A Study on the Comprehensive Cost Risk Evaluation of Highway Construction Based on the AHP-Improved Entropy Weight Method

Abstract

To address the challenges of multiple cost-influencing factors, high risks, and difficult control in highway construction projects, this study conducts a cost risk assessment based on the full-process perspective of project owners. Considering the long duration and distinct phases of highway construction projects, the study employs a literature-based statistical method to identify the factors influencing cost risks and establishes an evaluation index system for cost risk factors throughout the entire construction process. Based on questionnaire surveys, the study applies the Analytic Hierarchy Process (AHP) to calculate the initial weights of the cost risk factors. Then, the improved entropy weight method is used to compute the correction coefficients for the initial weights and determine the final weight of each influencing factor. By integrating the results from AHP, the comprehensive weights of all factors are obtained, thereby identifying the key factors affecting cost risks throughout the entire highway construction process. Additionally, cost risk prevention and control measures are proposed. The research findings indicate that among the 42 evaluation factors, the ten factors with the greatest impact on project cost risks are project positioning changes, price inflation, unclear or erroneous contract terms, lack of supervision by design units, delayed compensation payments, collusion in bidding (including bid-rigging and cover bidding), lack of coordination among different departments leading to schedule risks, construction claims risks, risks associated with bidding methods, and financing risks. These ten key factors are analyzed in detail, and corresponding risk prevention and control measures are proposed.

1. Introduction

Over the past decade, the construction of highways has seen rapid development globally, especially in China, where the highway mileage has exceeded 170,000 km [1]. This rapid development in highway construction has significantly enhanced the overall technical level of the road network and optimized the transportation structure [2]. It has also played an important role in alleviating the “bottleneck” constraints of transportation, thereby strongly promoting economic development and social progress [3]. However, with the rapid development of highway construction, many existing problems have become more pronounced, especially regarding project cost risks [4]. The phenomenon of exceeding the budget occurs from time to time. If not properly managed, this will not only bring negative public opinion to the government and transportation authorities at all levels [5], but also lead to project delays, quality degradation and other problems, and may even affect the sustainability of the project [6], resulting in serious economic losses. Highway construction projects are large-scale government projects with typical stage-cycle characteristics [7]. Due to their large scale, long duration, high implementation difficulty and complex processes [8], there are many factors that affect the project cost during the construction process, and these factors are difficult to estimate. The risks faced in each construction stage are relatively high [9]. Therefore, studying the factors affecting cost risks throughout the entire highway construction process holds significant theoretical and practical value [10]. According to research, the construction cost of highways in China is approximately 80 million yuan per kilometer in plain areas and often exceeds 100 million yuan per kilometer in mountainous regions, resulting in extremely high investment and construction costs that make cost risk management particularly challenging [11]. In response to these issues, both domestic and international scholars have conducted extensive research on the factors influencing highway construction costs and have achieved notable results.

Cost overruns in highway construction projects are a common issue worldwide [12,13]. According to studies [14,15,16], the proportion of actual costs exceeding the budget in highway construction projects can be as high as 13.5% to 55%. This kind of cost overrun not only affects the economic benefits of the project, but also may lead to serious social and political consequences [17]. In terms of cost risk assessment, traditional risk assessment methods mainly rely on expert experience, which is considered to have strong subjectivity and is difficult to accurately reflect the actual situation [12]. In recent years, scholars have begun to explore more scientific and objective evaluation methods. Refs. [18,19,20] proposed a cost risk assessment model based on the Analytic Hierarchy Process (AHP), determining the weights of various risk factors through expert scoring [21]. However, the AHP method is highly subjective and can be easily influenced by the personal experience and preferences of experts [22,23,24]. To overcome this limitation, ref. [25] introduced the entropy weight method into cost risk assessment, using the objective information of data to determine weights and improving the objectivity and accuracy of the assessment. The entropy weight method is an objective weight determination method based on information entropy, which reflects the importance of each factor in the data by calculating its entropy value [26,27,28] combined the entropy weight method with AHP, proposing the AHP–entropy weight method, which takes into account both the subjective judgment of experts and the objective information of data, thereby enhancing the scientificity and reliability of the assessment. Ref. [18] further applied the AHP–entropy weight method to highway construction projects, constructing a cost risk assessment index system, determining the weights of each risk factor, and conducting a comprehensive evaluation of project cost risks. In the comprehensive evaluation of cost risk factors, the multi-index comprehensive evaluation method is widely used. This method constructs an evaluation index system, quantitatively analyzes each factor, and thus comprehensively assesses the cost risk level of the project. For example, ref. [29] conducted a risk evaluation study of construction projects, using the AHP to calculate the weights of the Private Finance Initiative (PFI) financing model, and employed grey clustering risk evaluation to assess risk values. Ref. [30] used principal component analysis and goal programming to establish a model for quality–cost–benefit–safety–progress objectives and analyzed the advantages and disadvantages of risk evaluation at the current stage. This method can provide a scientific basis for decision-making for project managers, helping them better control project cost risks.

