Uncontrollable Factors Analysis on Sustainable Highway Routine Maintenance Management: A Case Study of Shaanxi Province in China

Abstract

To figure out the primary factors that significantly impact the sustainability of highway routine maintenance management (HRMM), this paper examined 23 highway operating subsidiaries (evaluated decision-making units, DMUs) affiliated with Shaanxi Transportation Holding Group (STHG) in Shaanxi Province as an example. First, data envelopment analysis (DEA) was used to evaluate the performance of HRMM for each DMU. Subsequently, a truncated regression model was utilized to analyze the primary factors that impact the outcomes of HRMM. The conclusions indicated that except for the widely recognized input and output factors, there exist some uncontrollable factors that can affect HRMM efficiency, including the amount of natural dustfall, urbanization rate, tunnel length, and bridge length. These findings offer suggestions for STHG focusing on DMUs facing challenges with high dustfall and urbanization rate and long bridges and tunnels when allocating maintenance resources to improve HRMM efficiency and achieve sustainable highway maintenance management. Moreover, the methodology for analyzing uncontrollable factors can also serve as a valuable reference for other maintenance types or fields, contributing to the broader goal of promoting sustainability in transportation infrastructure development.

1. Introduction

With the growing travel demand, highway maintenance is facing grave challenges due to the long-term effects of environmental and traffic loading factors. In response to the above problem, highway agencies are increasingly focusing on the sustainability of highway maintenance, which refers to the application of environmentally friendly, efficient, and sustainable technologies and management practices to maintain and manage highway infrastructure assets, which can achieve the preservation and appreciation of highway assets while the reducing environmental impact and ensuring user safety. In recent years, numerous scholars have conducted research on the innovation of maintenance decision-making [1,2], maintenance management [3,4], maintenance assessment [5,6,7], and maintenance technology [8,9], which provide new development directions for sustainable highway maintenance.

Among the above sustainable maintenance aspects, this paper mainly focuses on performance evaluation in maintenance assessment. Performance evaluation aims to enhance the effectiveness of asset management practices, and it has been widely applied in areas such as corporate management [10], factory equipment maintenance [11], and manufacturing [12]. In the context of transportation asset management, corresponding standards and guidelines have been introduced [13,14,15,16]. Highways, as critical national infrastructure assets, attract significant attention from transportation departments regarding the final conditions and service levels. Transportation departments increasingly emphasize performance-based management in the maintenance and operation of highways to ensure an objective and scientifically-driven assessment [17], which plays an important role in sustainable highway asset management.

To objectively and fairly evaluate highway maintenance management (HMM), many scholars have integrated the concept of performance evaluation into management practices [18,19,20,21]. The fundamental content of performance evaluation is the measurement of efficiency, which can be achieved through two principal methodologies: stochastic frontier analysis (SFA, parametric approach) and data envelopment analysis (DEA, non-parametric approach). In contrast to SFA, DEA does not necessitate any parametric assumptions about the production frontiers and employs linear programming techniques to assess the relative efficiency of organizations, making it well suited to multi-input and multi-output problems. Since its inception, DEA has been employed extensively for performance evaluation in a multitude of fields, including higher education, healthcare, supply chain management, the defense sector, and transportation [22,23,24,25,26,27].

The asset management goal of highway management agencies is to attain optimal maintenance management results by minimizing the inputs of maintenance in order to maximize the generated maintenance benefits and achieve the sustainable development of highway infrastructures. In essence, this can be viewed as a process involving multiple inputs and multiple outputs. Based on this characteristic, DEA is one appropriate method to evaluate highway maintenance management performance (HMMP), which can be mainly classified into two aspects in existing studies: maintenance operations [28,29,30,31,32,33] or bridge maintenance [19,34,35,36,37].

It is noteworthy that highways are subject to a myriad of complex factors (i.e., climate, the natural environment, etc.) during operation, and these factors are objective and not under human control, which can be referred to as external factors or uncontrolled factors. Especially for routine maintenance, the fundamental type throughout the entire highway asset lifecycle, involving routine cleaning and minor repairs to ensure that highway assets are maintained at a high level, plays a significant role during the sustainable development of the operation period. Identifying the impact on highway routine maintenance management (HRMM) of uncontrollable factors is critical to improving highway routine maintenance management performance (HRMMP); however, few studies have focused on this problem.

Consequently, this paper intends to explore how uncontrollable factors affect HRMMP based on a case study of 23 highway operating subsidiaries affiliated with Shaanxi Transportation Holding Group (STHG) in Shaanxi Province so as to fulfill sustainable HRMM. First, in accordance with the principles of the DEA method’s evaluation indicators selection and considering the content and background of routine maintenance management work, input and output indicators were selected. Next, according to the characteristics of HRMM, the input-oriented DEA model was employed to calculate the routine maintenance management efficiency values of each subsidiary. Lastly, based on the obtained efficiency values, this paper utilized a truncated regression model to analyze the impact on HRMMP of potential uncontrollable factors, which explained the key aspects to be considered in sustainable HRMM.

2. Literature Review

2.1. Performance Evaluation of HMM

In the process of performance evaluation, the determination of evaluation subjects, indicators, and methods is important. For HMM, when selecting evaluation indicators, it is essential to consider the actual situation of the evaluation subject (i.e., operating agency or bridge), the relevant influencing factors, the main work contents, and the involved information comprehensively to ensure the comprehensiveness and scientific rationality of the indicators. Simultaneously, the selection of evaluation indicators will also depend on the characteristics of the evaluation method. It is required to satisfy the conditions of the evaluation model while objectively and accurately reflecting the substance of the evaluation subject.

Table 1. Review of performance evaluation of HMM.

Reference	Evaluation Subject	Evaluation Indicators	Evaluation Method
[38]	Highway infrastructure maintenance options	Pavement states, controls, estimated transition times, treatment information	A state increment method of life-cycle cost analysis
[39]	Bridge decks	Life cycle inventory, agency costs, social costs	An integrated life-cycle assessment and cost model
[40]	Highway management agency	Business indicators (i.e., highway maintenance quality), customer indicators (i.e., user satisfaction), internal management indicators (i.e., implantation of maintenance expenditures), learning and growth indicators (i.e., achievements in scientific research)	Balance scorecard method
[41]	Public–private partnership transportation infrastructure projects	Financial ability (i.e., overall asset operating ability), multi-stakeholder satisfaction (i.e., government satisfaction), operation and maintenance management (i.e., Road traffic quality), sustainability (i.e., social sustainability impact)	An improved balance scorecard method
[28]	Highway maintenance operations	Total area served, traffic, load, climate factors, maintenance expenditure, change in pavement condition	DEA
[31]	Road maintenance agencies	Budget, number of staffs, value of asset, number of working units and sub-units, location factor, road improvement realization ratio, road maintenance realization ratio, budget realization	DEA
[42]	Highway maintenance sections	Budget, total manpower, quantity of maintenance machines, length of highway section, routine expenditure on maintenance, expense on salvage, revenue from helping digging and mending roads	DEA
[35]	Bridges	Cost for maintaining the bridges, regional effect variable, total area served, change in overall bridge condition	DEA
[37]	Bridges	Change in area on various appraisal rating components of bridges, expenditures on interstate bridge replacement or rehabilitation, average daily traffic on interstate bridges per deck area, proportion of truck vehicle miles traveled on interstates, average age of bridges, annual freeze–thaw cycles, annual precipitation	DEA
[36]	Bridge resilience	Age, area, design high flood level, finish road level of the bridge, bridge resilience index	DEA
[43]	Roadway maintenance crews	Government credits, specific consultant dollars spent, capital costs, pavement grading factor, length of road section managed, number of accident locations remade, volume of shoulder and middle repair and maintenance carried out	DEA
[34]	Bridges	Bridge condition rating, expenditure, traffic loading, climate severity, age	A nonparametric efficiency testing with a linear programming-based approach
[44]	Road maintenance policies	Pavement condition, traffic load, climate condition, maintenance expenditure	A micro-level (road section) system dynamics model

reviews the partial research on the performance evaluation of HMM, indicating that scholars have various research contents and focuses based on evaluation indicators. The construction process and contents of evaluation indicators can provide a reference for the subsequent evaluation of HRMMP in this paper.

