entropy value is to measure the degree of information disorder. The larger the entropy value, the larger the disordered program, the less the amount of information, and the smaller the weight. When the entropy weight method is used to assign the index weight, it can eliminate certain subjective influences and obtain more objective and scientific results. Therefore, this paper combines the DEA model with the entropy weight method to construct an input-output benefit evaluation model of the incremental cost of green building.

This paper evaluates the incremental cost-effectiveness of multiple green buildings of similar scale, that is, objectively describes the investment level, resource allocation, and environmental benefits of multiple similar green buildings. In this process, multiple indicators need to be comprehensively evaluated. The entropy method can not only assign scientific values to each indicator, but also reflect the degree of correlation between indicators. Its weight value assignment procedure is as follows:

Assuming there are n samples and m evaluation indicators, the initial data matrix $\mathrm{X}={\left(x_{ij}\right)}_{m\times n}$ can be formed. The larger the gap between the same set of evaluation indicators is, the greater the impact of the indicator change on efficiency evaluation will be reflected. However, if this set of indicators is zero, this indicator is invalid. The information entropy energy can be scientifically assigned to each index according to the discrete degree of the utility value of each evaluation index, which lays a foundation for the evaluation of the comprehensive efficiency of the data envelopment method. The operation steps are as follows:

The first step is to standardize the indicator, suppose there are n green buildings in a certain area and m efficiency evaluation index systems,$r_{ij}\left(i=1,2,\dots ,n,j=1,2,\dots ,m\right)$ is the value of the ith sample on the jth indicator. It is assumed that the ideal value of evaluation index j is $r_j$, and the specific value is determined by the difference in the properties of evaluation index. When the indicator is positive, the larger the value of $r_j$, the better, and it is recorded as $r_{jmax}$; when the indicator is negative, the smaller the value of $r_j$ is, the better, and it is recorded as $r_{jmin}$. The ideal value of the evaluation index is obtained from the initial matrix $X={\left(x_{ij}\right)}_{m\times n}$, and the extreme value of the evaluation index is obtained through horizontal comparison. Define $r_j^{\prime }$ as the proximity of $r_j$, for positive indicators, $r_{ij}^{\prime }=\raisebox{1ex}{$r_{ij}$}\!\left/ \!\raisebox{-1ex}{$r_{jmax}$}\right.$, for negative indicators $r_{ij}^{\prime }=\raisebox{1ex}{$r_{ijmin}$}\!\left/ \!\raisebox{-1ex}{$r_{ij}$}\right.$.

The second step is calculate the proportion of each indicator, and denote it as $f_{ij}$,

$$f_{ij}=\frac{r_{ij}^{\prime }}{{{\displaystyle \sum }}_{i=1}^n{r}_{ij}^{\prime }}$$

(12)

The third step is to calculate the entropy value of the jth index, and denote it as $H_j$,

$$H_j=k{\displaystyle \sum _{i=1}^n}{f}_{ij}\ln f_{ij}$$

(13)

The fourth step is to calculate the information utility value of the jth index and denote it as $g_i$. For the jth index, the greater the information utility value of the index value in each sample, the greater the effect of the index on the sample evaluation. The formula for calculating the information utility value is, $g_j=1-H_j$. Finally, calculate the index weight value:

$$w_j=\frac{g_j}{{{\displaystyle \sum }}_{j=1}^m{g}_j}$$

(14)

The results and discussion may be presented separately, or in one combined section, and may optionally be divided into headed subsections.

4. Empirical Analysis of Input-Output Benefit of Green Buildings

Because the decision-making units in the DEA model must be of the same type and comparable units. Therefore, through the project site survey and network information collection, this paper collects the relevant data of 8 green building cases that have obtained the three-star mark, and evaluates the collected green building projects (DMU1–DMU8) respectively.