As important infrastructure projects [31], cost management of highway construction projects has always been one of the key factors for project success [32]. Cost risks run through the entire project process, including planning, design, construction, and operation and maintenance stages [33]. In recent years, many scholars have also studied the factors influencing cost risks of highway construction projects from different perspectives. In the planning stage, the accuracy of project cost estimation is crucial for subsequent cost control. Ref. [32] examined the accuracy of cost estimation in Swiss highway construction projects and found that while projects tend to exceed estimated costs during the planning phase, actual costs in the construction phase are often lower than the estimated amounts, and the median deviation of cost estimates was only 4.7%. This indicates that cost estimation in the planning stage may be overly conservative. In addition, factors such as project scale, type, planning duration, start year, and historical policy changes can all affect the degree of cost overrun [34]. In the construction stage, the factors influencing cost risks are more complex [35,36,37] proposed an expert system based on Improved Particle Swarm Optimization (IPSO) to optimize construction equipment management and reduce construction time and costs. The study shows that the system can significantly reduce construction time and costs while maintaining construction quality, achieving optimization effects of 35.4% and 39.1%, respectively. Environmental factors in the construction process should also not be overlooked [38,39] studied the exposure of construction workers to harmful emissions in road repair projects and found that asphalt paving is the activity with the highest exposure risk for workers. Measures such as using high-reflectivity sidewall materials and high-efficiency lighting devices can effectively reduce carbon emissions and costs. In the operation and maintenance stage, cost risks are mainly related to the service life of the road and maintenance strategies [40,41,42] introduced the Life Cycle Cost Analysis (LCCA) procedure adopted by the California Department of Transportation (Caltrans), which selects efficient sequences for future maintenance and repair (M&R) through automated functions to compare the cost-effectiveness of different options. In addition, ref. [43] studied the feasibility of phased construction of perpetual pavements in China and found that although the initial cost increased slightly (2–5%), this construction method can create a more sustainable and reliable pavement structure. From a full life cycle perspective, cost risk management needs to consider factors from multiple stages [44,45,46] proposed an integrated life cycle analysis model that combines Life Cycle Assessment (LCA) and Life Cycle Cost Analysis (LCCA) to evaluate the economic and environmental impacts of vehicle and construction activities throughout the pavement’s service life. In addition, policy factors also have an important impact on cost risks [47,48] explored the changes in highway cost allocation in the era of connected and autonomous vehicles (CAVs), pointing out that the emergence of CAVs will lead to significant changes in pavement infrastructure expenditures and revenues, and a new cost allocation framework needs to be reconstructed to adapt to the new traffic patterns.

The above research findings have laid a certain theoretical foundation for this paper, but there are also shortcomings, mainly reflected in two aspects: First, the research perspective is mostly from the construction side, with fewer studies from the project owner’s perspective, and most of them focus on a single stage of the construction project, without studying cost risks from the perspective of the entire project management process. Second, the research methods mostly use subjective weighting methods, and the research results may be limited by the experience of experts, and cannot accurately identify important risks. Therefore, based on the research of the above experts and scholars, this paper takes the factors influencing the cost risks of the entire process of highway construction projects as the research object and uses the AHP-Improved Entropy Weight Method to study the factors influencing the cost risks of highway construction projects.

2. Research Methods

2.1. Construction of the Comprehensive Evaluation System and Indicator Measurement

The comprehensive evaluation system is divided into three hierarchical levels from top to bottom: the objective level A, the criterion level B, and the scheme level C, which consists of specific evaluation elements and indicators. Highway construction projects are characterized by large investments and long durations, and they are subject to external risks as well as numerous internal risk factors at each stage. According to the entire process of highway construction, the project can be divided into six stages: project initiation, design, bidding, land acquisition and demolition, construction, and completion. From the perspective of the project owner, this study identifies seven first-level influencing indicators through literature review and expert consultation, following the principles of scientificity and comprehensiveness. These indicators are as follows: Y1 external risk factors, Y2 project initiation stage risk factors, Y3 design stage risk factors, Y4 bidding stage risk factors, Y5 land acquisition and demolition stage risk factors, Y6 construction stage risk factors, and Y7 completion stage risk factors. These indicators are further divided into 42 sub-risk factors, denoted as Zi (i = 1, 2, 3, …, 42). For details, see

Table 1. Hierarchical index system of highway construction project cost risk factors.

