Application of an Integrated DEMATEL-ISM-BN and Gray Clustering Model to Budget Quota Consumption Analysis in High-Standard Farmland Projects

Abstract

To overcome the absence of a standardized budget quota system for high-standard farmland projects and the resultant extended compilation cycles and high workloads, this study systematically analyzes quota consumption and innovatively proposes an integrated DEMATEL-ISM-BN and gray clustering analytical model. Through a literature review and engineering feature analysis, a hierarchical factor system was established, encompassing six dimensions (environmental, technical, labor, machinery, material, and management) and 24 indicators. The DEMATEL-ISM method quantified factor weights and structured them into a five-level hierarchy, while Bayesian networks (BNs) enabled probabilistic productivity predictions (29% conservative, 45% moderate, and 26% advanced). Gray clustering was integrated to derive a comprehensive representative consumption value, and validation across six regions demonstrated a comprehensive productivity index of 0.986 (CV = 2.6%) for 17 earthwork projects, confirming model robustness. This research constructs a standardized “factor structure analysis–probabilistic deduction–regional clustering” framework, providing a theoretical foundation for precise budget compilation in high-standard farmland and proposing a novel methodological paradigm for quota consumption research.

1. Introduction

High-standard farmland is not only a new-age “fertile soil project” armed with hard-core technology but also a systematic solution for integrating food security, ecological security, and rural revitalization. High-standard farmland refers to “a type of high-quality farmland with good topographical conditions, supporting farmland power, complete facilities, water conservation and high efficiency, easy to mechanize operations, fertile soil, ecological and environmental friendliness, and strong disaster resistance, and capable of adapting to modern agricultural production and management methods”. Its construction content mainly includes infrastructure projects (such as field improvement, farmland roads, drainage and irrigation systems, ecological protection and farmland environment maintenance, power transmission and distribution facilities, etc.) and engineering projects to enhance the strength of the land (such as soil improvement projects). In order to effectively implement the policy of “storing grain in the land and storing grain in technology”, alleviate the shortage of water resources, and promote sustainable development, the construction of high-standard farmland has become the focus of national investment. In this context, the significance and role of high-standard farmland projects have become more and more prominent [1,2]. However, in adopting quota standards from large- and medium-scale water conservancy projects, high-standard farmland projects encounter challenges such as inconsistent productivity levels and missing sub-items. The absence of targeted quota standards leads to deviations in investment management. With the expansion of the scale and complexity of the high-standard farmland project, the complex pattern of high input and high output exacerbates the contradiction between the production efficiency and quality requirements, and accurate project cost prediction is crucial for evaluating the feasibility of the project and selecting the optimal design program, It can also ensure the accurate setting of investment limit targets during the construction design phase, laying a solid foundation for the smooth progress of subsequent work, which directly affects the economic feasibility and overall quality of the project [3,4,5]. Based on this, the scientific construction of a high-standard farmland project budget quota system shows its significant necessity. Given the complex construction conditions and relatively small scale of these projects, determining quota consumption presents significant challenges. Developing a precise and efficient standard quota system will facilitate rational resource allocation and accurate cost estimation, supporting budget formulation and feasibility studies while optimizing financial planning and maximizing profitability.

Research on quota compilation has shifted away from traditional models, integrating modern technological approaches and empirical methods to enhance the accuracy and efficiency of quota estimation. Recent advancements in this field have yielded several breakthroughs. Ref. [6] adopts a hierarchical analysis (AHP) method to establish an indicator system for screening, which realizes a more structural and consistent selection of indicators; refs. [7,8] adopts the Monte Carlo technique to simulate the generation of a large number of sample data for the situation of poor sample data, which improves the accuracy of the estimation results and provides theoretical and data support for the formal compilation of construction quotas; refs. [9,10,11] adopt the fuzzy closeness and gray correlation degree method to select the most representative samples as the basis for quota determination, in which the model can accurately calculate the unknown quantity of sample engineering quota consumption and the productivity level of the corresponding quota of the target project, solving the problem of the cumbersome and lengthy quota preparation process, providing a certain reference for the reasonable preparation of quota; and in the case of sufficient sample data, refs. [12,13] use a BP neural network and add the improved algorithm of the neural network model for quota determination, making full use of its nonlinear learning and generalization ability, and further improving its operation speed and prediction accuracy for the future of quota preparation data information technology to provide methodological support and efficiently meet real-time demands by offering the possibility to be dynamically updated and predictable social development needs, in line with the development of the times.

Studies addressing regional differences in productivity levels for quota consumption determination incorporate gray clustering methods. Zheng Xiuzhen proposed an improved analytic hierarchy process (IAHP) combined with gray clustering to classify projects based on similar construction techniques, followed by a data sliding translation method to adjust the raw statistical data within each category, improving comparability [14]. Yang Liu developed a comprehensive evaluation system integrating three-scale and gray clustering theories, ensuring practical applicability and broad regional representativeness through systematic data integration and objective analysis of productivity differences across regions [15]. Gao Jinyuan combined the fuzzy analytic hierarchy process (FAHP) with gray clustering analysis to clarify weight relationships among influencing factors, achieving more precise and detailed analytical outcomes [16]. Despite these advancements, certain limitations persist in quota compilation research. First, the current studies primarily rely on the AHP or entropy weight method (EWM) to determine indicator weights, overlooking interdependencies among indicators and limiting the weighting approach’s comprehensiveness. Further exploration of more suitable weighting methods is needed. Second, limited quantitative research has been conducted on evaluating gray-category quota levels, leading to inaccuracies in probability estimates and potential biases in decision-making.

Most of the existing modeling studies use a combination of some decision-making tools, for example, refs. [17,18] use a Decision-Making Trial and Evaluation Laboratory (DEMATEL)–Interpretative Structural Modeling (ISM) approach to identify the causal hierarchy of influencing factors, which helps to clarify the logic of the system, but is unable to perform uncertainty reasoning and quota productivity level assessment; refs. [19,20] use ISM–Bayesian network (BN) to realize probabilistic reasoning in structured systems, which improves the model’s ability to describe the dynamic evolution of risk, but does not consider the interactions between factors. This model presents descriptive power, but does not consider the strength of influence between factors and cannot scientifically determine factor weights. These methods are effective in structural analysis and probabilistic inference, but few attempts have been made to integrate both causality and uncertainty modeling within a unified and comprehensive framework that does not fully reflect the complexity among multiple factors and construction scenarios in a given area.

The present study adopts an innovative approach by first identifying key influencing factors in high-standard farmland projects’ quota consumption and applying the DEMATEL method for quantification. The hierarchical relationships among influencing factors are then analyzed using ISM. A combined ISM and BN model is applied to evaluate quota productivity levels, integrating gray clustering methods. The DEMATEL-derived indicator weights and the BN-derived probabilities of gray-category levels are incorporated into a DEMATEL-ISM-BN and gray clustering-based quota consumption estimation model. This model determines budget quota consumption, enabling the calculation of high-standard farmland project budget quotas. Many studies have utilized the DEMATEL-ISM-BN model—for example, refs. [21,22,23] utilized the model to better understand the causality and hierarchy of complex systems when dealing with uncertainty in complex systems compared to the traditional partial tool combination model. However, research in quota preparation is still limited. In contrast, this study is the first to apply DEMATEL-ISM-BN specifically for modeling quota consumption in high-standard farmland projects and innovatively integrates gray clustering to solve the problem of inter-geographic differences in quota productivity levels. This cross-method integration forms a standard yet flexible modeling framework, which, by combining causal logic, probabilistic reasoning, and regional variation adaptation, goes beyond the traditional weight-based models alone, and provides greater robustness and reliability in the face of fuzzy data, while enhancing the scientific validity and depth of application of traditional quota compilation methods, providing a new way of thinking about the study of quota consumption.