4.1. Selection of Input and Output Indicators

In order to improve the ecological efficiency of green buildings and obtain higher benefits with less resource input, the input index should be selected as a smaller index, and the output index should be selected as a larger index. Combined with the construction of the previous index system, the input indicators for the incremental cost-benefit evaluation of green houses are selected as follows: the incremental cost in the preparation stage X1, the incremental cost in the construction stage X2, the incremental cost in the operation stage X3, and the incremental cost in the demolition recovery stage X4, The output indicators are: economic benefit Y1, environmental benefit Y2, and social benefit Y3.

4.2. Data Collection and Processing

In this paper, eight typical cases of green buildings are selected for empirical research. The original data of the projects are collected through fieldwork, internet information retrieval, etc. and substituted into the calculation model of incremental cost incremental benefit of green buildings set in Section 2 to obtain the incremental cost and incremental benefit under each dimension. The specific results are shown in

Table 4. The value of each indicator of the project entity.

DMU	Input Indicator (10,000 yuan)				Output Indicator (10,000 yuan)
	X1	X2	X3	X4	Y1	Y2	Y3
DMU1	159.06	5053.79	690.44	46.34	3846.72	901.61	564.04
DMU2	191.41	3633.32	101.78	36.4	2020.31	805.56	806.32
DMU3	120.56	4451.45	898.94	53.32	3176.71	901.55	461.7
DMU4	80.12	3472.45	586.6	46.4	3023.2	780.1	266.6
DMU5	154.3	6052.1	632.2	35.8	5340.1	1260	640.3
DMU6	206.4	5800.3	1250.5	73.1	3260.8	897.2	609.3
DMU7	221.9	7683.2	854.6	52.1	6443.2	721.2	674.1
DMU8	211.48	7361.43	888.41	45.71	6133.36	703.25	621.81
Value	168.15	5438.51	737.93	48.65	4155.55	871.31	580.52
$r_{jmax}$	221.9	7683.2	1250.5	73.1	6443.2	1260	806.32

.

First, standardize the input-output index data to obtain the standardized matrix of the index:

$$\mathrm{X}=\left[\begin{array}{cccccccc}0.72& 0.86& 0.54& 0.36& 0.70& 0.93& 1.00& 0.95\\ 0.66& 0.47& 0.58& 0.45& 0.79& 0.75& 1.00& 0.96\\ 0.55& 0.08& 0.72& 0.47& 0.51& 1.00& 0.68& 0.71\\ 0.63& 0.50& 0.73& 0.63& 0.49& 1.00& 0.71& 0.63\end{array}\right]$$

$$\mathrm{Y}=\left[\begin{array}{cccccccc}0.60& 0.31& 0.49& 0.47& 0.83& 0.51& 1.00& 0.95\\ 0.72& 0.64& 0.72& 0.62& 1.00& 0.71& 0.57& 0.56\\ 0.70& 1.00& 0.57& 0.33& 0.79& 0.76& 0.84& 0.77\end{array}\right]$$

Then, according to the Formula (12), the proportion of input and output indicators can be calculated as shown in

Table 5. The weight value of green building input and output indicators.

	Indicator	Input Indicator				Output Indicator
${\mathit{f}}_{\mathit{i}\mathit{j}}$		X1	X2	X3	X4	Y1	Y2	Y3
$f_{1j}$		0.12	0.12	0.12	0.12	0.12	0.13	0.12
$f_{2j}$		0.14	0.08	0.02	0.09	0.06	0.12	0.17
$f_{3j}$		0.09	0.10	0.15	0.14	0.10	0.13	0.10
$f_{4j}$		0.06	0.08	0.10	0.12	0.09	0.11	0.06
$f_{5j}$		0.11	0.14	0.11	0.09	0.16	0.18	0.14
$f_{6j}$		0.15	0.13	0.21	0.19	0.10	0.13	0.13
$f_{7j}$		0.16	0.18	0.14	0.13	0.19	0.10	0.15
$f_{8j}$		0.16	0.17	0.15	0.12	0.18	0.10	0.13