Objective Level	Criterion Level Yi	Sub-Criterion Level Zi
Cost Risk Factors of Highway Construction Projects	Y1 Project Initiation Stage Risk Factors	Z1 Insufficient Funding
		Z2 Compatibility Risk
		Z3 Financing Risk
		Z4 Project Positioning Change
		Z5 Adjustment Risk of Road Network Planning
		Z6 Unscientific Feasibility Report
	Y2 Design Stage Risk Factors	Z7 Lack of Sufficient Competition Among Design Units
		Z8 Lack of Supervision Over Design Units
		Z9 Lack of Responsibility Among Design Personnel
		Z10 Low Design Quality
		Z11 Intervention by Local Government
	Y3 Bidding and Tendering Stage Risk Factors	Z12 Irregular Bidding and Tendering Process
		Z13 Inadequate Qualification Review of Construction Enterprises
		Z14 Presence of collusion, bid-rigging, or pre-arranged bidding
		Z15 Risk of Non-Execution of Tender Performance
		Z16 Unreasonable Evaluation Methods
		Z17 Local Protectionism, Administrative Interference, and Industry Monopoly
		Z18 Risks Generated by Tendering Methods
		Z19 Subcontracting by the Successful Bidder
		Z20 Risks Generated by Contract Pricing Model
		Z21 Unclear or Incorrect Contract Terms
	Y4 Land Acquisition and Demolition Stage Risk Factors	Z22 Untimely Compensation Payments
		Z23 Inadequate Publicity, Lack of Public Support
		Z24 Government Seeking Excessive Benefits for Residents
		Z25 Government Withholding Compensation Funds
	Y5 Construction Stage Risk Factors	Z26 Risk of project completion delays
		Z27 Risk of exceeding the project budget
		Z28 Risk of failing to meet quality standards
		Z29 Construction Enterprises Not Executing Tasks to Standards
		Z30 Poor Coordination Among Departments Leading to Schedule Risks
		Z31 Subcontract Management Risks
		Z32 Cultural Heritage Protection Risks
		Z33 Design Change Risks
		Z34 Construction Claims Risks
	Y6 Completion Stage Risk Factors	Z35 Incomplete Final Accounts at the End of the Completion Stage
		Z36 Risks Caused by Failure to Timely Restore Borrowed Land and Roads After Construction
		Z37 Quality Issues Leading to Re-work
	Y7 External Environment Risk Factors	Z38 Changes in Bank Interest Rates and Exchange Rates
		Z39 Government Efficiency
		Z40 Natural Disaster Risks
		Z41 Inflation
		Z42 Policy Risks

. Research ethics review certificate Number: FJUT-J2025003.

2.2. Determination of Indicator Weights Based on the AHP Model

2.2.1. Construction of the Judgment Matrix

The Analytic Hierarchy Process (AHP), introduced by the American operations researcher Thomas L. Saaty [49], is a systematic evaluation approach that builds a judgment matrix through the construction of a comprehensive evaluation framework and the determination of relevant indicators. First, pairwise comparisons are made between two schemes at the same level. Then, the relative importance of the two schemes at the same level with respect to the factors at the higher level is compared. Finally, the judgment matrix for pairwise comparisons at each level is constructed based on the comparison results [50]. The specific formula for constructing the judgment matrix is as follows:

$$A={(a_{ij})}_{m\times n}$$

(1)

The principle of constructing the judgment matrix is top-down and from higher to lower levels, and the judgment matrix is a reciprocal matrix. The meaning of the elements in the matrix refers to the importance of $a_i(i=1,2,\cdots ,m)$ to $a_j(i=1,2,\cdots ,n)$. Among them, element $a_{ij}$ has the following properties: $a_{ij}>0,a_{ij}=1/a_{ji},a_{ij}=1(i=j)$. To achieve scientific quantification of data in comparisons, the 9-point scale method is commonly employed [51].

2.2.2. Determination of Subjective Weights of Indicators

From 1 April 2025 to 25 April 2025, 168 questionnaires were collected through an expert-scoring survey. Respondents came from the Department of Transportation, Fujian High-Speed Group, design institutes, construction units, and technical consulting firms. All participating experts hold senior-engineer titles and possess extensive theoretical and practical experience in the research field. Informed consent was obtained from each expert individually by telephone or WeChat, oral consent was secured from every participant, and phone recordings were retained. (This investigation was approved by the Research Ethics Committee of Fujian University of Technology, approval number FIUT-J2025003). Criterion-level and sub-criterion-level judgment matrices were successively established based on the survey results, and the maximum eigenvalue and its corresponding eigenvector were calculated using the square root method to conduct a consistency test. The formula for the consistency check index is as follows:

$$CI=({\lambda }_{\max }-n)/(n-1)$$

(2)

In the formula, ${\lambda }_{\max }$ is the maximum eigenvalue, and $n$ is the number of elements. When $CR=(CI)/(RI)<0.1000$ (Among them, $RI$ is the average random consistency index), the consistency check is passed [50]. After passing the consistency check, the subjective weights ($W_{bj}$ and $W_{pj}$) of the criterion level Yi and the sub-criterion level Zi are obtained. Finally, the comprehensive weights ($W$) of the AHP method are derived. The specific calculation formula is as follows:

$$W=W_{bj}\times W_{pj}$$

(3)

2.3. Determination of Indicator Weights Based on the Entropy Weight Method

2.3.1. Establishment of the Indicator Matrix for the Entropy Weight Method

The indicator matrix for the entropy-weight method is constructed as shown in Equation (4). In the equation, m is the number of samples, n is the number of evaluation indicators, and $r_{ij}(i=1,2,\cdots ,m;j=1,2,\cdots ,n)$ represents the score assigned by expert (j) to indicator (i) [52,53].

$$\mathrm{R}=\left[\begin{array}{ccc}{\mathrm{r}}_{11}& \cdots & {\mathrm{r}}_{1\mathrm{n}}\\ \cdots & \cdots & \cdots \\ {\mathrm{r}}_{\mathrm{m}1}& \cdots & {\mathrm{r}}_{\mathrm{mn}}\end{array}\right]$$

(4)

