Sustainable Approach to Nonurban Road Network Maintenance Management: Herzegovina-Neretva County, B&H Case Study

Abstract

This paper presents a systematic and sustainable approach to nonurban road network maintenance management based on the integration of multicriteria decision-making methods and methods of monitoring and control in the service of planning, implementation and monitoring and control as the basic management processes. This approach is based on the developed maintenance management model for nonurban road network, which consists of a weighting sub-model based on the AHP method, a priority road ranking sub-model based on TOPSIS method and a monitoring and control sub-model based on the combination of TOPSIS and Earned Value Analysis (EVA). The described model with all its supporting sub-models is tested on the case study of the regional road network of Herzegovina-Neretva County. The analysis of the obtained results shows the effectiveness of the presented approach to road maintenance management and the possibility of its practical application.

1. Introduction

The transport sector, through road infrastructure development, including activities of road construction, maintenance and rehabilitation, plays an important role in ensuring economic country growth [1]. Therefore, in addition to road construction, nonurban roads, as well as all other elements of urban and nonurban road infrastructure, must be continuously maintained throughout their life cycle in order to effectively provide the services for which they are built in a satisfactory condition. Since the financial resources allocated within the annual budget for construction, maintenance and rehabilitation activities are regularly limited, the priority ranking of roads should become an indispensable part of the decision-making process of the authorities responsible for their maintenance. In contrast to urban roads, which ensure undisturbed flow traffic within cities, nonurban roads are roads outside urban areas, connecting cities and settlements mutually. As such, nonurban roads are intended to connect economically important areas and centers of local communities [2]. The sustainability of nonurban roads differs from the urban roads in terms of extensiveness, database availability, lack of a clear way of distributing financial resources intended for maintenance and dearth of this type of study dealing with the problem of rural road maintenance [3]. Moreover, nonurban roads often have higher speed limits than urban roads, which is why there is a higher risk of traffic accidents on these roads. Furthermore, a smaller number of inhabitants live in nonurban areas than in cities, so the proportional traffic intensity for nonurban roads is lower than for urban roads. In accordance with the higher traffic intensity, the emission of harmful substances into the environment is much higher in the urban areas. All of the above represent differences in defining and determining the weight of technical, economic, safety, ecological and social aspects of the research problem, which indicates different approaches to the maintenance of urban and nonurban roads. In the relevant literature, the determination of maintenance priorities is much more frequent for urban roads, and since nonurban roads are one of the conditions for the economic development of the cities they connect, it is very important to effectively maintain the nonurban roads that are the subject of this research.

Existing approaches to the nonurban road maintenance management are often not sustainable or efficient enough, because they are mostly based solely on a subjective assessment based on the experience and knowledge of the maintenance manager.

In order to meet the requirements of successful road maintenance management as a difficult and demanding task, it is necessary to know the real parameters of the road network on which maintenance activities are performed [4], i.e., the maintenance management of nonurban roads should be based on maintenance priorities considering the actual condition of the observed roads.

According to Chong et al. [5], management of maintenance priority is defined as the allocation of resources or preference setting to the maintenance cost. Due to time or budget constraints, maintenance prioritization is introduced, where it secures the maintenance fund for the tasks with higher priority [6]. Therefore, the main goal of this paper is to present a sustainable approach to nonurban road network maintenance and to validate its effectiveness on the real problem of maintenance management on the case of the selected regional road network.

1.1. Priority Ranking of Nonurban Roads Using Multicriteria Decision-Making Methods

Before the aforementioned distribution of limited financial resources intended for the annual maintenance of nonurban roads, it is necessary to determine the ranking list of maintenance priorities. However, taking into account the large number of involved stakeholders whose demands must be met, the conflicting goals, the influence of different criteria and the multidisciplinary nature of the problem, this task becomes extremely complex.

In order to successfully deal with the complex nature of such decision-making problems, decision makers ordinarily apply multicriteria decision-making methods (MCDM), taking into account various aspects of road maintenance, such as technical, economic, ecological, social and other aspects.

To date, a large number of multicriteria decision-making methods (MCDM) have been developed but the choice of the most suitable method depends on the nature of the problem on which the decision is made. In general, all approaches to the maintenance management of the nonurban road network can be divided into single and hybrid approaches, depending on whether they are based on one independent method or a combination of several compatible multicriteria decision-making methods at the same time [7].