2. Materials and Methods

2.1. Establishment of Quota Consumption-Influencing Factor Index System

The advancement of quota productivity levels in actual construction operations is reflected in the numerical values of quota consumption, which are influenced by multiple factors. Through a systematic analysis of the current implementation of high-standard farmland projects and the key elements of productivity, six dimensions were identified as the primary factors affecting quota consumption.

(1)

Environmental factors

The quota consumption level during construction is directly related to environmental quality, encompassing geographical, natural, social, and cultural aspects. The dynamic local climate, surface conditions, and site layout influence construction efficiency. Extreme environmental conditions may lead to fluctuations in worker productivity, increased equipment energy consumption, and extended process cycles.

(2)

Technological factors

The complexity of construction processes, the advancement of construction techniques, and the innovation of process methods significantly impact quota consumption. Quota productivity levels inherently reflect construction technology standards. Improvements in construction efficiency often rely on technological innovation. Compared with traditional methods, technological upgrades through process optimization and machinery iteration enhance productivity while reducing labor, material, and equipment consumption.

(3)

Labor factors

The influence of labor on quota consumption is reflected in factors such as workforce allocation, skill levels, work motivation, years of experience, technical proficiency, previous experience with similar projects, and adaptability to the working environment. Younger workers with strong technical skills tend to achieve higher efficiency due to greater adaptability to new technologies and processes and higher overall motivation. In contrast, older workers typically exhibit lower productivity due to slower adaptation to emerging technologies.

(4)

Mechanical factors

Routine maintenance and the condition of machinery largely determine mechanical quota consumption. Equipment that lacks systematic maintenance and has not undergone timely inspections faces a higher probability of unexpected failures, leading to unplanned downtime and prolonged project durations. Additionally, worker expertise, equipment power, compatibility, specifications, operational efficiency, and rental models all directly impact quota consumption.

(5)

Material factors

Multiple variables influence material quota consumption, with key determinants being material quality, transportation distance, processing precision, specifications, and supply conditions. Projects requiring high-precision processing and superior craftsmanship demand additional labor and mechanical resources.

(6)

Construction organization and management

This category includes aspects such as the rationality of organizational structure, quality of completion inspections, and effectiveness of management decisions. A well-structured construction organization ensures the feasibility of construction plans, optimizes site layout, enhances resource utilization efficiency, and minimizes resource wastage in production processes, thereby improving overall operational efficiency [24].

Due to the lack of sufficient research to analyze the influencing factors of the fixed consumption of high-standard farmland projects, reviewing other studies on quota; drawing on the local standards of some provinces and cities; and taking into account the opinions of the experts, the actual construction conditions, and the engineering characteristics of high-standard farmland projects, we establish the influencing factors of the fixed consumption of high-standard farmland projects from the six dimensions of the environment, technology, artificial labor, machinery, materials, and management of the construction organization, forming an indicator system. To ensure that the experts reach a consensus on the most relevant quota consumption-influencing factors in high-standard farmland construction, we used two rounds of the Delphi method [25]. In the first round, structured questionnaires for the secondary indicators were distributed to one expert from each of three different units in six regions: the Northeast Region, the Southeast Region, the Northwest Region, the Southwest Region, the Middle and Lower reaches of the Yangtze River, and the Yellow and Huaihai Regions. This formed a total of 18 experts, each of whom had more than 10 years of relevant experience. The experts rated the importance of each indicator on a 5-point Likert scale.

After analyzing the results, we calculated the mean score and coefficient of variation (CV) for each indicator. We then presented the experts with the anonymized summary results of the first round (mean score, standard deviation) and invited them to reassess their ratings in the second round. Convergence of responses was significantly higher in the second round, with Kendall’s W = 0.78, indicating better agreement among experts. Based on the selection criteria (mean ≥ 3.5, CV ≤ 0.3), 24 metrics were finally identified for subsequent DEMATEL-ISM-BN modeling. The details are shown in Figure 1.

2.2. Construction of the Quota Consumption Determination Model Based on DEMATEL-ISM-BN and Gray Clustering

To enhance the scientific accuracy and rationality of quota consumption estimation, a combined model integrating the DEMATEL, ISM, BN, and gray clustering methods was developed. This model refines the determination of quota consumption by systematically analyzing and quantifying influencing factors. The workflow of the integrated model is illustrated in Figure 2.

2.2.1. DEMATEL-Based Calculation of Indicator Weights

The DEMATEL method was initially introduced by the Geneva Battelle Memorial Institute between 1972 and 1976. DEMATEL quantifies the strength of interdependencies, calculates centrality indices, and normalizes the data to derive the weights of influence of each factor within the system. The calculation steps for determining indicator weights using DEMATEL are outlined as follows [26]:

(1)

Collection of Expert Opinions

A panel of m experts is formed, and each expert evaluates the pairwise influence of n factors. The impact of factor i on factor j is rated on a scale from 0 to 4, where 0 indicates “no influence,” 1 represents “minor influence,” 2 denotes “moderate influence,” 3 signifies “strong influence,” and 4 indicates “very strong influence.” Based on the expert assessments, an n×n non-negative matrix is constructed, as shown in Equation (1):

$$X^k=\left[\begin{array}{c}{\chi }_{ij}^k\end{array}\right],$$

(1)

where k represents the index of the expert participating in the evaluation. Since there are m experts, a total of m square matrices are obtained.

(2)

Construction of the Direct Influence Matrix

The average matrix is computed based on the evaluation results provided by m experts, as shown in Equation (2), to derive the internal direct influence matrix Z:

$$z_{ij}={\displaystyle \frac{1}{m}}{\sum }_{i=1}^m{x}_{ij}^k,$$

(2)

(3)

Normalization of the Direct Influence Matrix

Using Equations (3) and (4), a normalized direct influence matrix Y is obtained, with all matrix elements constrained within the range [0, 1]:

$$Y=\lambda \ast Z,$$

(3)

$$\mathrm{or}$$

$${\left[\begin{array}{c}{y}_{ij}\end{array}\right]}_{n\times n}=\lambda {\left[\begin{array}{c}{z}_{ij}\end{array}\right]}_{n\times n},$$

(4)

$$\lambda =\mathrm{M}\mathrm{i}\mathrm{n}\left[{\displaystyle \frac{1}{\underset{1\le i\le n}{max}\sum _{j=1}^n\left|z_{ij}\right|}},{\displaystyle \frac{1}{\underset{1\le j\le n}{max}\sum _{i=1}^n\left|z_{ij}\right|}}\right],$$

(5)

According to Markov chain theory, Y^m represents the power of matrix Y, including Y², Y³, …, and Y^∞, ensuring the convergence of the matrix inverse solution, as shown in Equation (6).

$$\mathrm{l}\mathrm{i}{\mathrm{m}}_{\mathrm{m}\to \mathrm{\infty }}{Y}^m={\left[0\right]}_{n\times n},$$

(6)

(4)

Construction of the Total Influence Matrix

The total influence matrix T is obtained by processing the normalized direct influence matrix using the following Equation:

$$T=Y{\left(I-Y\right)}^{-1},$$

(7)

where I represents the identity matrix.