2.3.2. Normalization of the Indicator Matrix

Given the differences in nature and magnitude among the evaluation indicators, the indicator matrix R should be normalized to obtain the dimensionless indicator matrix $X={(x_{ij})}_{m\times n}$. As shown in Equation (5).

$$X_{ij}={\displaystyle \frac{r_{ij}}{\sqrt{{\displaystyle \sum _{i=1}^m{(r_{ij})}^2}}}},i=1,2,\cdots m;j=1,2,\cdots n$$

(5)

2.3.3. Determination of Entropy Weights

The entropy value $b_j$ for the j-th indicator of the samples is given by:

$$b_j=-{\displaystyle \frac{1}{\ln m}}{\displaystyle \sum _{i=1}^m{a}_{ij}\ln a_{ij},}i=1,2,\cdots m;j=1,2,\cdots n$$

(6)

In Equation (6), $a_{ij}$ represents the proportion of the i-th sample under the j-th indicator, the calculation formula is given in Equation (7).

$$a_{ij}={\displaystyle \frac{x_{ij}}{{\displaystyle \sum _{i=1}^m{x}_{ij}}}},i=1,2,\cdots m;j=1,2,\cdots n$$

(7)

Then, the entropy weight (correction coefficient) $v_j$ for the j-th indicator is:

$$v_j={\displaystyle \frac{1-b_j}{n-{\displaystyle \sum _{j=1}^n{b}_j}}},i=1,2,\cdots m;j=1,2,\cdots n$$

(8)

Finally, the correction coefficient for the indicator is obtained as:

$$V={(v_1,v_2,\cdots ,v_n)}^T$$

(9)

2.3.4. Improved Entropy Weight (Correction Coefficient)

When using the entropy weight method, it is possible that the information content of a certain indicator is too small, leading to an excessively large weight. This can cause the weight values of other indicators to be too small, thereby affecting the final comprehensive evaluation score. Therefore, an upper limit for the weight values is proposed to improve the entropy weight method.

2.3.5. Comprehensive Weight of AHP-Improved Entropy Weight Method

Since the AHP is highly subjective, while the improved entropy weight method is more objective, the weights calculated from Equations (3) and (9) are combined to derive the comprehensive weights of each influencing factor, as shown in Equation (10).

$${\theta }_j=\sqrt{v_j{w}_j}/\sum _{j=1}^n\sqrt{v_j{w}_j}$$

(10)

3. Results and Analysis

3.1. Reliability and Validity Analysis of the Questionnaire

3.1.1. Reliability Analysis

In this study, SPSS 26 software was employed to calculate the reliability of the questionnaire using Cronbach’s alpha coefficient, which ranges from 0 to 1 [54]. When the Cronbach’s alpha coefficient exceeds 0.9, the questionnaire is considered to have very high reliability. If the coefficient falls between 0.7 and 0.8, it suggests potential design issues in the questionnaire scale, though it still retains reference value. However, if the coefficient is below 0.7, it indicates significant design flaws, necessitating a redesign of the questionnaire. The reliability analysis conducted in this study yielded a Cronbach’s alpha coefficient of 0.972, demonstrating high reliability and indicating that no adjustments are needed for the dimensions of highway construction project risk assessment.

3.1.2. Validity Test

The validity of the questionnaire was analyzed using exploratory factor analysis in SPSS 26 software. The Kaiser-Meyer-Olkin (KMO) test coefficient ranges from 0 to 1, with values closer to 1 indicating better questionnaire validity [55]. The calculation results are shown in

Table 2. Validity analysis table.

KMO and Bartlett’s Test
KMO Measure of Sampling Adequacy		0.937
Bartlett’s test of Sphericity	Approximate Chi-square	5801.169
	Degrees of freedom	861
	Significance	0

. As seen from Table 2, the KMO test coefficient for this study is 0.937, indicating that the questionnaire has good validity.

3.2. Initial Weight Calculation Based on AHP

By using the expert scoring method and based on the results of 168 questionnaires collected, the judgment matrices for the criterion layer and sub-criterion layer were established successively. Consistency tests were then conducted on each judgment matrix. The calculated results of the consistency ratio (CR) were 1.42 × 10⁻¹¹, −3.32 × 10⁻¹¹, 4.78 × 10⁻¹¹, 2.12 × 10⁻¹¹, −5.00 × 10⁻¹¹, 2.25 × 10⁻¹¹, 8.58 × 10⁻¹¹ and 4.46 × 10⁻¹¹, all of which are less than 0.1, thus passing the consistency test. According to Formula (2) and using MATLAB R2024a software for computation, the results are shown in

Table 3. Calculation results of each risk factor weight.