:

Let n = 8, k = 0.48, so according to Formulas (13) and (14), the entropy value of input and output indicators can be calculated: $H_X^T=\left[\begin{array}{ccc}0.98& 0.98& \begin{array}{cc}0.95& 0.99\end{array}\end{array}\right]$,$H_Y^T=\left[\begin{array}{ccc}0.97& 0.99& 0.98\end{array}\right]$. Then, the entropy weights of the input and output indicators can be obtained:${\phi }^{\gamma }=\left[\begin{array}{ccc}0.12& 0.11& \begin{array}{cc}0.33& 0.07\end{array}\end{array}\right]$, ${\mu }^{\gamma }=\left[\begin{array}{ccc}0.20& 0.05& 0.11\end{array}\right]$.

The weight of each index in the BCC model is calculated by the entropy weight method, and then the input and output index data in the BCC model are substituted into the calculation using the Deap2.1 software (Center for Efficiency and Productivity Analysis Department of Econometrics University of New England Armidale. The location is New South Wales, Australia), and the input and output validity analysis results of the DEA model can be obtained as shown in

Table 6. The results of input and output validity based on DEA model.

Firm	θ	vrste	Scale	NRIS
DMU1	0.904	0.919	0.984	irs
DMU2	1.000	1.000	1.000	-
DMU3	0.960	0.965	0.995	irs
DMU4	1.000	1.000	1.000	-
DMU5	1.000	1.000	1.000	-
DMU6	0.750	0.762	0.984	irs
DMU7	0.928	1.000	0.928	drs
DMU8	0.926	0.980	0.945	drs
Mean	0.934	0.953	0.980

Note: represents comprehensive technical efficiency; vrste represents pure technical efficiency; scale represents scale efficiency (drs: diminishing returns to scale, -: constant returns to scale, irs: increasing returns to scale).

:

4.3. Green Building Incremental Cost Benefit Evaluation

4.3.1. Comprehensive Technical Effectiveness Analysis

The comprehensive technical efficiency value can reflect the proportion of the current investment level of the decision making unit that can reach the maximum output value. The comprehensive technical efficiency value can take 1 as the reference standard to judge whether the decision-making unit is effective. When the comprehensive technical value is equal to 1, it means that under the current technical conditions, the output value reaches the optimal level, and the decision-making unit is feasible. When the comprehensive technical efficiency value is less than 1, it means that under the current technical conditions, the output value has not reached the optimal value, and there is still room for continuous improvement.

From a longitudinal analysis, it can be seen from Figure 2 that the comprehensive technical effectiveness of the eight green building projects presents different trends. Taking the average value of comprehensive efficiency as a reference value, the following conclusions can be drawn:

(1)

The comprehensive technical efficiency value of DMU2, DMU4 and DMU5 is 1, which indicates that the three decision making units are effective, and according to Table 6, there is no redundant input or insufficient output, that is, the comprehensive performance of these three green building projects reaches the best level. Its incremental cost input-output benefit has reached a relatively ideal state. In theory, these green building projects have no incentive to increase cost input, they can improve the innovation level of green technology measures on the basis of maintaining the existing status, and strive to find ways to reduce incremental costs.

(2)

Similarly, it can be seen from the figure above that the comprehensive efficiency values of the remaining five decision-making units are all less than 1, indicating that these five decision-making units are invalid decision-making units, and the results of the output benefits corresponding to their incremental costs are not ideal. The reason for the ineffectiveness may be the unreasonable ratio of input and output, or the scale factor of the decision-making unit. The project construction party should strengthen the integration of resources, improve the allocation of production resources, improve the management level, and increase the benefits and income.