2.2. Uncontrollable Factors Considered in Performance Evaluation of HMM

The maintenance and operation of highways are influenced by various factors, each with a specific impact to a greater or lesser extent. These factors, known as external, uncontrollable (used in this paper), or challenge factors, are objective and outside the control of decision makers (i.e., climate and location), whose impact must be considered in the performance evaluation of HMM [18,45].

Table 2. Review of uncontrollable factors considered in performance evaluation of HMM.

Reference	Uncontrollable Factors
[30]	Factors that (1) affect the deterioration of bridges (i.e., climate, traffic, accidents damaging bridges, age of bridges, etc.) and (2) affect the maintenance efforts (i.e., type of paved lanes, location, terrain, total area served, etc.)
[46]	Traffic, load, min temperature, max temperature, rainfall, snowfall, mountainous dummy
[37]	traffic, and climate conditions across the states
[18]	Base infrastructure information (i.e., extent of tunnels, extent of bridges, road surface, etc.), state of base infrastructure and additional infrastructure (i.e., age of road section, traffic signals, condition of road section, etc.), and weather (i.e., temperature, freeze–thaw cycles and precipation)

reviews the partial research on uncontrollable factors considered in the performance evaluation of HMM, which can inform the selection of the uncontrollable factors of HRMMP in the following parts.

2.3. Approaches to Deal with Uncontrollable Factors in DEA

As previously stated, uncontrollable factors have a significant impact on HMMP, particularly in performance evaluation using DEA. Uncontrollable factors may impact the ability of the decision-making unit (DMU) to increase outputs with a given number of inputs or limit the ability of the DMU to decrease inputs while maintaining a certain level of outputs. To address the above issues, there are two main types of approaches in past studies: one-stage approaches and multi-stage approaches [45]. One-stage approaches take uncontrollable factors into account when running a DEA model by refining the traditional DEA formula [47,48] or categorizing the uncontrollable factors of the DMU operation environment to compare the efficiency of DMUs in different environments [49,50]. Multi-stage approaches are carried out to explore the relevant effects by performing a regression analysis of uncontrollable factors based on the obtained DMU efficiency values [51,52,53]. The details and application situation of the above approaches can be found in the research of [45].

For the performance evaluation of HMM, one-stage approaches have been employed the most. One practice is to run the DEA model with and without considering the uncontrollable factors and analyze the impact of these factors on the HMMP by comparing the two results obtained [35,37]. Another one is to categorize the environment in which the DMU is located based on uncontrollable factors (i.e., climate and terrain condition) to capture their effects [28]. One disadvantage of the above approaches is that it is difficult to determine the specific quantitative impact of each factor on HMMP, making it challenging to use as a guide for decision-making. One study [46] provided an alternative method, two-stage bootstrapping regression, analyzing how uncontrollable factors affect the highway deterioration processes, which has inspired subsequent research. Through the above analysis, based on the characteristics of HRMM and DEA efficiency values, this paper opted for the regression method to explore the effects of uncontrollable factors on HRMMP.

2.4. Uncontrollable Factors Analysis of DEA Efficiency Values

The efficiency value $\theta$ obtained by DEA is a restricted dependent variable situation when analyzed as a dependent variable because it falls between 0 and 1 ($\theta \in \left(\mathrm{0,1}\right]$). The traditional ordinary least squares (OLS) estimation method for regression, whether applied to the entire sample or a subsample after the discrete points have been excluded, results in inconsistent estimation due to the inclusion of the nonlinear term in the disturbance term [54]. Two primary methodologies are utilized to address the challenge of regression analysis of restricted dependent variables: the Tobit model and the truncated regression model.

• The Tobit method, introduced by Tobin in 1985, employs maximum likelihood estimation (MLE) to estimate censored regression models. Censored regression is one of the scenarios for a restricted dependent variable analysis. In the linear model $y_i=x_i^{’}\beta +{\epsilon }_i$, when censoring $y_i$ as $c$ for certain cases where $y_i\ge c$ or $y_i\le c$ (where $c$ is a constant), this type of data is referred to as “censored data” [55].
• In the linear model $y_i=x_i^{’}\beta +{\epsilon }_i$, it is assumed that due to certain reasons, data can only be observed when $y_i\ge c$ (where $c$ is a constant). Therefore, when $y_i<c$, no data regarding the variables $\left\{y_i,x_i\right\}$ are available, and this phenomenon is referred to as “truncation”. For instance, data can only be observed when $y_i$ is greater than c, resulting in a “left truncation” at $c$.

In past studies, researchers have commonly employed the Tobit model to analyze the factors influencing DEA efficiency values [56,57,58,59,60]; however, the actual DEA efficiency value does not exhibit censoring issues and does not fall into the category of censored data. Considering the initial efficiency value $\theta \in \left(\mathrm{0,1}\right]$ as a whole and denoting the efficiency value $\theta$ in the worst state as ${\theta }_{min}$, the application of the Tobit method implies that $\theta$ values are censored data within the data set; consequently, all values below ${\theta }_{min}$ are replaced by ${\theta }_{min}$, as illustrated in Figure 1a. Nevertheless, for any evaluated DMU, the efficiency value will never be lower than ${\theta }_{min}$ in the worst state, much less reach or descend below 0. To put it another way, the scenario depicted in Figure 1a is not compatible with the actual DEA efficiency values. As shown in Figure 1b, the data in the range between 0 and ${\theta }_{min}$ are unobservable, which can be referred to as truncating at the left. Consequently, DEA efficiency values are more consistent with the truncated data, which can be processed by a truncated regression model [61,62,63,64].

2.5. Knowledge Gap

The literature review above highlights the following two research gaps:

• The importance of routine maintenance in the preservation and appreciation of highway assets has been overlooked in studies that focus on overall highway maintenance or bridge maintenance, that is, there is a lack of research specifically focusing on HRMMP.
• Researchers often concentrate solely on the methods and conclusions of performance evaluation, neglecting to investigate the factors that influence HMMP, particularly in HRMMP. This lack of investigation hinders a more comprehensive understanding of maintenance management performance assessment and improvement.

Therefore, according to the characteristics of routine maintenance and management, this paper employed the DEA method to construct the performance evaluation indicators set and evaluated HRMMP. In addition, a truncated regression model was proposed to analyze the impact of uncontrollable factors on HRMMP, overcoming the shortcomings of the Tobit model.