Objective Layer	Criterion Layer Yi	Weight	Sub-Criterion Layer Zi	Weight	Initial Weight ${\mathit{W}}_{\mathit{i}}$	Initial Weight Ranking
Factors of Highway Construction Projects	Y1 Project Initiation Stage Risk Factors	0.149	Z1	0.171	0.0255	6
			Z2	0.158	0.0235	26
			Z3	0.174	0.026	2
			Z4	0.166	0.0248	13
			Z5	0.166	0.0247	15
			Z6	0.168	0.0251	9
	Y2 Design Stage Risk Factors	0.118	Z7	0.181	0.0213	40
			Z8	0.202	0.0238	23
			Z9	0.199	0.0235	27
			Z10	0.211	0.0249	11
			Z11	0.217	0.0256	4
	Y3 Bidding and Tendering Stage Risk Factors	0.23	Z12	0.098	0.0226	34
			Z13	0.094	0.0216	37
			Z14	0.105	0.024	19
			Z15	0.099	0.0227	32
			Z16	0.094	0.0216	37
			Z17	0.094	0.0216	39
			Z18	0.103	0.0236	25
			Z19	0.105	0.0241	18
			Z20	0.101	0.0233	29
			Z21	0.104	0.0239	20
	Y4 Land Acquisition and Demolition Stage Risk Factors	0.095	Z22	0.27	0.0257	3
			Z23	0.229	0.0218	36
			Z24	0.245	0.0233	28
			Z25	0.254	0.0241	17
	Y5 Construction Stage Risk Factors	0.219	Z26	0.116	0.0255	5
			Z27	0.114	0.025	10
			Z28	0.113	0.0248	12
			Z29	0.108	0.0237	24
			Z30	0.109	0.0238	21
			Z31	0.113	0.0247	14
			Z32	0.106	0.0232	30
			Z33	0.112	0.0244	16
			Z34	0.109	0.0238	21
	Y6 Completion Stage Risk Factors	0.067	Z35	0.339	0.0227	33
			Z36	0.318	0.0213	41
			Z37	0.345	0.0231	31
	Y7 External Environment Risk Factors	0.122	Z38	0.169	0.0207	42
			Z39	0.208	0.0254	8
			Z40	0.181	0.0221	35
			Z41	0.227	0.0277	1
			Z42	0.209	0.0255	7

. In the criterion layer, Y3 is the highest, and Y6 is the lowest. In the sub-criterion layer, Z37 is the highest, while Z13, Z16, and Z17 are the lowest.

3.3. Weight Calculation Based on the Improved Entropy Method

First, the weights of the indicators are calculated using Equation (9). Then, considering the weight distribution of the risk factors, 0.027 is selected as the upper limit of the weights. That is, if the weight of a certain indicator $V_i$ > 0.027, it will be set to 0.027. The remaining part will be distributed to the other indicators using the following formula, and the adj weights are denoted as $V_i^{\prime }$, as shown in Equation (11).

$$V_i^{\prime }=V_i+V_i\times (V_i-0.027)/{\displaystyle \sum _{k=1}^m{V}_k}\times (V_j-0.027)(i\ne j,i=1,2,\cdots ,n)$$

(11)

Finally, the corrected entropy weights of each evaluation indicator are as follows:

$$V^{\prime }={(v_1^{\prime },v_2^{\prime },\cdots v_n^{\prime })}^T$$

(12)

Accordingly, the correction coefficients of the entropy weight method calculated based on Equation (12) are shown in

Table 4. Results of correction coefficient by entropy weight method.

Z1	Z2	Z3	Z4	Z5	Z6	Z7
0.0207	0.0228	0.02	0.026	0.0205	0.021	0.0321
Z8	Z9	Z10	Z11	Z12	Z13	Z14
0.0259	0.023	0.0186	0.019	0.0253	0.0294	0.025
Z15	Z16	Z17	Z18	Z19	Z20	Z21
0.0283	0.0308	0.0295	0.0271	0.0231	0.0222	0.0259
Z22	Z23	Z24	Z25	Z26	Z27	Z28
0.022	0.0294	0.0227	0.0231	0.0207	0.0202	0.0204
Z29	Z30	Z31	Z32	Z33	Z34	Z35
0.0231	0.0255	0.0209	0.0203	0.0225	0.0255	0.0219
Z36	Z37	Z38	Z39	Z40	Z41	Z42
0.021	0.0251	0.0367	0.0188	0.0288	0.0206	0.0207

.

3.4. Comprehensive Weight Calculation Results

Since AHP is significantly influenced by subjective factors and the improved entropy method is more objective, the weights calculated by both methods were combined. The comprehensive weights of each influencing factor were derived using Equation (10), and the results are shown in

Table 5. Comprehensive weight results of cost risk factors in highway construction projects.

Item	Z1	Z2	Z3	Z4	Z5	Z6	Z7
Weight	0.0248	0.0225	0.0248	0.0259	0.0219	0.024	0.024
Ranking	14	38	10	1	41	34	35
Item	Z8	Z9	Z10	Z11	Z12	Z13	Z14
Weight	0.0253	0.0244	0.0244	0.0243	0.0244	0.0242	0.0253
Ranking	4	22	21	25	19	29	6
Item	Z15	Z16	Z17	Z18	Z19	Z20	Z21
Weight	0.0248	0.0242	0.0241	0.0252	0.0248	0.0241	0.0254
Ranking	17	29	32	9	13	31	3
Item	Z22	Z23	Z24	Z25	Z26	Z27	Z28
Weight	0.0253	0.0242	0.0243	0.0248	0.0248	0.0241	0.0243
Ranking	5	27	26	11	15	33	24
Item	Z29	Z30	Z31	Z32	Z33	Z34	Z35
Weight	0.0244	0.0253	0.0221	0.0221	0.0248	0.0253	0.0228
Ranking	20	7	40	39	12	8	37
Item	Z36	Z37	Z38	Z39	Z40	Z41	Z42
Weight	0.0216	0.0248	0.0236	0.0242	0.0244	0.0255	0.0246
Ranking	42	16	36	28	23	2	18