Thus, Sayadinia and Beheshtinia [8] propose a hybrid approach to multicriteria decision making on prioritizing road maintenance in Tehran by combining AHP, ELECTRE II, ELECTRE III, ELECTRE IV and the Copeland technique. In this case, the AHP method is used to determine the weight of the criteria and the other mentioned methods are used for the priority ranking of the observed roads. Francello et al. [9] rank the critical sections of nonurban roads in Sardinia by applying the ELECTRE III method as part of the decision support system (DSS). Cheonklang et al. [10] apply the AHP method in the prioritization of rural roads in Northeast Thailand, giving the concept of the development plan of the observed roads. Nautyal and Sharma [11] apply the AHP method to determine the weight of criteria and final ranking of rural roads in the state of Himachal Pradesh in India. Prakasan et al. [12] also apply the AHP method in prioritizing urban road maintenance according to maintenance needs. Kilic Pamukovic et al. [13] design a hybrid approach to determining priorities in asphalt pavement maintenance by combining the AHP and PROMETHEE methods. Chundi et al. [14] also apply a hybrid multicriteria decision-making approach based on the AHP method in determining the relative weights of the criteria and the VIKOR method to form the final maintenance plan for road pavements in the state of Odisha.

1.2. Integration of the Basic Management Processes in Service of Nonurban Road Maintenance

From the previously presented relevant scientific literature, it is possible to see how most authors, when determining the priority of road maintenance using multicriteria decision-making methods, are mainly focused on the decision-making process within the management function of planning, thus presenting a priority maintenance plan for the observed roads. However, road maintenance management must include, in addition to planning, other management processes, such as implementation and maintenance monitoring and control.

According to Certo and Certo [15], the mentioned management processes are integrated in such a way that the result of one management process depends on the results of another. Thus, planning as the first management process results in a priority maintenance plan as output information connected to the remaining management processes of implementation and monitoring and control. Implementation implies the realization of activities from the priority plan, while, through the process of monitoring and control, a comparison is made continuously between the planned and implemented, and corrective actions are taken in case of deviations from the plan [2]. In other words, according to Erdogan et al. [16], in each step of the road maintenance project life cycle, new intermediate products are created, with the critical outcome of one phase forming an essential input to the next step.

Furthermore, according to Radujković et al. [17], monitoring and control of the plan is often neglected in practice, which is why planning as a primary management function loses its true meaning. Therefore, according to Brockmann et al. [18], it is necessary to develop the planning system with regard to controlling where some controlling requirements will influence the extent of planning.

Considering all the above, the management processes of planning, implementation and maintenance monitoring and control must be interconnected and inseparable. Therefore, the main goal of this research is to present an approach to the maintenance management of nonurban roads for which the sustainability stems precisely from the interconnectedness of the fundamental management processes into a single entity realized by establishing a few sub-models based on a unique combination of selected methods of multi-criteria analysis and earned value analysis, which reflects the original contribution of this research. A proposed approach to managing the maintenance of the road network outside urban areas is presented below.

2. Sustainable Approach to Nonurban Road Network Maintenance Management—Materials and Methods

Due to the aforementioned facts, with the aim of creating an effective maintenance system, Figure 1 shows a general approach to managing the maintenance of the nonurban road network. The presented approach, according to [19], is based on the Plan-Do-Check-Act (PDCA) cycle as an iterative method of continuous improvement of the management system through the interconnection of the basic management processes of planning, implementation and maintenance monitoring and control through feedback links.

2.1. Planning Process of Nonurban Road Network Maintenance Management

Road maintenance management begins with road maintenance planning as the primary maintenance management process. As such, the planning, as an integral part of managing both urban and nonurban road traffic, is a very complex and socially sensitive process [20].

The output of the management planning process is the initial maintenance plan for the nonurban road network, which further serves as an input for the management process of implementing when certain maintenance activities are carried out on observed nonurban roads. As such, the management process of planning within the presented model consists of four steps, namely, the determination of the area for model implementation, the establishment of a hierarchical structure of goals, the determination of the relative weight of the criteria and the ranking of nonurban roads and the distribution of financial resources according to the maintenance priorities (Figure 2).

As part of the last two steps of the planning process and as an integral part of the nonurban road network maintenance management model, two sub-models are established based on the application of selected multicriteria decision-making methods.

2.1.1. Determination of the Research Area of the Presented Approach

In the planning process, it is necessary to determine the implementation area of the presented model. In this paper, the proposed model will be implemented and validated on a total of 12 regional roads of the Herzegovina-Neretva County, which are located in the southern part of Bosnia and Herzegovina, thus forming a nonurban road network with a total length of 364.61 km (Figure 3).

2.1.2. Establishment of a Hierarchical Structure of Goals

The first step in solving poorly structured problems, such as the problem of maintaining the nonurban road network, is the establishment of a hierarchical structure of goals, in which the previously mentioned nonurban roads represent alternatives in priority maintenance.