3. Data Collection

STHG is primarily responsible for the investment, construction, and operation of highways within Shaanxi Province. It adopts a hierarchical management model of group–operation company–maintenance management subsidiary for HMM; the organizational structure and corresponding responsibilities are depicted in Figure 2.

In a previous study conducted by the authors, Shaanxi Province can be typically divided into three regions based on topography [65]: the Shaanbei plateau (northern Shaanxi), the Guanzhong plain (central Shaanxi), and the Shaannan mountains (southern Shannxi). There are 23 maintenance management subsidiaries (23 DMUs) responsible for the maintenance management of different road sections, the distribution of which is illustrated in Figure 3. The relative maintenance management data from 2020 to 2022 was provided by STHG, which involves the climate conditions, traffic, maintenance mileages, maintenance management resources, road conditions, etc., of each subsidiary, providing a strong foundation for the following research.

4. Methodology

4.1. Input-Oriented DEA Model

Traditional DEA models consist of the Banker–Charnes–Cooper (BCC) model, which is based on variable returns to scale (VRS), and the Charness–Cooper–Rhodes (CCR) model, which is based on constant returns to scale (CRS). The efficiency obtained by the CCR model is known as combined technical efficiency (TE) because it incorporates scale efficiency (SE), while the efficiency obtained by the BCC model is pure technical efficiency (PTE). SE can be calculated by Equation (1).

SE = TE/PTE

(1)

CRS efficiency values reflect TE under a constant scale, highlighting the excellence of highway management agencies in terms of maintenance operation mechanisms and overall management levels. In contrast, VRS efficiency values indicate PTE under a variable scale, revealing whether there is redundancy in the maintenance management resources invested by highway management agencies. Moreover, the models mentioned above can be categorized as either input-oriented or output-oriented. From an input-oriented perspective, organizations usually want to keep the amount of input resources to a minimum while maintaining a constant level of output. From an output-oriented point of view, organizations strive to achieve more outputs while maintaining a constant level of input resources. Highway management agencies often have limited resources for maintenance, focusing on minimizing inputs while sustaining a certain level of maintenance performance; therefore, the input-oriented DEA model was selected to evaluate HRMMP, which is shown in

Table 3. Input-oriented DEA models.

Objective Function	${\mathit{\theta }}^{\mathbf{*}}=\mathit{min}\mathit{\theta }$
DEA model	BCC	CCR
Subject to	${\displaystyle \sum _{j=1}^n}{\lambda }_j{x}_{ij}\le \theta x_{io}$ ${\displaystyle \sum _{j=1}^n}{\lambda }_j{y}_{rj}\ge y_{ro}$ ${\displaystyle \sum _{j=1}^n}{\lambda }_j=1$ ${\lambda }_j\ge 0$	${\displaystyle \sum _{j=1}^n}{\lambda }_j{x}_{ij}\le \theta x_{io}$ ${\displaystyle \sum _{j=1}^n}{\lambda }_j{y}_{rj}\ge y_{ro}$ ${\lambda }_j\ge 0$
	$i=\mathrm{1,2},\dots ,m;r=\mathrm{1,2},\dots ,s;j=\mathrm{1,2},\dots ,n$

Note: $\theta$ is a decision variable representing the efficiency value, $x_{io}$ and $y_{ro}$ refer to the ith input and rth output of a particular DMU_o to be evaluated, $x_{ij}$ and $y_{rj}$ refer to the ith input and rth output of jth DMU, ${\lambda }_j$ denotes the linear combination coefficient of jth DMU, $m$ denotes the number of inputs, $s$ denotes the number of outputs, and $n$ denotes the number of DMUs.

.

4.2. Return to Scale (RTS)

The concept of returns to scale (RTS) is a crucial foundation in economics for analyzing the variations in production factors and outputs. With the ongoing evolution of DEA methodology, the application of RTS has been extended. When inputs and outputs vary in the same proportion, the evaluated DMU is in a CRS state. If the proportional change in output exceeds that of the input when increasing or the proportional change in output is less than that of the input when decreasing, the evaluated DMU is in an increasing returns to scale (IRS) state. Conversely, if the smaller proportional change in output exceeds that of the input when increasing or the proportional change in output when increasing is less than that of the input, the evaluated DMU is in a decreasing returns to scale (DRS) state. IRS and DRS fall under the VRS category.

There are the three following criteria to determine the RTS of DMU:

• When ${\theta }_{CRS}={\theta }_{VRS}$, the evaluated DMU satisfies CRS. Or else:
• When ${\sum }_{j=1}^n{\lambda }_j^{*}<1$, the evaluated DMU satisfies IRS.
• When ${\sum }_{j=1}^n{\lambda }_j^{*}>1$, the evaluated DMU satisfies DRS.

4.3. Truncated Regression Model

For a random variable y in the linear model $y_i=x_i^{’}\beta +{\epsilon }_i$, when it experiences truncation, the corresponding probability density function is altered. Let the initial probability density function be denoted as $f\left(y\right)$; then, the conditional probability density function after left truncation at point c is represented by Equation (2) [54].

$$f(y|y>c)=\left\{\begin{array}{c}\frac{f\left(y\right)}{P(y>c)}, y>c\hfill \\ 0, y\le c\hfill \end{array}\right.$$

(2)

The area under the probability density function curve must sum to 1. Due to truncation, where data are unobservable at the left of point c, the probability density at the location of c is elevated to ensure that the area under the curve adds up to 1. This elevation continues until the entire area under the curve adds up to 1 [55]. For illustration, the impact of truncated data on the classical normal distribution’s probability density function is visually evident in Figure 4.

Then, the conditional expectation of the truncation distribution in the case of “left truncation” is calculated; the simplest case $y\sim N\left(\mathrm{0,1}\right)$ of the normal distribution is still used as an example.

$$E(y|y>c)=\frac{\varphi \left(c\right)}{1-\varphi \left(c\right)}$$

(3)

For any real number $c$, the inverse Mills’s ratio (IMR) is defined as $\lambda (c)=\frac{\varphi \left(c\right)}{1-\varphi \left(c\right)}$, which is the density function $\varphi \left(c\right)$ of the standard normal divided by the area $1-\varphi \left(c\right)$ (referred to as the gray area, as illustrated in Figure 5) under the curve larger than $c$. Consequently, $E\left(y\right|y>c)=\lambda (c)$ can be obtained, as shown in Equation (3).

For a general normal distribution $y\sim N(\mu ,{\sigma }^2)$, let $z\equiv \frac{y-\mu }{\sigma }\sim N\left(\mathrm{0,1}\right)$, so that $y=\mu +\sigma z$. Therefore, the conditional expectation in the case of a general normal distribution with truncation is shown in Equation (4).

$$\begin{gathered} E\left(y\right|y>c)=E(\mu +\sigma z|\mu +\sigma z>c)=E[\mu +\sigma z|z>(c-\mu )/\sigma ] \\ =\mu +\sigma E\left[z\right|z>(c-\mu )/\sigma ]=\mu +\sigma \lambda [(c-\mu )/\sigma ] \end{gathered}$$

(4)

Assume that ${\epsilon }_i|x_i\sim N(0,{\sigma }^2)$, so that $y_i|x_i\sim N(x_i^{\mathrm{’}}\beta ,{\sigma }^2)$, and then Equation (5) can be obtained from Equation (4).

$$E\left(y_i\right|y_i>c)=x_i^{\mathrm{’}}\beta +\sigma \lambda [\left(c-x_i^{\mathrm{’}}\beta \right)/\sigma ]$$

(5)

The sample data can only be observed in the case of left truncation ($y_i\ge c$); if OLS is applied to estimate $y_i=x_i^{\mathrm{’}}\beta +{\epsilon }_i$, the nonlinear term $\sigma ·\lambda \left[\right(c-x_i^{\mathrm{’}}\beta )/\sigma ]$ will be omitted and then included in the perturbation term. It can be seen that $\sigma ·\lambda \left[\right(c-x_i^{\mathrm{’}}\beta )/\sigma ]$ is a function of $x_i$, and thus the inclusion of the nonlinear term in the perturbation term in the OLS regression leads to estimation bias.