. The overall ranking in Table 5 shows that the calculated results are reasonable and closely align with actual project experience; the top cost-risk factors for expressway projects are Z4 (change in project positioning), Z41 (price inflation of materials/labour) and Z21 (ambiguous or erroneous contract clauses), which frequently trigger quantity changes, redesign or claims and are hard to control once they arise, whereas the lowest-ranked factors are Z31 (subcontractor-management risk), Z5 (adjustment of regional road-network planning) and Z36 (failure to reinstate temporary accesses/land after construction), risks that are either manageable through tighter site administration, initiated only sporadically by government authorities, or rare and confined to the contractor’s warranty period, thus confirming the validity of the model output.

4. Discussion

A comparison was made between the weights of influencing factors calculated by AHP and the comprehensive weights calculated by the AHP-improved entropy method. Series 1 represents the weights of influencing factors calculated by AHP, while Series 2 represents the comprehensive weights calculated by the AHP-improved entropy method, as shown in Figure 1. From Figure 1, it can be seen that the weights calculated by AHP have changed significantly compared to the comprehensive weights calculated by the AHP-improved entropy method. In Series 1, the top ten factors are Z41 (inflation), Z3 (financing risk), Z22 (untimely compensation payments), Z11 (intervention by the local government), Z26 (risk of project completion delays), Z1 (insufficient funding), Z42 (policy risks), Z8 (lack of supervision over design units), Z39 (government efficiency), and Z6 (unscientific feasibility report), as well as Z27 (risk of exceeding the project budget). In Series 2, the top ten factors are Z4 (project positioning change), Z41 (inflation), Z21 (unclear or incorrect contract terms), Z8 (lack of supervision over design units), Z22 (untimely compensation payments), Z14 (presence of collusion, bid-rigging, or pre-arranged bidding), Z30 (poor coordination among departments leading to schedule risks), Z34 (construction claims risks), Z18 (risks generated by tendering methods), and Z3 (financing risk). From the comparison results, it can be analyzed that the AHP method relies entirely on expert scoring and subjective judgment, which is easily influenced by the personal preferences and experience of experts, leading to a strong subjectivity in weight allocation. In contrast, the AHP-improved entropy method combines the objectivity of the entropy method, which adjusts weights based on the degree of data variation, thereby reducing the impact of subjective factors on weight allocation. After correction, the comprehensive weights compared with the initial weights show that Z41, Z8, Z3, and Z22 still rank in the top ten. This indicates that these factors are still considered important after both subjective weight calculation and objective correction. This further demonstrates that the use of the AHP-improved entropy method for the comprehensive cost risk evaluation of highway construction projects is reasonable.

The research results of this study were compared and analyzed with existing similar achievements. Ref. [14] conducted research on the cost risk variables of highway construction from the owner’s perspective and ranked the factors affecting the construction cost of highways, considering that design changes due to the lack of supervision of design units and rising prices are the main factors for cost overruns, which basically coincides with factors Z41 and Z8 identified in this study. Ref. [56] carried out research on the cost risks of highway projects and believed that rising prices, contract risks, poor coordination among various departments, and construction claims risks are the main factors affecting the cost risks of highway construction, which basically coincides with factors Z41, Z21, Z30, and Z34 in this study’s results. Ref. [56] explored how to construct a cost impact factor system for highway construction projects through factor analysis methods and concluded that changes in project positioning, design changes, and management coordination among various departments are the main factors affecting costs, which basically coincides with factors Z4, Z8, and Z30 in this study’s results. In Ref. [57] the research on risk management decision-making of highway pavement construction based on utility theory, it was believed that contract risks, financing risks, and collaborative management among participating parties are the main factors affecting costs, which basically coincides with factors Z21, Z3, and Z30 in this study’s results. Through comparative analysis, it is known that the main influencing factors of highway construction projects identified in this study basically coincide with existing research results in the top ten rankings, further verifying the rationality of the research results of this study.

In addition, this paper also conducted a detailed analysis of the top ten influencing factors in the research results and provided specific measures and suggestions for each of them.