The hierarchical structure of goals in this research is defined by a sustainable approach to nonurban road network maintenance as a main goal. According to compromise solution of all stakeholders involved in the decision-making process, the first level of objectives contains preserving technical road value, i.e., maximization of technical road characteristics, preserving the economic road value as maximization of economic indicators and preserving the social road value as maximization of social benefits. The last level in the presented hierarchy structure of goals (HSG) represents criteria which are used for multicriteria analysis. Preservation of the road’s technical value is divided into eight technical criteria (C1, C2, C3, C6, C8, C9, C10, and C11), three of which affect the ecological aspect of maintenance, such as traffic intensity (C1), length (C2) and width of the nonurban road (C9). Preservation of the economic road value is expressed through maintenance cost as economic criteria (C7). Finally, preserving the social road value is divided into two social criteria (C4 and C5). The mentioned criteria are included in the hierarchical structure of goals as indicators of the state of nonurban roads that could be measured on the ground at the time of the research. The described hierarchical structure of the goals is shown in Figure 4 and the criteria, with a description of the criteria, are given in

Table 1. List and description of criteria for evaluating the nonurban roads condition.

Criteria Label	Name of the Criteria	Description of the Criteria
C1	Traffic intensity	Average daily amount of traffic expressed in the number of vehicles per day that pass the observed nonurban road
C2	Road length	Segment length expressed in km
C3	Road level	Road level expressed in the number of road lanes in each direction and road width (1, 2, …)
C4	The social significance of the nonurban road	The social significance of the nonurban road expressed in the number of inhabitants in the area through which the observed road passes
C5	The economic importance of the nonurban road	The impact of the observed road on the economic development of the country
C6	California Bearing Ratio (CBR)	California Bearing Ratio (CBR) as a strength measure; strength of the road subgrade and of the materials used in road construction.
C7	Maintenance cost	The costs of regular summer or winter and extraordinary road maintenance expressed in the selected monetary unit (BAM)
C8	Construction and rehabilitation time	The last known year of construction or renovation of the nonurban road
C9	Road width	Road width expressed in meters (m)
C10	Pavement Type	The difference between macadam and asphalt pavements, taking into account that macadam pavements necessarily need modernization and, as such, represent a higher investment priority in maintenance
C11	Movement of inappropriately heavy vehicles	Actual road traffic load is represented by models of heavy goods vehicles that have the greatest impact on road construction [22]

.

The identified stakeholders are divided into three expert groups, where the first expert group consists of users as the population living in the observed nonurban area. Each nonurban area consists of one observed regional road, and one resident from each nonurban area was taken as a respondent, i.e., a total of 12 respondents, which corresponds to the total number of observed regional roads in the case study.

The second expert group consists of representatives of the regional administration, i.e., the Ministry of Transport and Communications of Herzegovina-Neretva County, to which the observed regional roads belong.

Finally, the third interest group consists of the road and maintenance experts, i.e., university professors with a research area in organization, technology, maintenance management and roads from the Faculty of Civil Engineering, Architecture and Geodesy, University of Split in Croatia, and from the Faculty of Civil Engineering, Architecture and Geodesy, University of Mostar in Bosnia and Herzegovina. With the aim of preserving the technical, economic and social value of nonurban roads as sub-goals within the hierarchical structure of goals, a total of 11 criteria are defined and described in detail in Table 1.

The presented criteria were selected based on the possibility of collecting data on an individual road section or alternatively by recording the real condition of observed nonurban roads. In addition to the above criteria, safety criteria expressed in the number of traffic accidents on individual roads can be of great importance in determining maintenance priorities. Although a lot of effort has been placed by agencies across the world to reduce the number and severity of crashes, the effects of crashes on road transport networks are still a major source of morbidity and, according to World Health Organization (WHO), road traffic injuries are ranked eighth as the leading cause of death among people of all ages. Because of that, it is very important to take accidents data into account and to incorporate these into some of the methods utilized for assessing safety [23]. For example, Fu and Sayed [24] propose a multivariate method for evaluating real-time safety from conflict extremes, which consists of novel multivariate extreme value theory (EVT) models. The proposed approach presents flexible integration of multiple conflict indicators and several joint safety indices that comprehensively characterize the safety level of a road facility from multiple dimensions. Until the moment of this research, only summary data for observed nonurban road network were collected, which are visible in

Table 2. Summary data on the number of traffic accidents on the observed roads.

Regional Roads on Observed Nonurban Roads
Period	Total Number of Traffic Accidents	The Number of Traffic Accidents with Fatalities	The Number of Traffic Accidents with Injured Persons
2015	2127	29	584
2016	2325	30	661
2017	2016	35	517
2018	2059	29	545
2019	2029	17	523

, but the application of the described approach to safety assessment on the nonurban road network can certainly represent one of the directions of future research.