(3)

The average value of the comprehensive efficiency value of the eight projects is 0.934 as the dividing line, and the projects with higher than 0.934 are considered as high-efficiency projects, and those lower than 0.934 are considered as low-efficiency projects. According to the appeal classification, DMU2, DMU3, DMU4, and DMU5 are high-effectiveness items, and DMU1, DMU6, DMU7, and DMU8 are low-effectiveness items. This shows that the DMU1, DMU6, DMU7, and DMU8 projects have excess input resources and insufficient output capacity during the construction process. Among them, DMU6 is taken as an example to analyze the redundancy and deficiency of its input and output, as shown in

Table 7. The detailed results of the DMU6 slack variable.

Indicators	Original Value	Radial Movement	Slack Movement	Projected Value
X1	206.4	−53.697	−2.754	149.949
X2	5800.300	−1508.991	0.000	4291.309
X3	1250.500	−325.327	−535.699	389.474
X4	73.100	−19.018	−15.099	38.983
Y1	3260.800	0.000	0.000	3260.496
Y2	897.200	0.000	33.396	930.496
Y3	609.300	0.000	0.000	609.300

.

From the appeal data, it can be seen that the incremental cost of the green building preparation stage X1, the incremental cost of the construction stage X2, the incremental cost of the operation stage X3, and the incremental cost of the demolition and recovery stage X4 all have excess investment. (The redundancy value of X1 is 53.697, the redundancy value of X2 is 1508.991, the redundancy value of X3 is 325.327, the redundancy value of X4 is 19.018) and the environmental benefit Y2 has the phenomenon of insufficient output. This shows that the utilization rate of DMU6 resource input is too low. The construction unit should improve its own technical level, introduce advanced green construction technology to reduce the cost input in the construction stage, and at the same time improve the enterprise management level and reduce the cost input in the operation stage.

4.3.2. Pure Technical Effectiveness Analysis

Through the DEA model calculation, the comparative analysis of pure technical efficiency values can be obtained as shown in the following Figure 3. From the vertical analysis, it can be seen that the technical performance values of decision making units, DMU2, DMU4, DMU5 and DMU7 are all stable and larger than the mean value. However, the pure technical efficiency of decision-making units DMU1 and DMU6 is lower than the average performance value of decision-making units, which indicates that the incremental cost of these two green building projects has not been fully utilized, and there is a phenomenon of waste of investment. The construction unit should adjust their strategies and use the incremental costs for high-efficiency green building technical measures to improve the input-output ratio. In addition, the pure technical efficiency values of DMU7 and DMU8 are relatively effective, but their comprehensive benefits are ineffective operation. Therefore, the ineffectiveness of DMU7 and DMU8 is mainly caused by the problems of scale.

4.3.3. Scale Performance and Returns to Scale Analysis

According to the related concepts of DEA, scale effectiveness is determined by the ratio of comprehensive effectiveness to pure technical effectiveness, as shown in Figure 4.

Through longitudinal comparison, it can be seen that the scale efficiency values of DMU7 and DMU8 are lower and lower than the average level of scale efficiency of decision making units, which indicates that the project’s resource investment and management instability during the development process have resulted in a low project scale return value. And from Table 6, it can be found that the DMU7 and DMU8 green building projects have the problem of diminishing returns to scale, indicating that investing a certain scale of incremental cost only obtains less incremental benefits. Then the construction units should appropriately shrink the cost, reduce the cost input in the construction and operation stages, strengthen the internal management of the enterprise, try to carry out green technology innovation, and improve the conversion rate of incremental costs. In addition, it can be seen that DMU6 is in a state of increasing returns to scale. For projects with increasing returns to scale, an appropriate increase in input on the basis of existing input can increase output by a higher proportion. This type of green building has the enthusiasm to increase the cost input, but it is necessary to pay attention to the appropriateness of the increase in input, so as to prevent the occurrence of excessive input costs resulting in the decline of output benefits.