To address the above problems, MLE is used to obtain a consistent estimate of the truncated regression. The initial probability density function for MLE of the regression model is shown in Equation (6).

$$f(y_i)=\frac{1}{\sqrt{2\pi {\sigma }^2}}\mathit{exp}\left\{-\frac{1}{2}(\frac{y_i-x_i^{\mathrm{’}}\beta }{\sigma }{)}^2\right\}=\frac{1}{\sigma }\varphi \left(\frac{y_i-x_i^{\mathrm{’}}\beta }{\sigma }\right)$$

(6)

The conditional probability that the sample data can be observed is shown in Equation (7), where the perturbation term obeys a normal distribution, that is, ${\epsilon }_i/\sigma \sim N\left(\mathrm{0,1}\right)$.

$$\begin{gathered} P\left(y_i>c|x_i\right)=1-P\left(y_i\le c|x_i\right)=1-P\left(\frac{y_i-x_i^{\mathrm{’}}\beta }{\sigma }\le \frac{c-x_i^{\mathrm{’}}\beta }{\sigma }|x_i\right) \\ =1-P(\frac{{\epsilon }_i}{\sigma }\le \frac{c-x_i^{\mathrm{’}}\beta }{\sigma }|x_i)=1-\varphi (\frac{c-x_i^{\mathrm{’}}\beta }{\sigma }) \end{gathered}$$

(7)

Then, the conditional density after truncation is shown in Equation (8).

$$f(y_i|y_i>c,x_i)=\frac{\frac{1}{\sigma }\varphi \left[\right(y_i-x_i^{\mathrm{’}}\beta )/\sigma ]}{1-\varphi \left[\right(c-x_i^{\mathrm{’}}\beta )/\sigma ]}$$

(8)

The research frame in this study is shown in Figure 6.

5. Performance Evaluation

5.1. Selection of Potential Input and Output Indicators

Most organizations consider financial, material, and human resources as the three input factors in the performance evaluation process, and the results obtained through the transformation of inputs naturally become outputs. For the highway routine maintenance management process, financial input factors include the total maintenance costs, material input factors include maintenance materials and equipment other than contractors’ input, and human input factors include maintenance management personnel. Additionally, activities conducted by the maintenance management department, such as road inspections and road appearance improvements, which contribute to maintenance management, should also be considered. The output factors that require consideration primarily encompass maintenance mileage, traffic volume, various technical condition indices, user satisfaction, user costs, and so on.

By investigating the HRMM work and operational mechanisms of STHG, combined with Table 1, a compilation and summary were conducted to obtain the potential input and output indicators set illustrated in

Table 4. Potential evaluation indicators of HRMM.

Type	Potential Indicators	Indicator Explanation
Input	Maintenance and management personnel (MP)	Number of management and inspection personnel
	Own maintenance equipment (ME)	Number of routine maintenance equipment items other than contractors’ input
	Maintenance and management cost (MC)	Management cost + inspection cost + maintenance cost
	Relative maintenance and management activity (MA)	Number of activities implemented by each DMU such as road checking, road appearance improvement, and employee training
Output	Maintenance mileage (MM)	Road section length under the jurisdiction of each DMU
	Tollbooth and service area (TSA)	Number of tollbooths and service area under the jurisdiction of each DMU
	Maintenance quality indicator (MQI)	Various technical condition indicators of highways
	Traffic volume	The annual throughput of each type of vehicle counted at each tollbooth converted to the annual average daily traffic (AADT) volume
	Satisfaction of users	Users’ subjective perception of the overall level of service, comfort, appearance, and safety on highways
	Effectiveness of users	Cost savings of transportation, reduction in number of traffic accidents, time savings of travel
	Employment created	Local employment generated by maintenance work

.

5.2. Correlation Tests of Input and Output Indicators

The premise of DEA is that changes in input indicators should lead to positive proportional changes in output indicators [66]. Therefore, based on the availability and effectiveness of the data, the input and output indicators selected from Table 4 and data corresponding to STHG in the year 2022 are shown in

Table 5. Input and output indicators and maintenance data in the year 2022.

DMU	Input Indicator				Output Indicator
	MP	MC (104 CNY)	ME	MA	MM (km)	MQI	AADT	TSA
1	1022	148.2	36	19	80.35	94.68	379,859	15
2	425	63.2	34	17	115.00	94.84	15,881	10
3	971	138.2	7	11	183.00	96.65	94,105,623	17
4	208	20.4	11	10	18.02	88.70	4955	13
5	767	82.9	5	20	135.70	95.44	26,193	13
6	636	114.3	23	18	188.87	94.37	68,649	13
7	429	75.1	31	23	132.29	95.76	58,171	10
8	474	82	30	30	92.31	96.41	18,106	10
9	589	140.5	16	18	122.22	94.01	23,153	11
10	566	103.2	29	13	162.00	96.00	6443	14
11	233	36.3	10	7	20.58	97.20	45,810	4
12	377	57.7	13	25	94.51	96.11	1590	10
13	413	334.8	21	14	192.18	96.80	33,274	13
14	482	100.5	18	32	56.91	96.54	32,419	6
15	412	471	35	23	135.50	96.91	20,495	12
16	388	82.7	14	9	118.81	96.92	17,565	10
17	216	65.4	14	11	109.85	96.26	7887	5
18	363	52.5	9	18	93.55	97.74	33,051	10
19	324	59.4	18	28	116.35	97.07	10,869	10
20	359	95.5	19	16	149.96	98.80	15,963	10
21	197	40.2	6	19	61.20	97.95	6328	5
22	384	75.5	13	30	122.61	97.11	18,571	13
23	584	126.9	24	10	204.02	95.70	17,230	11

. Spearman’s correlation tests were performed on the input and output data of 23 DMUs using the correlation analysis feature in the SPSS 26.0 software [67], as shown in

Table 6. Results of Spearman’s rank correlation test for 2022 annual data.

Indicator	MM	MQI	AADT	TSA
MP	0.443 * (0.039)	−0.598 ** (0.003)	0.528 * (0.012)	0.570 ** (0.006)
MC	0.640 ** (0.001)	−0.263 (0.238)	0.427 * (0.047)	0.558 ** (0.007)
ME	0.344 (0.117)	−0.318 (0.150)	0.239 (0.284)	0.311 (0.159)
MA	−0.120 (0.595)	0.095 (0.676)	0.118 (0.600)	0.002 (0.992)

Note 1: the numbers in parentheses represent the correlation coefficients, and the numbers outside the parentheses represent the significance level of the indicators. Note 2: * denotes significance at the 0.05 level, and ** denotes significance at the 0.01 level.

.