(5)

Determination of Influence Factor Centrality and Causality

For a given factor i, the centrality ϑ_i is obtained by summing its influence on other factors and the influence it receives. The causality ψ_i is determined by calculating the difference between these two values. The specific relationship is expressed as follows:

$$T=\left[\begin{array}{c}{t}_{ij}\end{array}\right],i,j=\mathrm{1,2},\dots ,n,$$

(8)

$${\vartheta }_i={\sum }_{j=1}^n{t}_{ij}+{\sum }_{j=1}^n{t}_{ji},i=\mathrm{1,2},\dots ,n,$$

(9)

$${\psi }_i={\sum }_{j=1}^n{t}_{ij}-{\sum }_{j=1}^n{t}_{ji},i=\mathrm{1,2},\dots ,n,$$

(10)

where t_ij represents the total influence exerted by factor i on factor j.

If ψ_i > 0, the factor is classified as a causal factor, exerting a significant influence on other factors. Conversely, if ψ_i < 0, it is categorized as an outcome factor, primarily influenced by other elements in the system.

(6)

Weight Calculation

The traditional DEMATEL method is primarily used to analyze interactions among factors. However, the pairwise comparison matrix utilized in the AHP or Analytic Network Process (ANP) is fundamentally consistent with the initial direct influence matrix constructed in DEMATEL. Given this similarity, the quantitative data generated by DEMATEL can also be applied to weight determination. Various computational models have been proposed for weight calculation within the DEMATEL framework. Previous studies have employed different approaches. Reference [27] determined indicator weights by normalizing centrality ϑ_i, while reference [28] directly used ϑ_i for weight determination. Reference [29] calculated weights based on the total influence matrix, whereas references [30,31] integrated both centrality ϑ_i and causality ψ_i to derive factor weights. To fully incorporate expert knowledge, the present study adopts a combined approach based on the methodological frameworks of references [26,27]. The evaluation indicators’ centrality and causality are computed, leading to a weight distribution scheme containing n elements. The final weight vector is expressed as w = (w₁, w₂, …, w_n). The calculation formula is given by the following:

$$w_i={\displaystyle \frac{\sqrt{{\vartheta }_i^2+{\psi }_i^2}}{\sum _{i=1}^n\sqrt{{\vartheta }_i^2+{\psi }_i^2}}}$$

(11)

2.2.2. Construction of the ISM Model

The ISM is a systematic analytical approach used to examine the hierarchical relationships among factors in complex systems. By constructing a reachability matrix and performing hierarchical decomposition, ISM transforms ambiguous system relationships into a clear multi-layered structural model. Integrating DEMATEL with ISM effectively addresses the limitations of insufficient consideration of inter-factor interactions, enhancing the objectivity and reliability of the derived weights.

According to reference [32], the ISM analysis follows these steps:

(1)

Based on the total influence matrix T obtained from the DEMATEL method, the overall influence matrix H is computed as

H = T + I,

(12)

(2)

Using the threshold value β determined from the total influence matrix T, the adjacency matrix Q is constructed as

$$Q=\left\{\begin{array}{lll}1& Z_{ij}\ge \beta \left(i=\mathrm{1,2},\dots ,n;j=\mathrm{1,2},\dots ,n\right)& \\ 0& Z_{ij}<\beta \left(i=\mathrm{1,2},\dots ,n;j=\mathrm{1,2},\dots ,n\right)& \end{array}\right.$$

(13)

(3)

The reachability matrix K is constructed to satisfy the following condition:

$$K={\left(\begin{array}{c}Q+I\end{array}\right)}^{k-1}\ne {\left(\begin{array}{c}Q+I\end{array}\right)}^k\ne {\left(\begin{array}{c}Q+I\end{array}\right)}^{k+1},$$

(14)

(4)

The reachability set R is determined based on the following rule: in the reachability matrix K, if the element in row K, column j, is 1, then the factor corresponding to column j is included in the reachability set. The antecedent set P is constructed similarly. In matrix K, if the element in row K_i, column j, is 1, then the factor corresponding to row j is included in the antecedent set. The intersection set consists of elements that simultaneously belong to the reachability set R and the antecedent set P.

(5)

A stepwise decomposition is applied to verify whether each influencing factor meets the specified conditions. If the conditions are satisfied, the factors contained in R_i are identified as the highest-level elements and are subsequently removed from the reachability matrix. This iterative process continues until all factors are fully assigned to hierarchical levels, ensuring a structured representation of their relationships.

$$R_i=R_i\cap P_i\left(i=\mathrm{1,2},\dots ,n\right),$$

(15)

where R_i represents the reachability set of the i-th factor, while P_i denotes the antecedent set of the i-th factor.

2.2.3. Construction of the BN Model

A BN is a probabilistic graphical model that applies statistical methods to address uncertainties within a system. It is based on Bayesian theory [33]. One of the primary advantages of the BN is its ability to simplify joint probability calculations. Given a set of independent discrete random variables, denoted as $U=\{X_1,X_2,\dots ,X_n\}$, the joint probability distribution P can be expressed using the chain rule and conditional independence as

$$P\left(U\right)={\prod }_{i=1}^{n}P\left(X_i|pa\left(X_i\right)\right)(i=\mathrm{1,2},\dots n),$$

(16)

The BN model constructed in this study is based on an analysis of the causal pathways influencing quota consumption. The hierarchical structure derived from the ISM method is transformed into a probabilistic inference model.

2.2.4. Construction of the Gray Clustering Model

In the process of constructing the gray clustering model, assume there are m clustering indicators, n clustering objects, and k distinct gray categories. Each clustering object i (i = 1, 2, …, n) is assessed using clustering indicators j (j = 1, 2, …, m), and observational data x_ij are obtained. A whitening weight function is then applied to compute the clustering coefficient of each object in relation to category k (k = 1, 2, …, s), enabling a comprehensive evaluation and classification of planning attributes. The overall process consists of the following core steps [15]:

(1)

For each indicator j, the most representative attribute point λk in gray category k must be identified. This reference point is selected based on the highest probability position within the gray category and serves as the basis for calculating weights.

(2)

The value range of indicator j is divided into adjacent subintervals according to practical considerations. These intervals are denoted as [λ₁,λ₂], …, [λ_k,λ_k+1], …, [λ_s,λ_s+1]. By sequentially connecting adjacent interval boundaries, the final triangular whitening weight function f_j^k(·) for indicator j corresponding to gray category k is constructed, as illustrated in Figure 3.

(3)

Based on the observed value x of indicator j, the whitening weight function f_j^k(·) is defined to determine the membership of the gray category:

$$f_j^k\left(x\right)=\left\{\begin{array}{lll}0& x\notin \left[{\lambda }_{k-1},{\lambda }_{k+1}\right]& \\ {\displaystyle \frac{x-{\lambda }_{k-1}}{{\lambda }_k-{\lambda }_{k-1}}}& x\in ({\lambda }_{k-1},{\lambda }_k]& \\ {\displaystyle \frac{{\lambda }_{k+1}-x}{{\lambda }_{k+1}-{\lambda }_k}}& x\in \left({\lambda }_k,{\lambda }_{k+1}\right)& \end{array}\right.,$$

(17)

(4)

The DEMATEL method is applied to compute the weight η_j, which reflects the relative importance of each influencing indicator in the comprehensive gray clustering analysis.