5. Conclusions

This paper starts from the definition of green building. Firstly, it analyzes its incremental costs and incremental benefits from the perspective of the whole life cycle. Secondly, the DEA-entropy weight method is used to evaluate and analyze the input and output benefits of incremental costs, to identify the effectiveness of DEA, so as to facilitate developers to make timely adjustments and improve the input and output benefits of incremental green building costs, so as to stimulate developers’ willingness to develop green monitoring and promote the development of green building. The main conclusions as follows:

(1)

For projects with poor overall performance, that is, projects whose DEA evaluation result is relatively ineffective, it indicates that the green building has excess resources, which is not conducive to the promotion and use of green buildings. Developers should strengthen the internal management level of the enterprise and the green technology innovation ability, control the investment scale in an appropriate scale state, increase the input-output ratio, and maximize its incremental cost effectiveness. The government needs to organize experts and scholars to study the incremental costs and benefits of green buildings, and standardize the relevant indicators in the construction process, so as to promote the optimization of incremental costs and benefits, and at the same time provide reasonable economic subsidies to consumers to encourage consumption buy green houses.

(2)

For projects with better performance, that is, projects whose DEA evaluation result is relatively effective, it shows that the green building can obtain the output of large incremental benefit through the input of small incremental cost In this case, developers should, on the basis of accurately positioning their own advantages, give full play to their advantageous technologies and make continuous improvements, and at the same time strengthen technological innovation and improve the application level of various types of green building technical measures. While, the government can further mobilize the enthusiasm of green building developers through policy support, green star subsidies and other means.

The incentive mechanism for green building development is mainly based on the idea of sustainable development and based on the concept of eco-city, and proposes corresponding incentive measures to better promote the development of green buildings. In the case of the invalid DEA for green buildings, this paper will put forward some policy suggestions for the development of green buildings:

(1)

Support the establishment of green building development legal system. As the deepening and extension of building energy-saving work, the working basis of promoting green building development is only Green Building Action Plan and other department regulations issued by the relevant ministries and commissions of the State Council. The related work of green building is hard to coordinate various departments to form the joint work force effectively, thus reducing the relevant policy implementation forces. No legal system has been established to support the development of green building in China. This is also one of the restriction factors resulting in the slow and unbalanced development of green building in China.

(2)

Formation of green building market atmosphere. In Australia, in addition to Green Star, there are still numerous other companies and organizations providing green building assessment systems, such as Green Magazine which possesses a certain practical significance. Similarly, the stabilizing effect of non-profit organizations in the US deserves our reference in the green development process. On the contrary, although some large-scale real estate enterprises in China have enacted green building development strategies, the quantity and area of the projects obtaining green building label are expanding rapidly year by year, the projects which can truthfully reflect the practical effect of green building are very few, accounting about 6% of the total. Aimed at unqualified green building practical using quality and insufficient post-assessment in energy-saving effect, the comprehensive benefit displayed by green building is not significant. Combined with the under advertised green building philosophy of the social public, various circles of the society are hindered to have correct understanding to the essential connotation of green building. It is the priority among priorities to develop green building in China by promoting green building concept and penetrating green concept into the public.

(3)

Enhance green building ability construction. Green building in China lays particular stress on green building exhibition and brand effect, resulting in a higher technology application grade. This is determined by China economic development level and green building development stage as well as green building development value dominant demand. Therefore, it is required to accelerate to promote green technology practice accumulation and expansion on such basis, drive the industrial development, ensure to bring authentic effect by the subsequent operation, such as positively introduce advanced enterprises and enhance the improvement effect of their advanced experiences to local enterprises.

In short, improving the input-output benefit of the incremental cost of green buildings can better promote the development of green buildings. In the cost-benefit analysis of green buildings, this paper fails to consider the impact of market prices and regional factors on the incremental cost-benefit of green buildings, which makes the research limited. In the future, in-depth research can also be conducted on the quantification of incremental costs and incremental benefits of green buildings, as well as the input-output benefit evaluation of incremental costs.