Analyzing the results of the correlation analysis presented in Table 6, it is observed that MP and MC among the input indicators exhibited positive correlations with MM, AADT, and TSA among the output indicators. Conversely, ME and MA among the input indicators showed either no correlation or a negative correlation with MQI among the output indicators. These findings suggest that the initially identified input–output indicators, based on subjective significance, may not necessarily hold practical meaning in the analytical process. In consideration of the correlation analysis results, the revised selection of input indicators included MP and MC, while the output indicators consisted of MM, AADT, and TSA.

Building upon this analysis, a correlation test was conducted on the input and output data for each DMU from 2020 to 2022, and the results are presented in

Table 7. Results of Spearman’s rank correlation test for 2020–2022 annual data.

Indicator	MM	AADT	TSA
MP	0.298 * (0.030)	0.431 ** (0.001)	0.616 ** (0.000)
MC	0.592 ** (0.000)	0.079 (0.572)	0.363 ** (0.007)
ME	0.057 (0.683)	0.110 (0.432)	0.098 (0.487)
MA	−0.241 (0.082)	0.250 (0.072)	−0.079 (0.574)

Note 1: the numbers in parentheses represent the correlation coefficients, and the numbers outside the parentheses represent the significance level of the indicators. Note 2: * denotes significance at the 0.05 level, and ** denotes significance at the 0.01 level.

. Based on the outcomes shown in Table 7, the ultimate selection of the input indicators included MP and MC, while MM and TSA were chosen as the output indicators.

5.3. Determination of Efficiency Value and RTS

Based on the identified input and output indicators from the above analysis, the efficiency value of HRMMP for each DMU under the CCR and BCC scenarios was calculated, respectively, using the input-oriented DEA model, and the RTS of each DMU was determined; the results are presented in

Table 8. Efficiency value and RTS of each DMU in the year 2022.

DMU No.	θCCR (CRS State)	Σλ	θBCC (VRS State)	SE	RTS
1	0.801878741	1.240857	0.933271453	0.859212761	DRS
2	0.82410613	1	1	0.82410613	IRS
3	0.95188034	1.564246	1	0.95188034	DRS
4	0.370941655	1	0.866359447	0.428161378	IRS
5	0.899305267	1.168489	0.951625815	0.94501983	DRS
6	0.601581645	1.623292	0.611227373	0.984219084	DRS
7	0.328685125	1.137	0.330405272	0.994793827	DRS
8	0.542082174	0.950978	0.565212975	0.959075957	IRS
9	0.856745906	1.459957	0.87933692	0.974309036	DRS
10	0.342037832	1.392475	0.412463752	0.829255494	DRS
11	1	0.363343	1	1	CRS
12	0.843600459	0.815351	1	0.843600459	IRS
13	0.672331412	1	0.789429714	0.851667223	IRS
14	0.805618446	0.689907	0.810125722	0.994436325	IRS
15	0.943455743	0.923077	0.960413285	0.982343496	IRS
16	1	1.188827	1	1	CRS
17	0.933260635	1	0.959180602	0.97297697	IRS
18	0.845864089	0.807235	0.91136005	0.928133825	IRS
19	1	1	1	1	CRS
20	1	1.557848	1	1	CRS
21	1	0.566875	1	1	CRS
22	0.869893063	1.410357	1	0.869893063	DRS
23	0.809871334	1.790861	0.81755848	0.990597437	DRS

.

According to Table 8, it can be observed that under the CCR model (CRS state), DMUs 11, 16, 19, 20, and 21 were on the efficiency frontier (${\theta }_{CCR}={\theta }_{BCC}=1$). Furthermore, under the BCC model (VRS state), the DMUs on the efficiency frontier (${\theta }_{BCC}=1$) included DMUs 2, 3, 12, and 22 in addition to those under the CRS state. For a DMU that is effective under a CRS state, it remains effective under a VRS state; however, effectiveness under a VRS state does not guarantee effectiveness under a CRS state. When a DMU is effective under both conditions, it is in a state of RTS with CRS, such as DMUs 11, 16, 19, 20, and 21. When the efficiency values under a CRS state and VRS state are not both 1, or when they are both not 1, there exist other RTS: IRS (DMU 2, 4, 8, 12, 13, 14, 15, 17, and 18) or DRS (DMU 1, 3, 5, 6, 7, 9, 10, 22, and 23). In summary, when the ${\theta }_{CCR}$ and ${\theta }_{BCC}$ values in Table 8 are not equal to 1, it indicates that the respective DMU is ineffective under a CRS state or VRS state.

Regarding the RTS, among the 23 DMUs, 5 operated under a CRS state. Additionally, nine DMUs experienced IRS, indicating an ongoing improvement in their maintenance management efficiency and an optimistic trend in efficiency development. On the other hand, nine DMUs faced DRS, suggesting a regression in their maintenance management efficiency. In comparison to the subsidiaries with IRS, those experiencing DRS may need to allocate more effort and intensify their optimization of input resource allocation in their later-stage management efforts.

6. Uncontrollable Factors Analysis

6.1. Selection of Potential Uncontrollable Factors

HRMMP is influenced by various uncontrollable factors, including natural conditions like climate and geography, maintenance history, years of operation, unexpected situations such as traffic accidents and natural disasters, and regional socio-economic development. Section 5.3 demonstrates significant variations in the HRMMP efficiency values among the 23 DMUs. It is unclear whether uncontrollable factors, in addition to their input resources, impact sustainable HRMM. To explore the problems, combined with Table 2 and the investigation into the HRMM work of STHG, the potential uncontrollable factors were analyzed as follows.

• Climate condition. When analyzing sustainable HRMM, it is important to consider the influence of climatic conditions, which can vary greatly. This study mainly focused on daily weather statistics in areas where each DUM is located, including the number of extreme weather days such as moderate-to-heavy rain days, snowy days, and hazy days. Additionally, the quantity of natural dustfall in the area was measured using the annual province-wide environmental quality status information provided by the Shaanxi Provincial Department of Ecology and Environment.
• Geographic location. The geographic location is mainly based on topography and geomorphology, which is reflected in this study by three main categories: the Shaanbei plateau, the Guanzhong plain, and the Shaannan mountains.
• Maintenance history. Maintenance history mainly refers to the data on corrective maintenance, preventive maintenance, emergencies, and special maintenance organized by each DMU of the specific road section from the opening of the operation to date, which was used to analyze the impact on HRMM.
• Years of operation. Years of operation refer to the service life of the road from the year of commissioning to the present.
• Emergencies. The data on emergencies mainly count the number of traffic accidents, landslides and mudslides, and other natural disasters that occurred during the statistical year of each DMU as analysis data.
• Regional characteristics. Regional characteristics primarily include population size, urbanization rate, and gross domestic product (GDP), as well as other indicators of socio-economic development in the regions where each DMU is located.
• Special asset type. Bridges and tunnels are considered special asset types that require more attention to routine maintenance than other asset types such as pavements and subgrades. This is due to the incalculable impact of damage to bridges and tunnels. The available data show that the length of bridges and tunnels managed by each DMU had significant variations, the impact of which on HRMMP cannot be ignored.

Based on the above analysis and available data,

Table 9. Potential uncontrollable factors of HRMM.