(5)

Computation of the comprehensive gray clustering coefficient σ_i^k.

$${\sigma }_i^k={\sum }_{j=1}^m{f}_j^k\left(x_{ij}\right){\eta }_j,$$

(18)

(6)

The category assignment for object i is determined by identifying the maximum gray clustering coefficient. If $\underset{1\le k\le s}{max}\left\{{\sigma }_i^k\right\}={\sigma }_i^{k\star }$, then object i is classified into gray category k^*.

3. Case Study

Based on the indicator system defined in Figure 1, the integrated modeling workflow demonstrated in Figure 2, and the methodology described above, an empirical case study will be carried out in this section, combining the national high-standard farmland projects through the DEMATEL-ISM-BN and gray clustering method to construct a mathematical calculation model, building a mathematical model system for the national high-standard farmland projects of fixed consumption.

Engineering projects from six major regions, Northeast China, Southeast China, Northwest China, Southwest China, the Middle and Lower Yangtze River Basin, and the Huang-Huai-Hai Region, were selected for analysis. Covering the major geographic and ecological subdivisions of China’s high-standard farmland projects, these are representative and widely adaptable, and they can comprehensively reflect the differences in quota consumption under different natural, economic, and management conditions. The local standards of the High-Standard Farmland Construction Guidelines (DB21/T 3722) [34] from Liaoning Province were referenced, along with ongoing construction data. The sub-item “manual earth excavation (Type I and II soil)” was chosen as an empirical case to systematically illustrate the quota consumption calculation process based on the proposed mathematical model.

3.1. Calculation of Indicator Weights Using the DEMATEL Method

To facilitate data analysis, expert scoring was used to quantify the relationships among influencing factors. Based on the established indicator system for quota consumption, a five-level scoring system was applied. These scores were used to represent the degree of mutual influence between factor pairs. In order to improve the reliability of the results, we included two experts from different units in each of the Southeast, Northwest, Southwest, Middle and Lower Yangtze River, and Yellow and Huaihai zones, as well as three in the Northeast—a total of 13, all having worked in the field of high-standard farmland for more than 10 years—to score the degree of influence between the influencing factors in a bidirectional way, and then, we used the Delphi method in the form of a questionnaire to assess the direct influence relationship between the factors. And, in order to eliminate the individual differences in the scoring of experts, the arithmetic mean of the 13 matrices was calculated and rounded to the nearest integer [35]. This process yielded the final direct influence matrix, represented by Equation (2), as shown in

Table 1. Direct influence matrix.

Factors	A1	A2	A3	A4	A5	B1	B2	…	E3	E4	F1	F2	F3	F4	F5
A1	0	1	1	0	1	1	1	…	0	0	0	0	0	0	1
A2	2	0	2	2	2	2	2	…	1	1	1	2	1	1	1
A3	3	3	0	1	2	2	1	…	1	1	1	1	2	1	1
A4	1	2	2	0	2	1	1	…	1	1	1	2	2	1	1
A5	2	2	2	3	0	1	1	…	1	1	1	2	2	1	2
B1	3	3	2	1	2	0	3	…	2	2	2	2	2	2	2
B2	2	2	2	2	2	3	0	…	2	2	1	2	2	2	2
B3	2	2	2	1	1	3	2	…	2	2	2	2	2	2	3
B4	1	2	2	1	2	2	2	…	2	2	2	2	2	2	2
C1	1	1	1	1	1	2	2	…	1	1	1	2	2	2	1
C2	1	1	1	0	1	1	1	…	1	0	1	1	1	1	1
C3	1	1	1	1	1	2	2	…	1	1	2	3	2	2	1
D1	1	1	1	1	1	2	1	…	1	1	1	1	1	0	0
D2	1	1	1	1	1	2	2	…	1	2	1	1	1	1	1
D3	2	2	2	1	2	2	2	…	2	2	2	2	1	1	1
E1	2	2	2	1	1	2	2	…	1	2	2	1	1	1	3
E2	1	2	2	1	1	3	2	…	1	2	1	1	1	1	2
E3	1	2	2	2	2	1	0	…	0	2	1	2	1	1	1
E4	0	1	1	0	0	2	2	…	1	0	1	1	1	1	1
F1	1	1	1	1	1	2	2	…	1	1	0	2	2	2	1
F2	1	2	2	2	2	2	2	…	2	1	2	0	3	3	1
F3	2	2	2	1	2	2	2	…	1	1	3	3	0	3	2
F4	1	2	2	1	1	2	2	…	1	1	3	3	3	0	2
F5	2	3	2	2	2	2	2	…	2	3	3	3	3	2	0

.

Based on Equations (9) and (10), the cause degree and centrality of each factor were calculated using MATLAB 2019. The indicator weights were then determined according to Equation (11). The computed results are presented in

Table 2. Results of the DEMATEL analysis of the factors affecting rationed consumption.

Primary Indicator	Secondary Indicator	Centrality	Cause Degree	Primary Indicator Weight	Secondary Indicator Weight	Ranking	Factor Attribute
A	A1	2.8790	−1.0614	0.1780	0.0298	24	Result
	A2	4.2698	−0.4008		0.0416	13	Result
	A3	4.0198	−0.3138		0.0391	15	Result
	A4	3.2039	0.1154		0.0311	23	Cause
	A5	3.7549	−0.0197		0.0364	19	Result
B	B1	5.6252	0.5656	0.2025	0.0548	1	Cause
	B2	5.0019	0.4894		0.0488	4	Cause
	B3	5.3460	0.5187		0.0521	2	Cause
	B4	4.8020	0.4358		0.0468	5	Cause
C	C1	4.6457	−0.0722	0.1176	0.0451	9	Result
	C2	3.3590	−0.9045		0.0337	21	Result
	C3	3.9883	0.2979		0.0388	16	Cause
D	D1	3.7446	−0.6409	0.1251	0.0369	18	Result
	D2	4.3422	−0.6048		0.0425	12	Result
	D3	4.7137	0.1010		0.0457	7	Cause
E	E1	4.5242	−0.1956	0.1585	0.0439	10	Result
	E2	4.8056	−0.0135		0.0466	6	Result
	E3	3.2489	−0.1119		0.0315	22	Result
	E4	3.7499	0.0537		0.0364	20	Cause
F	F1	3.8317	−0.1707	0.2182	0.0372	17	Result
	F2	4.5087	−0.1094		0.0438	11	Result
	F3	4.6784	0.3706		0.0455	8	Cause
	F4	4.2599	0.4590		0.0416	14	Cause
	F5	5.0277	1.2120		0.0502	3	Cause

.

Based on the centrality and cause degree values from Table 2, a cause–effect diagram of influencing factors was generated using MATLAB, as shown in Figure 4.

3.2. Establishment and Analysis of the ISM Model for Influencing Factors

Based on the total influence matrix, the overall influence matrix was computed using Equation (12). The arithmetic mean and standard deviation of the elements in the total influence matrix were calculated, and their sum was used to determine the threshold value, yielding β = 0.12. The reachability matrix was derived using MATLAB, and hierarchical decomposition was performed to construct a multi-level hierarchical structure model for the influencing factors in quota consumption. The resulting ISM model is illustrated in Figure 5.