In contrast to the traditional approach to the analysis of road maintenance management solutions, which was mainly based on the distribution of financial resources, i.e., economic criteria, the proposed approach to nonurban road network maintenance management is based on three spheres of sustainability, taking into account economic, social and environmental aspect problems when determining the priority of the observed road. However, the hierarchical structure of goals (HSG) presented in Figure 4 consists of selected economic, technical and social criteria. Since some of the selected technical criteria are directly related to ecological criteria and, therefore, give the same rank of maintenance priority, only technical criteria were taken into account. For example, the inter-relationship between the average annual daily traffic (C1) as a technical criterion and the CO₂ emission level as an environmental criterion is shown in

Table 3. Relationship between technical and ecological criterion of HSG.

Vehicle Category		NRV	CO2Emmision (t)	CO2Emmision (t per Vehicle)	Aritmetic Mean of CO2Emmision (t/v)	Alternatives	AADT (Vehicles per Day)	CO2Emmision per Alternatives
Passenger vehicles	p < 1400 ccm	11,207	19,268	1.72	7.038
	p 1400–2000 ccm	7577	19,901	2.63
	p > 2000 ccm	835	3506	4.20
	D < 1400 ccm	1453	2015	1.39
	D 1400–2000 ccm	36,118	94,775	2.62
	D > 2000 ccm	6809	22,563	3.31		R-418	4874	34,304.06
	LPG	134	335	2.50		R-418b	2868	20,185.48
Cargo vehicles	p < 3.5 t	458	2193	4.79		R-419	382	2688.58
	D < 3.5 t	4253	22,735	5.35		R-425	6682	47,029.08
	D 3.5–12 t	1179	17,336	14.70		R-425a	9356	65,849.15
	D > 12 t	1042	23,143	22.21		R-426	1055	7425.27
Bus	D < 5 t	88	1902	21.61		R-427	852	5996.52
	D > 5 t	294	9115	31.00		R-428	376	2646.35
Moped	p < 50 ccm	74	16	0.22		R-435	2918	20,537.39
Motocycle	p 50–250 ccm	375	125	0.33		R-435a	897	6313.24
	p 250–750 ccm	308	150	0.49		R-436	379	2667.47
	p > 750 ccm	147	85	0.58		R-437	1196	8417.66

. Therefore, the observed nonurban roads were ranked only according to the defined technical criteria but detailed analysis of the impact on the environment of certain nonurban roads, the definition of a series of ecological criteria and the reranking of roads also can represent one of the directions of future research.

Furthermore,

Table 4. Regional road network of Herzegovina-Neretva County.

Alternative	Label	Name of the Road	Length of Road (km)	Road Class	Number of Lanes	Traffic Condition *
A1	R-418	Prozor-Mokronoge	24.67	Regional	2	4874
A2	R-418b	Prozor-Konjic	62.61	Regional	2	2868
A3	R-419	Blidinje-Jablanica	30.67	Regional	2	382
A4	R-425	Žitomislići-Hamzići	23.56	Regional	2	6682
A5	R-425a	Tromeđa-Gabela	18.95	Regional	2	9356
A6	R-426	Dračevo-Zavala	43.93	Regional	2	1055
A7	R-427	Stolac-Berkovići	6.52	Regional	2	852
A8	R-428	Ravno-Zavala	17.68	Regional	4	376
A9	R-435	Konjic-Borci	33.55	Regional	2	2918
A10	R-435a	Ćesim-Potoci	24.00	Regional	2	897
A11	R-436	Borci-Glavatičevo-Argud	45.66	Regional	2	379
A12	R-437	Fojnica-Ostrožac	32.81	Regional	2	1196

* Traffic condition is expressed through average annual daily traffic (vehicles per day) measured on presented nonurban roads.

shows the labels, names and lengths of observed nonurban roads as alternative solutions in maintenance management, making up a network of regional roads in Herzegovina-Neretva County, which need to be ranked according to the priority of maintenance.

After defining the research area and the hierarchical structure of goals, a sub-model of determination of the relative weights of criteria and a sub-model for priority ranking of nonurban roads is applied within the model of nonurban road network maintenance management. By implementing these two sub-models, which are described in detail below, and by distributing limited financial resources according to maintenance priorities, a maintenance plan is formed. This maintenance plan is further applied as input information for the management process of monitoring and control of nonurban road maintenance.