Uncontrollable Factors	Acronym	Description
Extreme weather	Weather	Days of extreme weather (i.e., heavy rain days, snowy days, hazy days, etc.)
Population	Population	Population in the regions where each DMU is located (million)
Urbanization rate	UR	Urban population/total population (%)
Amount of natural dustfall	Dustfall	Amount of natural dustfall on road sections where each DMU manages (t/(km2·month))
GDP	GDP	GDP in the regions where each DMU is located (CNY)
Years of operation	Age	Service life of highway from the year of commissioning to the present (year)
Region	Region	Shaanbei plateau (r1), Guanzhong plain (r2), and Shaannan mountains (r3)
Bridge length	BL	Length of bridges managed by each DMU (km)
Tunnel length	TL	Length of tunnels managed by each DMU (km)

summarizes the potential uncontrollable factors. In order to meet the requirements of the sample data volume in the truncated regression analysis, the efficiency values of each DMU from 2020 to 2022 were calculated. The data of the potential uncontrollable factors from Table 9 and the efficiency values of each DMU are listed in

Table 10. Potential uncontrollable factors data and efficiency values of each DMU.

DMU No.	Time	θCRS	θVRS	Weather	Population	UR	Dustfall	GDP	Age	Region	BL	TL
1	2020	0.7834	0.9138	41.02	262.887	46.7516	4.757	31,478	6	r3	75.97	58.17
1	2021	0.7843	0.9138	47.85	263.507	46.9506	8.4961	35,942.2	7	r3	75.97	58.17
1	2022	0.7828	0.9187	32.23	263.888	48.3045	8.9665	40,276.4	8	r3	75.97	58.17
2	2022	0.781	1	25.62	266.89	48.6	10.01	42,544	4	r3	21.99	12.89
3	2022	0.8944	0.9074	29.57	225.94	62.31	14.99	68,940	3	r1	48.3	24.2
4	2021	0.4028	0.9557	33.5	554.62	56.125	11.47	59,746	9	r2	8.43	0
4	2022	0.357	0.8664	31.5	577.55	56.955	11.0125	62,054.5	10	r2	8.43	0
5	2020	0.8109	0.8388	25.74	338.2	56.3	5.42	81,764	12	r1	3.78	0
5	2021	0.8272	0.8569	28.85	340.33	57.7	7.56	97,811	13	r1	3.78	0
5	2022	0.8337	0.864	28.37	341.78	58.94	8.65	112,845	14	r1	3.78	0
6	2020	0.5812	0.6435	46.18	566.65	61.4789	8.9914	50,883.3	9	r3	21.21	9.28
6	2021	0.587	0.6521	44.43	578.581	59.9461	10.6645	56,467	10	r3	21.21	9.28
6	2022	0.5884	0.6109	25.53	626.818	60.8339	9.7285	60,398.4	11	r3	21.21	9.28
7	2020	0.4816	0.5796	62	883.21	73.43	13.47	71,357	7	r2	33.31	0
7	2021	0.4765	0.5796	29	905.68	73.72	13.09	78,346	8	r2	33.31	0
7	2022	0.3245	0.5768	30	1000.37	74.01	11.86	85,114	9	r2	33.31	0
8	2020	0.5186	0.5318	35.36	237.17	49.04	4.33	29,574	9	r3	45.34	14.88
8	2021	0.6412	0.6522	46.28	238.13	45.61	8.14	33,695	10	r3	45.34	14.88
8	2022	0.5126	0.5189	27.28	238.02	47.12	7.51	34,674	11	r3	45.34	14.88
9	2020	0.8675	0.9072	36.3	237.17	49.04	4.33	29,574	8	r3	37.85	21.09
9	2021	0.8595	0.8978	48	238.13	45.61	8.14	33,695	9	r3	37.85	21.09
9	2022	0.806	0.8424	24.7	238.02	47.12	7.51	34,674	10	r3	37.85	21.09
10	2020	0.3308	0.4275	31.53	338.2	56.3	5.42	81,764	6	r1	21.28	8.04
10	2021	0.331	0.4275	25.47	340.33	57.7	7.56	97,811	7	r1	21.28	8.04
10	2022	0.3178	0.4125	28.59	341.78	58.94	8.65	112,845	8	r1	21.28	8.04
11	2022	1	1	30	238.02	47.12	7.51	34,674	12	r2	0	18.02
12	2021	0.8107	0.8116	33.69	340.33	57.7	7.56	97,811	11	r1	46.64	9.25
12	2022	0.7797	0.7804	25.99	341.78	58.94	8.65	112,845	12	r1	46.64	9.25
13	2020	1	1	24.94	506.351	51.2918	15.136	48,583.8	9	r2	25.47	5.41
13	2021	0.9955	1	36.21	446.962	50.7292	10.9732	54,042	10	r2	25.47	5.41
13	2022	0.6034	1	29.67	447.885	51.7248	10.7526	54,982.9	11	r2	25.47	5.41
14	2020	0.8056	0.8101	47.61	605.413	62.9423	9.5398	53,390.3	5	r3	56.13	21.3
14	2021	0.8056	0.8101	46.53	618.633	61.6327	10.9615	59,146.1	6	r3	56.13	21.3
14	2022	0.8056	0.8101	25.86	672.56	62.4473	9.9895	63,424.8	7	r3	56.13	21.3
15	2022	0.8871	0.8875	30	1000.37	74.01	11.86	85,114	4	r2	7.65	0
16	2020	0.8033	0.8297	46.68	458.245	57.1606	7.4726	43,907	10	r2	38.33	7.47
16	2021	0.7875	0.8116	41.99	466.496	55.2519	9.871	49,024.7	11	r2	38.33	7.47
16	2022	0.8332	0.8643	28.16	498.663	56.3366	9.114	52,217.1	12	r2	38.33	7.47
17	2022	0.8576	0.9	33.46	436.61	51.27	10.73	54,368	5	r2	17.86	2.83
18	2020	0.6613	0.6662	22.03	267.06	58.0577	11.0459	60,681.7	14	r1	22.5	3.31
18	2021	0.6343	0.6384	31.23	268.497	59.6467	12.2598	71,524.3	15	r1	22.5	3.31
18	2022	0.6591	0.6639	33.06	268.801	61.0631	12.6442	85,184.9	16	r1	22.5	3.31
19	2022	0.9774	1	31.32	225.94	62.31	14.99	68,940	4	r1	66.79	28.94
20	2022	1	1	32.92	225.94	62.31	14.99	68,940	6	r1	44.7	37.53
21	2020	1	1	23.32	225.28	59.09	14.35	48,300	7	r1	36.69	29.18
21	2021	1	1	30.72	226.31	60.79	15.02	56,086	8	r1	36.69	29.18
21	2022	1	1	30.5	225.94	62.31	14.99	68,940	9	r1	36.69	29.18
22	2020	0.7934	1	32.74	338.2	56.3	5.42	81,764	8	r1	10.72	0
22	2021	0.764	1	31.44	340.33	57.7	7.56	97,811	9	r1	10.72	0
22	2022	0.8088	1	29.28	341.78	58.94	8.65	112,845	10	r1	10.72	0
23	2020	0.8597	0.8882	36.04	338.2	56.3	5.42	81,764	5	r1	32.89	10.01
23	2021	0.8101	0.8311	30.56	340.33	57.7	7.56	97,811	6	r1	32.89	10.01
23	2022	0.7551	0.7835	28.09	341.78	58.94	8.65	112,845	7	r1	32.89	10.01

.