3.3. Estimating the Probability of Different Quota Productivity Levels Using BN

3.3.1. Data Collection

A quota productivity level questionnaire was designed based on Figure 1, and relevant data questionnaires were collected through distribution; 61 questionnaires were distributed, 59 were retrieved, and 40 were valid questionnaires. Based on the generic risk assessment method in ref. [36], the risk level was divided into three orders. Among them, the higher risk level corresponded to the lower level of fixed productivity. The probability of occurrence of risk and the degree of hazard were used as the vertical and horizontal axes of the risk matrix, where the larger the value, the deeper the corresponding degree, as shown in Figure 6. The R1 region is located in the low-risk zone (lower left corner) of the risk matrix, which indicates higher stability and thus corresponds to the “advanced” region of the quota productivity level; and the R3 region is located in the high-risk zone in the upper right corner. R3, in the upper right corner of the high-risk zone, corresponds to the “conservative type”; R2 is the middle transition zone, corresponding to the “more advanced type”. The classification standard comprehensively refers to the practice of risk control in project management, combined with the practical experience of high-standard farmland projects, and has been agreed upon by experts through discussions, with methodological basis, interpretability, and support from experts in the field; it can also effectively reflect the differences in the level of productivity of the quota between regions.

In order to ensure the reliability and validity of the research data, SPSS 25.0 statistical software was used to test the reliability of the questionnaire data. Among them, the reliability test measured the internal consistency of the data through Cronbach’s α coefficient, and the test results (

Table 3. Cronbach’s alpha coefficient in reliability analysis.

Cronbach’s Alpha	Standardized Cronbach’s Alpha Coefficient	Number of Items
0.960	0.961	24

) showed that the value of the α coefficient was greater than 0.9, which indicated that the data were extremely reliable. In terms of a validity test, it was verified by the Kaiser–Meyer–Olkin sampling suitability measure (KMO) and Bartlett’s spherical test, and the results showed that the KMO value was 0.944 > 0.8 and Bartlett’s spherical test was 0 < 0.001, as shown in

Table 4. Results of validity analysis.

KMO Measure of Sampling Adequacy		0.899
Bartlett’s Test of Sphericity	Approximate Chi-Square	1670.613
	Degrees of Freedom	276
	Significance	0.000

, which indicated that there was a significant correlation between the variables, and the sample data were suitable for factor analysis. Combining the results of the reliability test, the questionnaire data can be analyzed by Bayesian network analysis.

3.3.2. BN Model Probability Calculation

Based on the multi-level structure diagram derived from the ISM model, a corresponding BN model for quota productivity levels was developed using GeNIe 2.1 Academic, a Bayesian inference software. Due to the lack of prior data, the state dimensions of the 24 nodes in the system, High Risk (High), Medium Risk (Medium), and Low Risk (Low), were uniformly set to an equal probability distribution (each assigned 1/3). Standardized data were input through the software interface to match the node values and complete the parameter training process. Following computation, the model generated the final probability distribution of quota productivity levels, as shown in Figure 7. The probability of a conservative productivity level was 29%, a moderately advanced level was 45%, and an advanced level was 26%.

3.4. Calculation of Comprehensive Quota Consumption Based on the Gray Clustering Model

3.4.1. Establishment of the Indicator Evaluation Matrix

An evaluation was conducted on the construction conditions across six regions in China, with scores assigned to each influencing indicator. Through the practical research experience of a number of experts, the specific scoring rules for consumption-related indicators were finalized, as shown in

Table 5. Scoring criteria for quota consumption-influencing indicators.

Main Influencing Factors	Scoring Criteria		Score
Environment	Temperature and weather suitability	Neither temperature nor weather is suitable	0
		Either temperature or weather is suitable	1
		Suitable air temperature and weather	2
	On-site working conditions	Unsuitable due to site conditions (e.g., water accumulation, muddy, frozen ground)	1
		Site conditions are suitable	2
	Site cleanliness (storage of construction tools and materials)	Poor site conditions due to human factors	0
		Construction tools are neatly stored	1
		Functional areas are well planned and clean	2
	Surrounding environment	Surrounding environment is chaotic	1
		Surrounding environment is comfortable	2
	Dynamic changes in the project environment	Complex and dynamic environment	0
		Either complex or dynamic environment	1
		Simple and stable environment	2
Technology	Construction technical difficulty	High difficulty	1
		Medium difficulty	2
		Low difficulty	3
	Construction process steps	Non-standard operation, missing steps	0
		Steps are incomplete or lack precision	1
		Steps are complete but operations have minor flaws	2
		Steps are detailed and operations comply strictly	3
	Compliance with design requirements	Not compliant	0
		Basically compliant	1
		Fully compliant	2
	Dependence on technical processes (whether one process depends on the previous one)	High dependence on previous steps	1
		Low dependence on previous steps	2
Labor	Skill proficiency	Low	1
		Relatively low	2
		Relatively high	3
		High	4
	Years of experience	No relevant work experience	0
		Less than 3 years	1
		3–5 years	2
		More than 5 years	3
	Rationality of labor distribution	Poor distribution of skilled and general workers, lack of cooperation	0
		Skilled and general workers are well allocated and cooperate well	1
		Coordination between workers and machinery is moderate	2
		Coordination between workers and machinery is excellent	3
Machinery	Age of machinery	Old machinery	1
		Moderately aged machinery	2
		New machinery	3
	Technological advancement of machinery	Outdated	1
		Moderately advanced	3
		Advanced	5
	Applicability of machinery	Not applicable	0
		Moderately applicable	1
		Fully applicable	2
Materials	Material quality	Poor	0
		Good	1
		Excellent	2
	Processing precision	Low precision	1
		Medium precision	2
		High precision	3
	Transportation distance of materials	Long distance	1
		Moderate distance	2
		Short distance	3
	Specification and size compliance	Does not meet the standard	0
		Basically meets standard	1
		Fully meets standard	2
Construction Organization and Management	Rationality of organizational structure (e.g., excessive hierarchy or departments)	Unreasonable	0
		Moderately reasonable	1
		Reasonable	2
	On-site management level	Low	0
		Medium	1
		High	2
	Rationality of project management decisions	Unreasonable and inefficient	0
		Moderately reasonable and efficient	1
		Reasonable and highly efficient	2
	Changes in project organization	Changes in personnel and organizational structure	0
		No changes in personnel and organizational structure	1
	Completion inspection results	Rework required	0
		Repairs needed	1
		Qualified	2
		Excellent	3

, which reflects the differentiation and identification of the various types of indicators.

The quota consumption research team, in collaboration with the project sites, conducted an assessment of consumption indicators across six regions based on their actual conditions. The final evaluation results are presented in

Table 6. Realized scores of consumption-influencing indicators across six project regions.

Primary Indicator	Northeast	Southeast	Southwest	Middle and Lower Yangtze River	Huang-Huai-Hai	Northwest
Environment	10	9	8	9	3	7
Technology	10	10	9	6	2	8
Labor	9	10	6	9	6	8
Machinery	7	9	5	7	7	7
Materials	6	10	6	6	2	7
Construction Management	9	9	7	7	5	6

.

The evaluation matrix X for labor quota consumption-influencing indicators across the six project regions is given as follows:

$$\mathrm{X}=\left[\begin{array}{cccccc}10& 10& 9& 7& 6& 9\\ 9& 10& 10& 9& 10& 9\\ 8& 9& 6& 5& 6& 7\\ 9& 6& 9& 7& 6& 7\\ 7& 8& 8& 7& 7& 6\\ 3& 2& 6& 7& 2& 5\end{array}\right],$$

3.4.2. Establishment of the Triangular Whitening Weight Function

The influencing indicators of quota consumption were classified into three levels, Poor, Moderate, and Good, based on the construction conditions in different regions. The corresponding scoring intervals were set as [1, 4] for Poor, [4, 7] for Moderate, and [7, 10] for Good.