2.1.3. Sub-Model for Determination of Relative Criteria Weight

The sub-model for determination of relative weight of the identified criteria as a compromise solution for all stakeholders involved in the decision-making process about nonurban road maintenance management is based on the application of the analytical hierarchical approach (AHP) as one of the best-known and most-used multicriteria decision-making methods. According to Figure 5, steps by which this sub-model can be applied to the regional road network of Herzegovina-Neretva County in Bosnia and Herzegovina are:

• Forming of the criteria list by all stakeholders divided into three expert groups (users, regional administration and recognized experts in the field of management and roads);
• Comparing each identified criteria by each stakeholder using the Saaty scale and creating a pairwise comparison matrix A = (ajk)nxn;
• Forming of the normalized shape of matrix (A_norm) and determination of the weight vector of the criterion (w), which is equal to the arithmetic mean of each row in the normalized matrix;
• Calculation of consistency index (CI) and consistency ratio (CR);
• Recomparison of criteria in pairs and adjustment of pairwise comparison matrix if it is necessary (CR > 0.1).

In the first step of the presented sub-model, it is necessary to form a list of criteria from the hierarchical structure of goals, with which involved stakeholders will compare the criteria with each other using the fundamental scale [25,26] and forming a comparison matrix A = (a_jk)_nxn where n presents the number of considered evaluation criteria. Each element of matrix a_jk presents the importance of the jth criterion in relation to the kth criterion. After that, in the following step, it is necessary to form the normalized shape of matrix (B_norm), where each element is computed as:

$$b_{jk}=\frac{a_{jk}}{{\displaystyle \sum _{i=1}^m{a}_{ik}}}$$

(1)

Determination of each criterion weight vector is computed as the arithmetic mean of each row in the normalized matrix (B_norm) as follows:

$$w_j=\frac{{\displaystyle \sum _{i=1}^{m}bjk}}{m}$$

(2)

In the fourth step, with the aim of checking the consistency of the assessment, it is necessary to calculate consistency ratio (CR) based on relation of the consistency index (CI) and the random consistency index (RI). If the consistency ratio (CR) is greater than 0.1, inconsistent decisions of the involved stakeholders have been made and, in the fifth step, it is necessary to form a new comparison matrix and repeat the procedure until the CR value is less than 0.1 [27].

As mentioned earlier, one of the reasons for the complexity and poor structure of the problem of nonurban road maintenance management is the large number of stakeholders with different opinions, requirements and interests. Therefore, in the application of the sub-model for determination of the weight of criteria, all included stakeholders are divided into three expert groups, where each group separately determines the weights of individual criteria, and the compromise solution is obtained as the arithmetic mean of three different scenarios related to a particular expert group.

2.1.4. Sub-Model for Priority Ranking of Nonurban Roads

The sub-model for priority ranking of nonurban roads uses the output results of the previously described sub-model for determining the relative weight of criteria. This sub-model is based on the application of the TOPSIS multicriteria decision-making method [28,29] and, according to Figure 6, it is divided into a total of six steps:

• Forming an evaluation matrix with m alternatives and n attributes, where the intersection of each of them is given as x_ij, thus forming matrix (x_ij)_mxn;
• In order to present each element of the matrix (x_ij)_mxn in a dimensionless form, it is necessary to normalize the matrix into the form of the matrix R = (r_ij)_mxn. In this way, the actual measured values of individual criteria are scaled in the range between 0 and 1;
• Calculation of the weighted normalized decision matrix V = (v_ij)_mxn by multiplying each element of the normalized matrix R = (r_ij)_mxn by the relative weight of the criteria (w);
• Determination of the positive ideal solutions as ideal worst alternative of nonurban roads (A⁺) and negative ideal solution as ideal best alternative of nonurban roads (A⁻);
• Calculation of Euclidean distances of individual nonurban roads as alternative from ideal (S_i+) positive and negative(S_i−) solution;
• Calculation of the relative distance from the ideal solution (Q_i) and ranking nonurban roads according to maintenance priorities.

2.2. Monitoring and Control Process of Nonurban Road Network Maintenance Management

Regardless of the nonurban road maintenance management plan, if the monitoring and control process is not carried out during the annual maintenance, it is not possible to obtain information on the progress and efficiency of the maintenance management system. According to Enshassi [30], actual project progress is used to update the schedule and budget to determine the percentage of complete activities of the project and to determine how the uncompleted portion of the project will be affected. Therefore, an integral part of the proposed maintenance management model for nonurban road network is the management process of monitoring and control, which is carried out through comparison of the priority maintenance plan and the actual maintenance of nonurban roads, determination of actual progress and performance indicators, execution of corrective actions if it is necessary and creating an efficient maintenance system for the nonurban road network (Figure 7).

Maintenance monitoring and control process is based on integration of TOPSIS as the multicriteria decision-making method and Earned Value Analysis (EVA) as the monitoring and control method through the sub-model for maintenance monitoring and control for the nonurban road network, also named as Sub-model 3.

EVA is based on three key variables, i.e., progress and performance indicators which represent fundamentals of its analysis: budgeted cost of work performed (BCWP), budgeted cost of work scheduled (BCWS) and actual cost of work performed (ACWP) [31].