6.2. Multicollinearity Test of Possible Uncontrollable Factors

Prior to commencing regression analysis, it is crucial to conduct multicollinearity tests on potential uncontrollable factors using the STATA 18.0 MP software and to exclude factors exhibiting high collinearity. Conventionally, factors with a variance inflation factor (VIF) exceeding 10 may suggest the presence of multicollinearity. To begin the regression analysis, considering the efficiency values of CRS or VRS from 2020 to 2022 as the dependent variable and various potential uncontrollable factors as independent variables, the VIF values for each potential uncontrollable factor were calculated. In this context, the regional factors underwent virtualization using the STATA software. Three dummy variables, namely r1 (Shaanbei), r2 (Guanzhong), and r3 (Shaannan), were generated. To address multicollinearity concerns, only r2 and r3 were included as indicators in the analysis.

The analysis results shown in

Table 11. Covariance diagnosis results of uncontrollable factors.

Variable	VIF	1/VIF
Population	21.95	0.045563
r2	16.72	0.059800
r3	15.58	0.064194
UR	13.67	0.073133
GDP	6.61	0.151257
TL	4.40	0.227338
BL	3.20	0.312632
Dustfall	2.29	0.436760
Age	1.41	0.710871
Weather	1.36	0.734977
Mean VIF	8.72

revealed notable multicollinearity issues among the factors of population, UR, and region (r2, r3). Although UR had a lower VIF value compared to population and region, due to multicollinearity concerns, it was still chosen in the truncated regression analysis. Advanced econometric studies suggest that when researchers prioritize the significance of the model and the factors under analysis, multicollinearity issues can be disregarded. The absence of multicollinearity interference may amplify the significance of initially significant factors, rendering them more pronounced. Hence, population and region were not taken into further consideration due to the fact that the inclusion of these two factors would not have augmented the significance of the model or the analyzed factors. Consequently, the initial identification of factors influencing the DEA efficiency values encompassed seven variables: weather, age, dustfall, BL, TL, GDP, and UR.

6.3. Truncated Regression Analysis

From Section 6.2, the truncated regression model in this paper is shown in Equation (9):

$${\theta }_{it}={\beta }_0+{\beta }_1{weather}_{it}+{\beta }_2{age}_{it}+{\beta }_3{dustfall}_{it}+{\beta }_4{BL}_{it}+{\beta }_5{TL}_{it}+{\beta }_6{GDP}_{it}+{\beta }_7{UR}_{it}$$

(9)

where ${\theta }_{it}$ is the efficiency value of ith DMU in t year, ${\beta }_0$ is the interception, ${\beta }_1 ~ {\beta }_7$ are estimated coefficients, $i$ = 1, 2, …, 23, and $t$ = 2020, 2021, 2022.

Integrating the preliminarily identified uncontrollable factors into the truncated regression analysis, distinct truncated regression models were formulated with CRS and VRS efficiency values as dependent variables. The distribution of the efficiency values is shown in Figure 7; considering the minimum CRS efficiency value of 0.317837901 and the minimum VRS efficiency value of 0.412463752, truncated regression analyses were performed with left truncation at 0.3 and 0.4, respectively. The outcomes are detailed in

Table 12. Results of truncated regression analysis with θ_CRS and θ_VRS as the dependent variables.

Number of Observations = 53	CRS				VRS
	Limit: Lower = 0.3		$\mathbf{Prob} > {\mathit{\chi }}^2$ = 0.0351		Limit: Lower = 0.4		$\mathbf{Prob} > {\mathit{\chi }}^2$ = 0.0016
CRS	Coef.	p > |z|	[95% Conf. Interval]		Coef.	p > |z|	[95% Conf. Interval]
GDP	1.08 × 10−6	0.478	−25.1	4.08 × 10−6	1.04 × 10−6	0.396	−19.6	3.43 × 10−6
TL	0.0058584	0.073	−0.000537	0.0122539	0.0051855	0.049	0.0000334	0.0103376
BL	−0.002011	0.402	−0.006716	0.0026932	−0.004123	0.033	−0.007902	−0.000343
Dustfall	0.0238089	0.033	0.0018957	0.0457221	0.0255709	0.004	0.0080864	0.0430553
Age	−0.004689	0.637	−0.024159	0.0147812	−0.012255	0.123	−0.027819	0.0033094
Weather	−0.000622	0.867	−0.007925	0.0066812	0.0004603	0.877	−0.005358	0.0062786
UR	−0.009585	0.12	−0.021671	0.0025018	−0.012068	0.014	−0.021724	−0.002412
${\beta }_0$	1.022378	0.001	0.4065462	1.638211	1.338691	0	0.8463258	1.831056
$\sigma$	0.1779934	0	0.1394903	0.2164966	0.1446174	0	0.1149123	0.1743226

Note: $\sigma$ denotes the standard deviation of truncated residuals; “Coef.” and “Conf.” are the abbreviations of “coefficient” and “confidence”, respectively.

.

6.3.1. Discussion of the Results in the Truncated Regression Analysis of θ_CRS

From Table 12, it is evident that the overall model had statistical significance, as indicated by Prob > ${\chi }^2$ = 0.0351, which is less than 0.05. This signifies the overall importance of the model. Upon examining the specific factors and their p > |z| values, only the dustfall variable demonstrated statistical significance, with a p-value less than 0.05. The coefficient associated with dustfall was 0.238089, indicating a positive correlation. Therefore, it was concluded that dustfall significantly influences CRS efficiency values, with a positive correlation existing between dustfall and CRS efficiency values.

This positive correlation implies the importance that each DMU places on the daily cleaning of highways. Natural dustfall significantly increases the daily cleaning burden of facilities along highways, such as dust settling on guardrails and signs. Timely cleaning is essential, as failure to do so could not only affect the aesthetics and functionality of these facilities but also potentially compromise the visibility guidance performance for drivers, posing safety concerns.

Therefore, in regions with higher levels of dustfall, it can be understood that corresponding DMUs place a greater emphasis on the cleanliness and environmental friendliness of highways. The stronger the commitment of managers to maintaining the cleanliness and environmental friendliness of roads, the more comprehensive and effective the related management measures become. This aligns with the principles outlined in emphasizing the promotion of green maintenance, urging a focus on ecological priorities, efficient resource utilization, carbon emission reduction, and the promotion of sustainable green development in highway maintenance work.

6.3.2. Discussion of the Results in the Truncated Regression Analysis of θ_VRS

From Table 12, it is evident that the overall model had statistical significance, as indicated by Prob > ${\chi }^2$ = 0.0061, which is less than 0.05, signifying the overall significance of the model. Examining the specific factors and their p > |z| values, TL, BL, dustfall, and UR all achieved statistical significance. All four indicators had a significant impact on the VRS efficiency values. Specifically, TL and dustfall exhibited positive correlations with VRS efficiency values, with correlation coefficients of 0.0051855 and 0.0255709, respectively. On the other hand, BL and UR showed negative correlations, with correlation coefficients of −0.0041227 and −0.012068, respectively.