Project positioning changes may lead to variations in route length, the number of interchanges, and the scale of bridges and tunnels, which directly affect the project’s scope. For instance, an increase or decrease in route length or changes in the number of interchanges will alter the required volumes of earthwork, bridge construction, and pavement works, ultimately impacting the overall project cost. If the adjusted project requires additional quantities of work, the construction cost will inevitably rise. Moreover, changes in project positioning may introduce new construction techniques or materials, further increasing costs. Project positioning changes also have indirect impacts on both the design and construction phases. Such changes may necessitate new surveying, planning, and design work, increasing both design costs and time. For example, design teams may need to adjust their plans or even conduct new geological surveys. Likewise, construction plans may require modifications, affecting construction progress and efficiency. Changes in construction techniques might necessitate the reallocation or leasing of equipment, thereby increasing equipment costs. Beyond direct construction costs, project positioning changes can also impact other aspects of highway construction. These changes may require adjustments in land acquisition and demolition plans, increasing land use and resettlement compensation costs. Coordination between construction authorities, design firms, and contractors becomes more complex, raising administrative costs and management difficulties. Additionally, such changes may lead to contractual disputes and compensation claims, further escalating legal costs. Project positioning changes may also influence the long-term operation and maintenance costs of highways. If the modifications result in a more complex highway structure, maintenance and repair expenses could increase. Furthermore, the later a change is implemented, the higher the associated costs. The timing of project modifications significantly affects overall project outcomes—changes made in the early planning phase, while still costly, are relatively manageable. However, modifications during the construction phase or even after project completion not only increase costs and work volume but may also lead to delays and resource wastage. Suggestions for dealing with the impact of project changes on construction costs are as follows: Strengthen pre-construction surveys and arguments to ensure the accuracy and rationality of project positioning in the early stages of the project, reducing the possibility of changes; improve change management systems to establish clear approval processes, responsible entities, and cost-sharing methods for changes, ensuring the standardization and transparency of the change process; and enhance design management to improve the professional level and sense of responsibility of design units, strengthen cost control awareness in the design phase, and implement limit design systems to avoid changes caused by unreasonable design.

Price increases lead to rising raw material costs. Highway construction requires a large amount of raw materials such as cement, steel, and asphalt. In recent years, the prices of these raw materials have continued to rise, directly increasing construction costs. With changes in the labor market, labor costs are also constantly increasing. Highway construction requires a large workforce, and the increase in labor costs further drives up overall construction costs. Highway construction requires the use of a large amount of land, and rising land prices increase land requisition costs, especially in developed areas and areas with complex terrain where land costs are higher. Price increases also lead to higher equipment and machinery rental fees. Highway construction requires a large number of mechanical equipment, and the increase in rental costs directly affects construction costs. Price increases not only affect construction costs but also increase the operation and maintenance costs of highways. For example, expenditures on road maintenance, equipment renewal, and personnel wages are constantly increasing. Price increases also lead to stronger inflation expectations and rising financing costs. Highway construction usually requires a large amount of capital investment, and the increase in financing costs further drives up the overall project cost. To cope with the impact of price increases on highway construction costs, highway construction management should take comprehensive measures from multiple aspects such as optimizing project planning and design, strengthening cost management and control, improving construction efficiency, expanding financing channels, strengthening risk management, and promoting policy support and coordination. Specific measures include rational route planning, implementing limit design, establishing dynamic cost monitoring systems, optimizing procurement management, improving construction efficiency, promoting technological innovation, diversifying financing, arranging capital use reasonably, establishing risk warning mechanisms, purchasing engineering insurance, improving contract terms, strengthening contract execution supervision, seeking policy preferences, and strengthening inter-departmental coordination. Through these comprehensive measures, management can alleviate the cost pressure brought by price increases to a certain extent, ensuring the smooth implementation of the project and the realization of economic benefits.

Unclear or incorrect contract terms can lead to various cost risks, including additional work volume due to unclear scope and content of the project, difficulties in cost adjustment due to ambiguous pricing methods, funding turnover issues caused by unclear payment methods, increased cost burden due to unreasonable claims clauses, rectification costs due to unclear quality standards and acceptance clauses, cost overruns due to unregulated change management, and legal dispute costs due to unclear definition of responsibilities and obligations. To address these risks, it is necessary to carefully review contract terms before signing to ensure their clarity and consistency with the project’s actual situation, and strictly follow the contract during execution, promptly handling changes and claims to avoid cost overruns caused by contract issues.

Lack of supervision over design units can lead to unreasonable design schemes, insufficient design depth, lack of design optimization, mismatch between design and actual needs, poor quality of design documents, and lack of cost control in the design phase. These issues can increase work volume, trigger design changes, delay construction progress, and increase later operation costs, ultimately leading to a significant increase in highway construction costs. Therefore, strengthening the supervision of design units to ensure the rationality, economy, and feasibility of design plans can effectively control the construction cost of expressways.

Untimely compensation payments can lead to refusal of relocation by the displaced parties, affecting the delivery of the construction site and thereby delaying project progress. For example, the slow progress of house demolition will directly impact the completion of bypass roads and the smooth passage of construction traffic. Delays in project progress due to untimely compensation may require construction units to pay additional equipment rental fees and personnel idling costs. Moreover, if construction plans need to be adjusted due to demolition issues (such as adding temporary detour roads), construction costs will further increase. Untimely compensation can also increase the financial pressure on the construction unit, potentially causing tight funding chains and the need to raise additional funds to maintain project progress, thereby increasing financing costs. Failure to pay compensation in a timely manner may lead to dissatisfaction and resistance from the displaced parties, even resulting in irrational resistance behaviors such as “nail households,” increasing social conflicts and affecting the smooth progress of the project. Compensation payment issues can also increase the difficulty of overall project investment control and affect the project’s economic benefits. For example, delays and cost increases caused by demolition issues may make it difficult to complete the project within the budget. Therefore, ensuring timely and full compensation is a key measure to ensure the smooth progress of the project and control construction costs.