From these three data, it is possible to obtain the remaining indicators, such as schedule variance (SV) as the time deviation from the plan calculated as the difference between BCWP and BCWS, cost variance (CV) as the cost deviation from the budget calculated as the difference between BCWS and ACWP and time variance (TV) as the amount of time the project is ahead or behind, expressed in time units [2].

It is evident that the EVA, in comparison with traditional methods of monitoring and control which are based only on the comparison of the planned and executed state, also takes into account the earned value, which is the specificity of this method and the reason for its application within the maintenance management model for the nonurban road network.

Sub-Model for Maintenance Monitoring and Control for Nonurban Road Network

The sub-model for maintenance monitoring and control is based on the previously described Earned Value Analysis (EVA) as one of the most effective tools for monitoring and control, thus enabling closing of the loop in the PDCA cycle [32], which forms an integral part of the proposed maintenance management model for the nonurban road network. According to De Marco [30], monitoring and control is an iterative process to compare actual and planned performance, establish cost and time estimates upon completion, and, if necessary, take preventive and corrective actions based on such estimates.

Since the proposed model is based on optimization according to the maintenance cost criterion (C7), the deviation from the plan can be observed through the value of road maintenance index (MRI) as the ratio of budgeted cost of work performed (BCWP) and actual cost of work performed (ACWP). In that case, it is necessary to take corrective measures of reallocation of financial resources only for those nonurban roads for which the MRI value is not within the optimal limits between 0.9 and 1.1. From that reallocation of financial resources, it is possible to obtain a new maintenance cost (NMC) as follows:

$$\mathrm{NMC}=\frac{\mathrm{AB} - \mathrm{BCWP}}{\mathrm{MRI}}$$

(3)

where AB is the budget allocated according to the results of the TOPSIS method in relation to the total annual budget intended for nonurban road maintenance activities.

Based on the new maintenance cost (NMC), an evaluation matrix with m alternatives and n attributes is formed again, after which all other steps of Sub-model 2, shown in Figure 5, are carried out, ranking again only the critical nonurban roads, while the remaining nonurban roads whose MRI value was previously optimal do not enter in this iterative process. Therefore, the continuous relationship between sub-model for maintenance monitoring and control for nonurban road network (Sub-model 3) and sub-model for priority ranking of nonurban roads (Sub-model 2) is shown in Figure 8.

3. Model Validation and Discussion of the Obtained Results

Based on the previously presented methods and materials, the proposed approach to nonurban road maintenance management was tested on the real problem of maintaining the regional road network of Herzegovina-Neretva County.

Table 5. Averaged criteria weights.

Criteria Label	Criteria	Type of Criteria	Min/Max	Scenario 1	Scenario 2	Scenario 3	Average Weight
C1	Traffic intensity	Technical	Max	0.162	0.143	0.179	0.161
C2	Road length	Technical	Max	0.035	0.030	0.043	0.036
C3	Road level	Technical	Max	0.022	0.019	0.028	0.023
C4	The social significance of the road	Social	Max	0.048	0.042	0.043	0.044
C5	The economic importance of the road	Social	Max	0.086	0.143	0.087	0.105
C6	California Bearing Ration (CBR)	Technical	Min	0.212	0.176	0.218	0.202
C7	Maintenance Cost	Economic	Max	0.082	0.138	0.068	0.096
C8	Construction time	Technical	Min	0.086	0.065	0.073	0.075
C9	Road width	Technical	Max	0.027	0.024	0.048	0.033
C10	Pavement type	Technical	Max	0.072	0.064	0.066	0.067
C11	Movement of inappropriately heavy vehicles	Technical	Max	0.168	0.156	0.147	0.157

shows the results of the implementation of the sub-model for determining the weights of the criteria:

• For Scenario 1, which corresponds to the judgment of nonurban road users, i.e., the population living in areas that connect cities and settlements;
• For Scenario 2, which corresponds to the judgment of representatives of the regional administration;
• For Scenario 3, obtained by the judgment of road and maintenance management experts.

The column called average weight represents the compromise solution of all involved stakeholders as the arithmetic mean of all three described scenarios.

It can be seen that, according to the compromise solution, the California Bearing Ratio (CBR) is in first place in terms of relative importance as a strength measure of the road subgrade and of the materials used in road construction, while the road level expressed in number of road lines is the least important criterion in determining the maintenance priorities.

After implementing the sub-model for determining the weight of the criteria, it is necessary to implement the sub-model for ranking nonurban roads on the regional road network in Herzegovina-Neretva County.

Multiplying each element of the normalized matrix R = (r_ij)_mxn by the relative weight of the criteria (w) gives the weighted normalized decision matrix V = (v_ij)_mxn and is presented in

Table 6. The weighted matrix decision.