• Tunnel length. Table 12 illustrates a positive correlation between the VRS efficiency values and TL, indicating that an increase in TL promotes the HRMMP of each DMU. Highway tunnels play a crucial role in reducing the distances between locations. With the continuous improvement of the highway network, the transportation department imposes higher standards for tunnel construction and maintenance. In addition to reducing distances, tunnels also enhance road technical status, transport capacity, and accident reduction. Due to the semi-enclosed structure of tunnels, traffic accidents inside can lead to challenging-to-extinguish fires. Despite research on flame-retardant pavement materials, the spatial structure remains a significant challenge for rescue operations in fire events. For example, the Qinling–Zhongnan Mountain Tunnel, with the longest mileage in China, has emergency rescue centers near it. Therefore, maintenance and repairs, especially routine maintenance, are crucial. In recent years, the transportation department has consistently enhanced the highway emergency support system, with a particular focus on ensuring the safety of those involved. The cleanliness of tunnel walls and signs inside affects drivers’ visual judgment after entering. The reflective performance of the film at the tunnel entrance and the integrity of the drainage trench cover are crucial for driver safety. Therefore, maintenance measures like daily inspections are implemented to prevent accidents. The highway management agency pays particular attention to tunnel maintenance, especially for long tunnels within its jurisdiction. Thus, an increase in tunnel length promotes improvements in HRMMP to a certain extent.
• Bridge length. Table 12 indicates a negative correlation between the VRS efficiency values and BL, that is, as the length of bridges managed by each DMU increases, HRMMP tends to decrease. In contrast to tunnels, subgrades, and pavements, bridges are subject to greater influence from natural environmental factors due to their suspended structures. Consequently, the requirements for both construction and maintenance are higher. For instance, expansion joints in bridges, affected by the natural environmental and geographical factors, coupled with the impact of vehicle loads, are prone to damage in components such as rubber seals, steel components, and concrete, requiring prompt repairs. The repair process involves challenges related to traffic disruption, safety precautions for maintenance workers, and time constraints. It is imperative that the drainage holes on the bridge deck and the drainage pipes on the bridge sides be cleared frequently to prevent blockages that could impede the drainage process. The most significant damage to bridges comes from water infiltration through expansion joints and cracks in the bridge deck surface, leading to the corrosion of steel reinforcements and damage to concrete. Therefore, regular and timely maintenance measures are required for bridge facilities. With an increase in the number and length of bridges, the difficulty of such routine maintenance also escalates. The results in this paper found that as the length of the bridges managed by each DMU increased, there was a slight downward trend in HRMMP.
• Amount of natural dustfall. As shown in Table 12, there was a positive correlation between the VRS efficiency values and dustfall, indicating that an increase in dustfall had a certain promoting effect on the HRMMP of each DMU. This observation aligns with the positive correlation relationship between the CRS efficiency values and dustfall shown in Table 12.
• Urbanization rate. As shown in Table 12, there was a negative correlation between the VRS efficiency values and UR, indicating that with an increase in UR, the HRMMP of each DMU gradually decreased. UR, as a key indicator measuring the level of urbanization in a region, is raised to promote the adjustment of the urban–rural economic structure and the healthy development of the national economy. In light of these considerations, the expansion of the urban population and the growth of the urban economy, driven by the rise in UR, have the effect of stimulating the development of secondary and tertiary industries. Consequently, highways become a critical bridge and link connecting urban and rural areas. From the perspective of individual residents, the increase in UR signifies a significant improvement in the standard of living. There is a continuous increase in per capita motor vehicle ownership and demand for outbound travel, contributing to the rise in transportation demand. From the logistics industry’s viewpoint, the upsurge in UR results in substantial demand for express delivery items. Meanwhile, industries like agricultural processing, planting, breeding, and tourism witness a continuous increase in the demand for materials and the flow of manufactured products. This illustrates that the development of urban and rural enterprises is inseparable from the crucial transportation channel provided by highways. The increase in UR simultaneously amplifies the transportation demand for highways, leading to a further increase in the difficulty of HRMM.

One noteworthy point from the analysis is the positive correlation between tunnel length and efficiency values, while there was a negative correlation between bridge length and efficiency values. The results may be attributed to the fact that bridges are typically structures that span bodies of water, valleys, or other features on roads, necessitating special attention being paid to stability and safety. Additionally, the structural complexity of bridges may require more frequent inspections and repairs, which can increase the difficulty of maintenance. Compared to bridges, tunnels are less affected by the external environment and are less susceptible to erosion and damage caused by natural factors. Moreover, the internal environment of tunnels is relatively closed, which facilitates the implementation of routine maintenance and the monitoring of its efficacy. Therefore, an increase in tunnel length may not have a significant negative impact on HRMMP.

To summarize, the HRMMP of each DMU was closely associated not only with its own input–output capacity but also with uncontrollable factors such as the amount of natural dustfall, urbanization rate, tunnel length, and bridge length managed by each DMU. When evaluating HRMMP, it is crucial to thoroughly consider these uncontrollable factors on the basis of performance ranking and identify reasonable solutions for performance improvement. When allocating maintenance resources, STHG (decision maker) should focus on DMUs with high dustfall, long bridges and tunnels, and high urbanization rates. For DMUs in a DRS state, it is necessary to implement appropriate resource reallocation and management optimization. For DMUs in an IRS state, it is possible to achieve higher outputs by increasing inputs in order to further improve productivity and performance.

7. Conclusions, Limitations, and Future Work

This study employed input-oriented DEA models to calculate HRMMP efficiency values for 23 maintenance management subsidiaries (23 DMUs) under STHG in 2022 and explored what should be considered in sustainable HRMM; the main contributions are as follows.

• This study evaluated the HRMMP of highway management agencies from the perspective of routine maintenance, which fills the gap of less attention being paid in the area of routine maintenance. The evaluation results revealed variations in the maintenance performance of 23 DMUs. Specifically, five DMUs were in a CRS state, nine DMUs were in a DRS state, and nine DMUs were in an IRS state.
• Most existing research on the performance evaluation of HMMP primarily focuses on outcomes, often overlooking uncontrollable factors. To explore the impact on sustainable HRMM, this study drew inspiration from uncontrollable factors impacting on HMMP in other research areas, utilizing the truncated regression analysis method to address the limitations of the Tobit model in previous studies. The data from 2020 to 2022 were utilized in the truncated regression analysis, with the dependent variables being the CRS and VRS efficiency values and the independent variables being various potential uncontrollable factors. The analysis identified the actual uncontrollable factors influencing HRMMP, including the amount of natural dustfall, urbanization rate, tunnel length, and bridge length managed by each DMU.
• It is evident that HRMMP is not only related to inputs and outputs but also influenced by uncontrollable factors; HRMMP efficiency has a positive correlation with the amount of natural dustfall and tunnel length, while it has a negative correlation with bridge length and the urbanization rate. Therefore, in the performance evaluation process, relying solely on results is insufficient. Instead, one should comprehensively consider potential uncontrollable factors, objectively analyze evaluation results, and provide a scientifically sound approach for improvement.
• According to the results of the evaluation of HRMMP and uncontrollable factors analysis, STHG (decision maker) should pay much attention to DMUs with high dustfall and urbanization rates and long bridges and tunnels when allocating maintenance resources so as to achieve sustainable HRMM. For DMUs in a DRS state, appropriate resource reallocation and management optimization should be carried out. For DMUs in an IRS state, higher outputs can be achieved by increasing inputs to further improve productivity and performance.

Considering the data limitations, this study did not incorporate factors such as maintenance history and traffic accidents. Future research can achieve a more comprehensive understanding of maintenance management by analyzing these aspects.