Collusion and bid-rigging behaviors can lead to bid prices deviating from reasonable market levels. For example, by manipulating bid results through inflating or undercutting quotes, the winning bid price may exceed the actual cost or fall below a reasonable profit margin, thereby increasing project costs or creating quality risks. The winning bidder may lack true competitiveness due to collusion or bid-rigging, and after winning the contract, may reduce costs through practices such as cutting corners or using substandard materials, which could compromise the project’s quality and safety. These practices may also result in the winning bidder being incapable of fulfilling the contract, leading to delays in the project’s commencement or progress, thus increasing time-related costs. Additionally, collusion and bid-rigging can complicate the bidding process, raising the difficulty and cost of reviewing bid documents. Furthermore, potential contractual disputes and breaches may incur additional management costs. Moreover, since collusion and bid-rigging are illegal activities, companies involved may face administrative penalties (e.g., fines or revocation of qualifications), civil liabilities, and even criminal charges. This not only increases legal costs but also affects the company’s reputation and market competitiveness. Therefore, strengthening coordination and communication among various departments to ensure that the project progresses according to plan can effectively control costs and reduce project risks.

Poor coordination among departments leading to schedule risks can increase the direct costs of highway construction, such as labor costs: extended project duration means that construction workers need to stay on the site longer, significantly increasing labor costs due to idling and overtime; equipment rental costs: extended rental time for construction equipment increases equipment rental fees; and material costs: extended project duration may lead to rising material prices, increasing material procurement costs. Poor coordination among departments can also increase indirect costs, such as management costs: extended project duration increases the complexity of project management, requiring more management personnel and resources, thereby increasing management costs; and financing costs: extended project duration may delay. Construction claims risks can directly increase the direct costs (such as claim expenses, material and equipment costs, and labor costs) and indirect costs (such as management costs, legal and consulting costs, and financing costs) of highway construction projects. It may also lead to project schedule delays, contract change risks, and impacts on reputation and market. Therefore, both the construction unit and the construction contractor should strengthen contract management, standardize the construction process, and handle claim issues reasonably to reduce the impact of claim risk on project costs.

The risks generated by tendering methods can increase the direct costs (such as materials, labor, and equipment rental) and indirect costs (such as management, financing, and legal) of highway construction projects. They may also lead to schedule delays, quality degradation, damage to reputation, and legal disputes. Therefore, the construction unit should scientifically and reasonably formulate bidding plans, strictly review evaluation methods and maximum bid limits, and strengthen supervision and management of the bidding process to reduce the impact of bidding risks on project costs.

Financing risk can significantly increase the financing costs, debt burden, risk of capital shortage, risk of project schedule delays, risk of operational revenue, legal and policy risks, and exchange rate and interest rate fluctuation risks of highway construction projects. These risks not only directly affect the construction costs of the project but may also have long-term negative impacts on the project’s operational revenue and financial health. Therefore, optimizing the financing structure, broadening financing channels, strengthening capital management, and improving the legal and regulatory system are key measures to reduce financing risks and control project costs.

The research methods used in this project also have certain limitations. For example, when using the AHP method, the expert questionnaire survey method was adopted, and the results of 168 expert questionnaires were collected. Each expert’s knowledge, capabilities, and experience in the industry inevitably influenced the evaluation results. Furthermore, the study is constrained by factors such as the project’s contracting and management models. For instance, if the project adopts management models such as EPC, BOT, or PPP, it may exert certain influences on the research findings of this study.

5. Conclusions

This paper employs the AHP-improved entropy method to evaluate and study the cost risk factors of the entire process of highway construction projects, deriving the comprehensive weights and rankings of each risk factor, identifying the primary risk factors, and proposing suggestions for cost risk prevention and control measures. The main conclusions are as follows:

(1)

Through theoretical calculation and analysis, the primary risk factors affecting the cost of the entire process of a highway construction project have been identified, and corresponding prevention measures and suggestions have been proposed. These findings provide a reference for cost risk management for highway construction project owners, further addressing the issue of poor cost risk management effectiveness in highway construction projects and offering practical guidance for engineering construction management.

(2)

This paper applies the AHP-improved entropy-weight method to evaluate whole-process cost-risk factors in expressway projects. Coupling the two approaches not only overcomes the subjective limitations inherent in expert scoring but also tempers the purely objective nature of entropy weighting, yielding more reasonable assessment results. Nevertheless, the combined method still assumes that all influencing factors are independent and does not account for their mutual interactions; our research group is continuing to address this issue.

(3)

The cost-risk factors affecting the whole life-cycle of expressway projects selected in this paper were determined according to the current situation of highway construction in China and the relevant literature. With future economic growth and social progress, stricter requirements on environmental protection and carbon-emission control will inevitably emerge, and these two aspects will to some extent influence construction costs and increase cost-management risks. Therefore, our research team will next focus on incorporating environmental protection and carbon-emission indicators into the risk-evaluation framework.

(4)

The research conducted in this paper is based on highway construction projects in China. Given that there are certain differences in geographical location, environment, engineering characteristics, cultural differences, management systems, and management models of highways worldwide, the research findings also have certain limitations. The research team will conduct follow-up surveys in other regions to further refine the research results.