Alternative	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11
Type	Max	Max	Max	Max	Max	Min	Max	Min	Max	Max	Max
Weight	0.161	0.036	0.023	0.044	0.105	0.202	0.096	0.075	0.033	0.067	0.157
A1	0.521	0.394	1.000	0.991	0.583	0.847	0.334	1.000	1.000	1.000	0.653
A2	0.307	1.000	1.000	1.000	0.667	0.872	0.285	0.999	0.862	0.000	0.352
A3	0.041	0.489	1.000	0.552	0.500	0.985	0.060	0.995	0.991	0.000	0.621
A4	0.714	0.376	1.000	0.474	1.000	0.681	0.128	0.986	0.898	1.000	0.635
A5	1.000	0.303	1.000	0.381	0.917	1.000	0.103	0.987	0.898	1.000	0.505
A6	0.113	0.702	1.000	0.012	0.833	0.863	0.241	0.994	0.479	1.000	0.297
A7	0.091	0.104	1.000	0.981	0.333	0.941	0.036	0.994	0.539	1.000	0.457
A8	0.040	0.282	1.000	0.209	0.750	0.844	0.097	0.999	0.718	1.000	1.000
A9	0.312	0.536	1.000	0.536	0.417	0.794	1.000	0.993	0.646	1.000	0.269
A10	0.096	0.383	1.000	0.113	0.250	0.926	0.145	0.999	0.826	0.000	0.346
A11	0.041	0.729	1.000	0.729	0.083	0.809	0.277	0.988	0.718	0.000	0.245
A12	0.128	0.524	1.000	0.677	0.167	0.876	0.150	0.998	0.539	0.000	0.343

.

Determining of the positive ideal solution (A⁺) and the negative ideal solution (A⁻) and calculating distances between target alternative i and the worst condition (Si⁻⁾ and between target alternative i and the best condition (Si⁺) is given priority rank, expressed as similarity to the worst condition (Qi). According to the obtained rank, the nonurban road labeled as R-418, with the highest value of Qi, has the highest priority in nonurban road maintenance, while the road section marked with R-435a has the best condition of the road with the lowest maintenance priority.

Furthermore, the limited annual budget intended for maintenance activities is evenly distributed according to the obtained priority rank, as shown in

Table 7. Priority ranking of nonurban roads—Iteration 1.

Road Section	Label	Si+	Si−	Qi	Rank
A1	R-418	0.077	0.216	0.736	1
A2	R-418b	0.137	0.148	0.519	2
A3	R-419	0.170	0.127	0.428	6
A4	R-425	0.145	0.150	0.507	3
A5	R-425a	0.161	0.133	0.451	4
A6	R-426	0.173	0.118	0.407	7
A7	R-427	0.196	0.096	0.327	9
A8	R-428	0.193	0.103	0.349	8
A9	R-435	0.174	0.132	0.431	5
A10	R-435a	0.223	0.029	0.114	12
A11	R-436	0.218	0.055	0.202	11
A12	R-437	0.218	0.063	0.224	10

.

Through the implementation of the monitoring and control sub-model, the planned, realized and earned values of maintenance were determined. Based on those values, road maintenance index (MRI), the cost of the remaining percentage of maintenance and the new maintenance cost were determined.

According to the data from

Table 8. Results of monitoring and control process—Iteration 1.

No	Section	Qi	AB	BCWS	BCWP	ACWP	% of Execution	MRI	Cost of Remaining Execution	NMC
1	R-418	0.736	234,934.8	117,467.4	17,620.1	30,442.4625	15	0.58	199,694.5578	345,014.575
2	R-425	0.519	165,868.0	82,934.0	8293.4	10,077.415	10	0.82	149,281.2362	181,393.47
3	R-435	0.507	161,973.0	80,986.5	20,246.6	22,028.8125	25	0.92	The end of iteration
4	R-425a	0.451	144,169.3	72,084.6	27,031.7	30,164.85	37.5	0.90
5	R-426	0.431	137,677.0	68,838.5	27,535.4	17,853.5	40	1.54	82,606.17736	53,560.5
6	R-428	0.428	136,767.9	68,384.0	34,192.0	37,423.075	50	0.91	The end of iteration
7	R-427	0.407	129,852.1	64,926.0	8115.8	9680.6875	12.5	0.84	113,620.5612	135,529.625
8	R-418b	0.349	111,580.9	55,790.4	4184.3	2231.57025	7.5	1.88	103,212.2948	55,045.3995
9	R-419	0.327	104,564.9	52,282.5	18,298.9	107,256.5778	35	0.17	67,967.2017	398,381.5745
10	R-437	0.224	71,488.7	35,744.4	16,085.0	13,298.76	45	1.21	The end of iteration
11	R-436	0.202	64,657.5	32,328.8	4041.1	10,596.85938	12.5	0.38	56,575.34299	148,356.0313
12	R-435a	0.114	36,465.9	18,233.0	2734.9	2139.9	15	1.28	30,996.0286	24,252.2

, alternatives numbered 3, 4, 6 and 10 meet the conditions of effective maintenance according to the maintenance plan, while budget redistribution is carried out for the remaining sections.