According to the gray category classification principle, within the full scoring range [1,10], the midpoints of each sub-interval were selected as λ₁ = 2.5, λ₂ = 5.5, and λ₃ = 8.5. The three classification levels, Poor, Moderate, and Good, were mapped to conservative, moderately advanced, and advanced quota productivity levels at the construction sites. Based on this correspondence, the triangular whitening weight function for each gray category was constructed using Equation (18) as follows:

$${\mathrm{f}}_{\mathrm{j}}^1\left(\mathrm{x}\right)=\left\{\begin{array}{lll}0& , \mathrm{x}\notin \left[\mathrm{1,5.5}\right]& \\ \left(\mathrm{x}-1\right)/1.5& , \mathrm{x}\in \left(\mathrm{1,2.5}\right]& \\ \left(5.5-\mathrm{x}\right)/3& , \mathrm{x}\in \left(\mathrm{2.5,5.5}\right)& \end{array}\right.,$$

(19)

$${\mathrm{f}}_{\mathrm{j}}^2\left(\mathrm{x}\right)=\left\{\begin{array}{lll}0& , \mathrm{x}\notin \left[\mathrm{2.5,8.5}\right]& \\ \left(\mathrm{x}-2.5\right)/3& , \mathrm{x}\in \left(\mathrm{2.5,5.5}\right]& \\ \left(8.5-\mathrm{x}\right)/3& , \mathrm{x}\in \left(\mathrm{5.5,8.5}\right)& \end{array}\right.,$$

(20)

$${\mathrm{f}}_{\mathrm{j}}^3\left(\mathrm{x}\right)=\left\{\begin{array}{lll}0& , \mathrm{x}\notin \left[\mathrm{5.5,10}\right]& \\ \left(\mathrm{x}-5.5\right)/3& , \mathrm{x}\in \left(\mathrm{5.5,8.5}\right]& \\ \left(10-\mathrm{x}\right)/1.5& , \mathrm{x}\in \left(\mathrm{8.5,10}\right)& \end{array}\right.$$

(21)

(1) Calculation of the gray clustering comprehensive coefficient. Using Equation (17), the gray clustering comprehensive coefficient σ_i^k was computed for each clustering object. The calculated clustering comprehensive coefficient values are presented in

Table 7. Evaluation of clustering results.

Clustering Object	Conservative	Moderately Advanced	Advanced	σik *	Assigned Gray Category
Northeast	0	0.1946	0.3128	0.3128	Advanced
Southeast	0	0	0.3475	0.3475	Advanced
Southwest	0.0208	0.4731	0.4385	0.4731	Moderately advanced
Middle and Lower Yangtze River	0	0.4725	0.4289	0.4725	Moderately advanced
Huang-Huai-Hai	0.4254	0.3720	0.0882	0.4254	Conservative
Northwest	0	0.4660	0.5339	0.5339	Advanced

.

(2) Determination of Quota Consumption Standards Based on Productivity Levels. The raw construction site data from the six major regions, Northeast, Southeast, Southwest, Middle and Lower Yangtze River, Huang-Huai-Hai, and Northwest, were normalized, including data processing, anomaly identification, and outlier removal. The calculated average labor quota values for these regions were 4.97, 3.51, 5.33, 6.18, 6.39, and 2.78 workdays, respectively. According to the gray clustering analysis results (Table 7), the Northeast, Southeast, and Northwest regions were classified as advanced, the Southwest and Middle and Lower Yangtze River regions as moderately advanced, and the Huang-Huai-Hai region as conservative. Using the BN-based productivity probability distribution, a layered weighting method was applied to compute the comprehensive labor quota standard. The final representative labor quota value was determined as 5.42 workdays, based on the following formula: (4.97 + 3.51 + 2.78)/3 × 26% + (5.33 + 6.18)/2 × 45%+6.39 × 29% = 5.42.

Similarly, we can calculate the fixed productivity level index of high-standard farmland projects represented by 17 “earthworks”, and then finalize the fixed standard of high-standard farmland projects for the “earthworks” by using the local standard High-Standard Farmland Construction Guidelines from Liaoning Province, as can be seen in

Table 8. Results of the calculation of the productivity level index for the “earthwork” quota for high-standard farmland projects.

Serial No.	Designation	Unit	Representative Labor Quota Value/Workdays	Liaoning Local Standard Value/Workdays	Quota Productivity Level Index
1	Manual excavation (Class I and II soils)	100 m3	5.42	5.49	0.987
2	General sludge	100 m3	49.86	50.70	0.983
3	Hand-dug trenches (Class I and II soils)	100 m3	16.63	17.17	0.969
…	…	…	…	…	…
15	2 m3 excavator digging and loading dump trucks to transport soil	100 m3	0.82	0.80	1.019
16	1 m3 loader digging and loading dump trucks to transport soil	100 m3	1.22	1.20	0.935
17	Tree-felling	100 plants	13.53	14.47	0.986
Composite value of the productivity level index for the “earthworks” quota for agricultural water conservancy projects					0.986

.

The research of agricultural water conservancy project quota is carried out with the labor quota of “earthwork” as the research object, and its quota productivity index is calculated to be 0.986, based on which the quota consumption of the relevant subheads of earthwork in the local standard of Liaoning Province’s “Guidelines for the Construction of High-standard Agricultural Fields” is corrected, so that the budgetary quota system of the agricultural water conservancy project can be constructed in line with the characteristics of the region. In the field of engineering practice, for the heterogeneous characteristics of sub-projects, the hierarchical measurement model of the quota productivity level index (including classification modules of earthwork, stonework, concrete work, etc.) is constructed, which realizes the breakthrough of quota measurement accuracy through the hierarchical analysis of sub-projects, and the model has significant superiority over the traditional overall estimation method, which effectively overcomes the regional variability of the standard of quota.

4. Results and Discussion

4.1. Factor Analysis

4.1.1. Analysis of Causal Factors

A factor is classified as a causal factor when its cause degree is greater than zero, indicating a significant influence on other factors. As shown in Table 2, the causal factors in the quota consumption-influencing factor system include the surrounding environment (A4), construction technical difficulty (B1), construction process steps (B2), compliance with design requirements (B3), technical process dependency (B4), rationality of labor allocation (C3), machinery applicability (D3), specification compliance (E4), rationality of project management decisions (F3), organizational changes (F4), and completion inspection results (F5). These factors are ranked by causal strength as follows: F5 > B1 > B3 > B2 > F4 > B4 > F3 > C3 > A4 > D3 > E4. Among these, completion inspection results (F5) and construction technical difficulty (B1) exhibit the highest causality, exerting substantial influence on other factors and serving as primary causal drivers.

F5, as the leading causal factor, affects the final stage of a project and indirectly influences material consumption and labor allocation efficiency through a “quality feedback–process correction” loop mechanism. The high causality of B1 underscores the pivotal role of technical difficulty in resource allocation. Complex technical requirements increase machinery (D3) and labor (C3) costs while amplifying the coordination challenges between technical dependencies (B4), construction organization (F4), and process steps (B2). The ranking of other causal factors, such as compliance with design requirements (B3) and rationality of project management decisions (F3), further highlights the intertwined effect of technical (B-class) and construction management (F-class) factors as the primary drivers of quota consumption overruns. By quantifying the causal factor hierarchy, this study provides a priority intervention strategy for quota management. Optimizing acceptance standards (F5) and conducting early-stage technical difficulty assessments (B1) can minimize the chain reaction of consumption fluctuations. At the practical level, establishing a “technology–quality–organization” integrated control mechanism is recommended to enhance quota productivity levels.

4.1.2. Analysis of Result Factors

A factor is classified as a result factor when its cause degree is negative, indicating that it is significantly influenced by other factors. As shown in Table 2, the result factors in the quota consumption-influencing factor system include air temperature (A1), on-site working conditions (A2), site cleanliness (A3), dynamic changes in the project environment (A5), skill proficiency (C1), years of experience (C2), machinery age (D1), machinery advancement (D2), material quality (E1), processing precision (E2), transportation distance (E3), rationality of organizational structure (F1), and site management level (F2). These factors are ranked in descending order of absolute cause degree as follows: C2 > D1 > D2 > A2 > A3 > E1 > F1 > E3 > F2 > C1 > A5 > E2. Among these, years of experience (C2) and machinery age (D1) are the most susceptible to external influence, making them the primary result factors affecting quota consumption.

The high dependency of these result factors indicates that C2 and D1 are not independent variables but rather terminal manifestations of upstream causes such as technical management and organizational decisions. The ranking further highlights the sensitivity of technical indicators (D1, D2) and labor-related indicators (C2) to productivity fluctuations. For C2 and D1, short-term solutions include targeted training programs and equipment leasing strategies to mitigate immediate constraints. However, long-term improvements require addressing fundamental causes, such as enhancing decision-making rationality (F3) and standardizing technical processes (B4), to reduce passive reliance on these result factors. Resolving quota productivity challenges requires shifting from reactive responses to result indicators to a proactive control system centered on technical management and organizational decision-making. Establishing a feedforward control framework can interrupt the transmission of negative impacts, leading to substantial improvements in quota productivity levels.

4.1.3. Factor Weight Analysis

As shown in Table 2, the secondary indicators ranked by weight in descending order are the following: B1 > B3 > F5 > B2 > B4 > E2 > D3 > F3 > C1 > E1 > F2 > D2 > A2 > F4 > A3 > C3 > F1 > D1 > A5 > E4 > C2 > E3 > A4. The primary indicators, ranked by overall weight from highest to lowest, are construction organization and management (F) > technology (B) > environment (A) > materials (E) > machinery (D) > labor (C). Among the secondary indicators, the top five factors are construction technical difficulty (B1), compliance with design requirements (B3), completion inspection results (F5), construction process steps (B2), and technical process dependency (B4). Notably, four of these top five indicators belong to the technical category (B1, B3, B2, B4), highlighting technical execution as a critical control point for resource consumption. From the primary indicator perspective, the highest-weighted category is construction organization and management (F), suggesting that its influence on quota consumption is systemic and overarching. By quantifying these indicators, this study uncovers the “technology-driven” nature of quota consumption and the “management regulation” leverage effect, providing a layered intervention framework for optimizing quota productivity at its root.

4.1.4. Summary of Results

Summarizing the above results, the influence structure of fixed consumption is clearly visible. The dimensions of technology (B) and management (F) are always the core factors of causality, outcome dependence, and weighting, with technical execution determining the allocation of resources and construction management structure regulating work efficiency. This suggests that improving the level of fixed productivity requires attention to technical standardization, organizational stability, and process rationality.

In summary, targeted interventions should prioritize high causality, high-weighted indicators to achieve strong control, and those wanting to improve work should focus on creating technology-driven, management-enabled systems. These findings support the shift from reactive to proactive quota control.

4.2. Hierarchical Analysis of Influencing Factors

The multi-level hierarchical structure model of the factors influencing quota consumption (Figure 6) reveals that the top layer, L1, comprises 13 indicators: A4, A5,C3, E3, D1, D2, A1, A2, A3, C2, E4, F1, and F2. These indicators are the direct factors in forming and enhancing quota productivity levels. The intermediate layers L2, L3, and L4 serve as transitional stages for improving quota productivity, acting as connectors within the system. Indicators in these layers influence the entire system through the top-level indicators and are directly affected by the lower-level indicators. Specifically, L2 includes D3; L3 comprises C1; and L4 encompasses construction B1, B2, B3, B4, E1, E2, F3, and F5. The L5 layer, positioned at the lowest level of the hierarchical model, is the foundation of the quota productivity levels. The key factor at this level, F4, is fundamental in shaping overall productivity. Its influence extends through multiple pathways, affecting both intermediate- and top-level indicators, ultimately impacting the entire system.

Various influencing mechanisms exist within this multi-level hierarchical structure model. Based on the degree of influence in the ISM model, these mechanisms can be categorized into explicit mechanisms, other deep-seated influencing mechanisms, and non-deep-seated influencing mechanisms.

Fundamental mechanisms originate from the lowest level (L5) of the hierarchical model and gradually propagate to top-level indicators (L1). A representative causal pathway is project organizational changes (F4) → technical process dependency (B4) → on-site management level (F2). Frequent organizational restructuring (F4) may disrupt technical standard implementation (B4), leading to fluctuations in on-site management (F2). This chain of effects demonstrates how instability at the foundational level can be amplified through technical management, ultimately resulting in resource inefficiencies at higher levels, highlighting the importance of institutional stability. Secondary mechanisms typically originate from technical management improvements, enhancing overall system performance, for example, coordinated optimization of technical process dependency (B4) and construction process steps (B2) → enhanced completion inspection outcomes (F5) → reduced specification errors (E4). Standardizing construction processes (B2) helps eliminate technical gaps (B4), improve acceptance rates (F5), and minimize material wastage caused by dimensional inaccuracies (E4). This pattern suggests that mid-level technical and management optimization can enhance quota productivity independently of its foundational factors.

Non-fundamental influence mechanisms mainly reflect self-coordination among mid-to-high-level technical and management indicators to improve quota productivity and consumption efficiency. Unlike the fundamental mechanisms, these do not rely on organizational structure or institutional drivers but achieve resource efficiency gains through internal technological adaptation (e.g., C1 → D2 pathway). Success in this approach requires a strong adaptive capacity and dynamic adjustment strategies. For instance, integrating worker skill training (C1) with equipment upgrades (D2), establishing real-time feedback loops between skill assessment systems (C1) and mechanical performance databases (D2), and triggering targeted skill training when equipment error rates exceed thresholds can enhance operational efficiency.

In summary, enhancing quota productivity requires both deep institutional reforms and continuous technology–skill coordination. Only by reinforcing policy-driven technological advancements, leveraging management to unlock endogenous resource potential, and strengthening system resilience through redundancy design can traditional quota constraints be overcome, enabling a self-evolving productivity framework and a self-optimizing consumption cycle for sustainable development.

4.3. Probability Analysis of Quota Productivity Levels

Based on the hierarchical ISM model, risk matrix method, and BN model, the distribution of quota productivity levels and the logical relationships among influencing factors were analyzed. The results indicate a “high in the middle, low at both ends” probability distribution pattern, with 29% of projects classified as conservative, 45% as moderately advanced, and 26% as advanced.

The highest probability (45%) for moderately advanced productivity suggests that most high-standard farmland projects in China have reached an above-average level in technology application, management efficiency, and resource allocation, meeting basic agricultural production needs while still offering room for improvement. The combined probability of the moderately advanced and advanced levels reaching 71% highlights significant progress in water conservancy modernization, yet regional disparities may hinder efficiency in certain areas. Targeted infrastructure planning and modernization efforts are needed to reduce regional imbalances through policy incentives and financial support. Overall, high-standard farmland projects in China are undergoing a transition from moderately advanced to fully modernized systems. Addressing the shortcomings in conservative regions and further leveraging advanced technologies will be key to building an efficient and sustainable water conservancy system.