In this way, the cost criterion is corrected and the prioritization model is reapplied only for those sections that did not satisfy in the first iteration. Therefore, in

Table 9. Priority ranking of nonurban roads—Iteration 2.

Alternative	Label	Si+	Si−	Qi	Rank
A1	R-418	0.141	0.832	0.855	2
A2	R-418b	0.870	0.162	0.157	6
A3	R-419	0.144	0.947	0.868	1
A4	R-425	0.558	0.421	0.430	3
A6	R-426	0.880	0.136	0.134	7
A7	R-427	0.682	0.294	0.302	5
A10	R-435a	0.962	0.024	0.025	8
A11	R-436	0.661	0.315	0.323	4

. is presented the new ranking of the remaining nonurban roads using the TOPSIS method.

From the second iteration shown in

Table 10. Results of monitoring and control process—Iteration 2.

No	Section	Qi	AB	BCWS	BCWP	ACWP	% of Execution	MRI	Cost of Remaining Execution	NMC
1	R-419	0.868	369,696.1	258,787.2	129,393.6	214,513.1555	50	0.6	184,848.0279	306,447.365
2	R-418	0.855	364,164.3	254,915.0	101,966.0	113,651.86	40	0.9	The end of iteration
3	R-425	0.430	183,211.4	128,248.0	83,361.2	91,704.4765	65	0.9	The end of iteration
4	R-436	0.323	137,634.0	96,343.8	67,440.7	83,079.3775	70	0.8	41,290.19498	50,864.925
5	R-427	0.302	128,397.0	89,877.9	22,469.5	27,105.925	25	0.8	96,297.76649	116,168.25
6	R-418b	0.157	66,684.0	46,678.8	16,337.6	14,579.5923	35	1.1	The end of iteration
7	R-426	0.134	57,018.6	39,913.0	15,965.2	24,994.9	40	0.6	34,211.18394	53,560.5
8	R-435a	0.025	10,475.7	7333.0	4033.1	10,984.82	55	0.4	4714.057059	12,839.4

, it can be seen that, by maintenance monitoring and control at 70% of the observed maintenance period, the condition of system efficiency is satisfied for the sections under rank number 2, 3 and 6. The remaining sections enter the repeated iteration process until the moment when the MRI value for all those sections is not within the limits of acceptable values (0.9 ≤ MRI ≥ 1.1). The ideal MRI value is 1 when BCWS is equal to ACWP. However, if a deviation of 10% is taken, MRI values in the range of 0.9 to 1.1 are adopted as acceptable.

4. Conclusions

In order to cope with the poorly structured problems of managing the maintenance of the nonurban road network due to the large number of involved stakeholders, the conflicting goals and the complexity of decisions through the management process of planning, it is necessary to apply the most suitable multicriteria decision-making method.

The integrity of the maintenance management system is reflected in the interconnectedness of the fundamental management processes of planning, implementation and monitoring and control within the PDCA cycle.

In order to close the loop of the PDCA cycle, in this paper, multicriteria decision-making methods are combined with the selected monitoring and control method.

Thus, the combination of the AHP and TOPIS method with the EVA method in the proposed maintenance management model, together with the supporting sub-models, makes a unique and sustainable approach to nonurban road network maintenance management.

By prioritizing nonurban roads according to various economic, social, technical and ecological criteria, the analysis and selection of the best solution for managing the maintenance of the observed road network are carried out, thus contributing to the sustainable development of the observed nonurban areas and, at the same time, urban areas that connect nonurban roads to each other.

The validation of the maintenance management model on the case study of the regional road network placed in Herzegovina-Neretva County in Bosnia and Herzegovina shows the effectiveness of this approach, as well as the possibility of its universal application in the management of road maintenance, both in nonurban and urban areas, but also in the maintenance of all other road infrastructure elements.

As the purpose of the observed roads is to ensure the smooth flow of traffic in conditions of safety, one of the future directions of this research is the inclusion of safety criteria that will contribute to an even more effective ranking of roads according to their maintenance priorities, as well as a more detailed analysis of the harmful impact of the observed roads on the environment through various ecological criteria and definition of reduction measures in the form of maintenance activities of observed nonurban roads.