4.4. National Comprehensive Analysis of Representative Quota Consumption

Construction projects from six major regions, Northeast, Southeast, Northwest, Southwest, the Middle and Lower Yangtze River, and the Huang-Huai-Hai region, were selected to evaluate regional differences in quota consumption. Using the “manual excavation of earthwork (Class I and II soil)” as a case study, this study applied DEMATEL-derived primary index weights to compute gray clustering coefficients and conducted a refined analysis of regional labor quota consumption. The results highlight the innovative application of mathematical modeling in quota formulation. Data analysis reveals that the Northwest (2.78 workdays), Northeast (4.97 workdays), and Southeast (3.51 workdays) regions demonstrate higher productivity levels, likely benefiting from advancements in mechanization or optimized construction management. The Southwest (5.33 workdays) and Middle–Lower Yangtze (6.18 workdays) regions fall into the moderately advanced category, reflecting the impact of terrain and hydrological conditions on construction efficiency. The Huang-Huai-Hai region (6.39 workdays), categorized as conservative, suggests the presence of specific constraints affecting construction performance. The BN model produced a representative quota value of 5.42 workdays, with a 1.3% deviation from the current Liaoning standard of 5.49 workdays, validating the model’s scientific reliability. More importantly, the findings underscore a shift from an experience-based quota setting to a data-driven approach. From a technical perspective, the results confirm the explanatory power of multi-index quantification in regional quota variations. From a practical standpoint, they provide a scientific basis for dynamically adjusting quota standards. The regional clustering gradient observed in the analysis suggests that construction management authorities should implement a zone-specific dynamic adjustment strategy, compressing quotas in advanced regions to enhance efficiency while conducting diagnostic assessments in conservative regions to address performance limitations.

Extending to the 17 earthwork measurements, Figure 8 reveals the comparative relationship between the model measured values and the local standard values. The measured curve and the standard value curve show a high degree of convergence in most of the subheads; the data show that the domain of measured coefficient values of each subhead is stably distributed in the interval of [0.935,1.019], the integrated value of the coefficients is 0.986, and it has a low degree of dispersion (the coefficient of variation CV = 2.6%). In addition, the deviation of the quota standard derived from the model with the actual regional work efficiency is controlled within 1.4%, and this result not only confirms the engineering adaptability of the model but also reflects the excellent stability and engineering reliability of the measurement system through its small coefficient of variation.

5. Conclusions

To address the lack of standardization in quota formulation for high-standard farmland projects, a comprehensive modeling framework integrating DEMATEL-ISM-BN methods with gray clustering analysis was developed. This study reveals the multidimensional mechanisms influencing quota consumption and regional variations. Through a systematic analysis of the nonlinear relationships among influencing factors, three key conclusions were drawn:

5.1. Structural Analysis of Influencing Factors

Based on the literature review and expert consultation, 24 influencing factors were selected and analyzed using the DEMATEL-ISM method. This approach determined the importance of each factor and their interdependencies, generating a hierarchical structure and assigning weights for gray clustering calculations. The systematic analysis of these interactions mitigated the subjectivity of traditional methods. The findings indicate that technical factors (B1–B4) and construction management factors (F3–F5) serve as core driving forces, while labor-related (C2) and mechanical (D1–D2) factors act as outcome-driven indicators, reflecting the cascading effects of upstream management decisions. The dual-track mechanism of technology-driven and management-controlled processes provides a strategic direction for optimizing quota productivity.

5.2. Probabilistic Inference and Quota Classification

BN inference was applied to quantify the probability relationships among different productivity levels (gray classes) and integrate them into comprehensive quota consumption calculations. This approach effectively resolved the subjectivity of weight assignment in gray clustering. The quantitative assessment indicated that moderately advanced productivity (45%) dominates, while conservative and advanced levels coexist, highlighting the diversity and complexity of high-standard farmland project management.

5.3. Regional Application and Model Accuracy

The sample calculation of labor consumption for the sub-items in “earthwork projects” across the six major regions in China based on the gray clustering model revealed that the comprehensive coefficient between the measured values of the 17 sub-items and local standard values reached 0.986 (CV = 2.6%), with an average deviation of 1.4%. These results effectively demonstrate the scientific validity and applicability of data-driven models in engineering quota formulation.

5.4. Generalization and Methodological Contributions

The three-step analysis method of “factor structure analysis–probability deduction–regional clustering” proposed in this study breaks through the static limitation of traditional quota preparation and realizes whole-process coverage, from factor structure identification to dynamic prediction. DEMATEL-ISM clarifies the factor structure and weights, the BN quantifies the probability structure of different levels, and gray clustering completes the regional-level quota discrimination and standard output. The three logically progress and complement each other, which significantly improves the systematic and regional adaptability of quota compilation. This comprehensive model is a generalized and combined methodological framework applicable to the analysis of complex systems, and the model itself is not exclusively applicable to high-standard farmland projects. The model has good applicability in other projects with similar decision-making structures or in other regions with significantly different socio-economic structures, climatic conditions, and land systems; therefore, there is no essential difference in the core logic and methodology of the model in the framework of different projects, but it is necessary to make appropriate adjustments to the model for the type of project or localization, such as redefining the influencing factors, organizing the scoring of local experts, revising the Bayesian network’s conditional probability table, resetting the gray clustering boundaries, etc.

5.5. Policy Implications and Decision Support Potential

The model in this study reveals significant differences in the level of quota productivity in different regions, which has important policy reference value. Local governments can carry out refined management based on the results of this model. On the one hand, the model can be used to formulate proprietary quotas suitable for their own province or region and realize the principle of “allocating according to needs and setting limits in different districts”; on the other hand, by identifying influential factors, it can provide a scientific basis for labor allocation, training plan formulation, and investments in equipment, etc. In addition, the Bayesian network can realize uncertain reasoning based on different intervention scenarios, helping the government assess the potential causes affecting the productivity of quotas. Uncertainty reasoning helps the government assess the potential causes affecting quota productivity. Therefore, the model not only has the function of evaluation but also can be used as a decision-making aid in regional agricultural construction, helping to realize differentiated, precise, and efficient quota management and resource dispatching.

5.6. Digital Integration and Future Prospects

The DEMATEL-ISM-BN-gray clustering model proposed in this study has structured and modular features and has the feasibility and prospect of being embedded in digital platforms. In particular, the Bayesian network can realize real-time speculation and scenario simulation, and the gray clustering module can update the classification results through dynamic data. In the future, this model can be applied to web-based or mobile systems to help local agricultural administrations carry out quota planning and dynamic adjustment of resources. In addition, this model can be further associated with the Internet of Things (IoT) system and other systems to realize automatic data collection and intelligent response, as well as to promote the digital and intelligent development of agricultural engineering management.

5.7. Limitations and Future Work

However, several challenges remain. The accuracy of the DEMATEL method heavily depends on expert judgment, which may introduce subjective biases. Additionally, ISM may struggle to construct a clear and concise hierarchical recursive structure in systems with numerous interdependent factors. In BNs, computing conditional probability tables for multiple nodes presents significant challenges as system complexity increases. Addressing these issues in future research is essential to enhancing the robustness and applicability of this modeling approach.