Determination of the priority for arterial and collector road handling in Solok city, West Sumatra province

When handling roads, there should not be any roads that are neglected. Due to the limitation of funds, among the roads that have to be maintained, it is not necessarily possible to handle all of them with the same priority. It is necessary to prioritise road handling by considering the conditions and factors that influence its use. Roads that are used more often will be prioritised when it comes to maintenance. The data used in this study consisted of secondary and primary data. The secondary data was obtained from the Public Works Office of Solok City (Database of Solok City Roads, 2017) and Bappeda (RPJMD and RTRW). 8 segments of road were observed. Traffic volume surveys were conducted for 2 x 24 hours. Furthermore, questionnaires were distributed to support the secondary data, and 30 respondents answered. Six criteria were considered: Condition Factors (A), Traffic Volume Factors (B), Economic Factors (C), Policy Factors (D) Land Use Factors (E), and Side Building Factors and Road Complement (F). This study used the Analytic Hierarchy Process (AHP) method developed by Thomas L. Saaty. This method will simplify the complex multi-criteria problem into a priority scale hierarchy. The results of the AHP method analysis were included in a mathematical model as according to Brojonegoro (1991).The results showed that the priority for routine road maintenance was “Traffic Light Pandan Tanjung Paku” road section (033), the priority for periodic road maintenance was “SMP 1 Simpang Damar” road section (047) and the priority for road improvement in general was “Simpang Sigege Ampang Kualo” road section (051).a


Introduction
Solok City has 170 roads with an overall length of 206.6 km, and the roads cross two (2) sub-districts and thirteen (13) urban village. There are thirteen (13) primary and collector roads with a total length of ± 27.2 km. Because of the limited amount of funds available, it is necessary to select the priority for handling the roads.
At present, many methods are used to determine the priority for road handling. What is most often used is the Analytic Hierarchy Process (AHP) method. Saaty [1] developed this method. This method was chosen in this research because this model can support the decision-making by simplifying complex multi-criteria problems into a hierarchy of priority scale. Thus, the issues will appear to be more structured and systematic [2]. The analysis of road handling from the AHP method were entered into mathematical model calculations as according to Brojonegoro [3].
There were eight arterial and collector road segments studied in this research, consisting of 4 secondary arterial and 4 collector roads. This study aimed to determine the priority sequence of road handling in Solok City based on the Analytical Hierarchy Process (AHP) method. The results of this study are expected to be taken into consideration by relevant agencies when determining the priority for road handling in Solok City.

Data collection
The data used in the study consisted of secondary and primary data. The secondary data was obtained from the Public Works Office of Solok City [4] and Bappeda (RPJMD and RTRW) [5]. The primary data was in the form of the traffic volume of the eight segments selected, which was obtained by surveying the volume of vehicles and pedestrians. The surveys were conducted for 2 x 24 hours, on market days and non-market days. Solok City market day is on Tuesdays and Fridays. Furthermore, questionnaires were distributed to support the secondary data regarding the road conditions. The data of the arterial and collector road segments studied can be seen in Table 1.

Respondent perception survey
According to Hair [6], the minimum number of research samples with an unknown population number should be five times the variables analyzed. In this study, there were six variables or criteria used. Therefore the minimum number of samples required is 5 x 6 criteria = 30 samples. According to Singarimbun and Efendi [7], the minimum number of samples in the questionnaire trial was 30 respondents, which means that the distribution of values would be closer to the normal curve. In this research study, 30 respondents were involved, as can be seen in Table 2.

Data processing
After the data was collected, the data processing stage was conducted using the AHP method, incorporating the criteria and sub-criteria that had been previously determined. This will be formulated in the form of a hierarchical structure (Fig. 1). The hierarchical levels in the AHP method consisted of 3 (three) levels, namely: 1. Level 1 (goal) -to determine the priority of roads road handling based on a routine and regular handling, road rehabilitation, and road improvement.   The matrix was used to calculate an element's weight. Comparative results in the pairs of the elements will form a comparison matrix (Table 3).

The initial matrix calculation
The results of the pair-wise comparison has been expressed as vector W, with W = (W 1 , W 2 , W 3 .... W n ) and then the value of the intensity of the importance of the operating element. i.e. Ai against Aj was expressed equal to aij. The preference comparison matrix was processed by calculating each row using Eq. 2:

Vector Eigen calculation, maximum Eigenvalues, and control of Consistency Index
The obtained matrix was the eigen vector, which is also the criteria weight. The criteria weight or Eigen Vector is (Xi) in Eq. 3, maximum Eigenvalues in Eq. 4 and control of Consistency Index in Eq. 5.
where C I = Consistency index, λ maks = Value eigen maximum, n = matrix sizes.
Random matrix with a rating scale of 1 to 9 with its inverse as Random Index (RI). The Random Index (RI) of each matrix order is as shown in Table 5. For the AHP model, the comparison matrix was accepted if the ratio value was consistent and no more than 10%, equal to 0.1.
, 0 where C R = Consistency Ratio, R I = Random Index.

Weighting the criteria
After obtaining the criteria weight from the comparison of the criteria matrix, a scoring process or priority assessment was carried out for each criteria for each road section, using the 2 nd level criteria weight, 3 rd level (respondent analysis weight), and secondary data analysis results. In the matrix below is an example of the Road Condition (A) criteria value ( Table 6). The same has been done for other criteria. The Priority Value scoring results with AHP proceeded with equations according to Brodjonegoro [3]: 3 Results and discussion

Application of weight criteria for handling roads
The AHP method is known as one of the structured approaches involved in making decisions. The choice between the criteria and sub-criteria in this model is considered to be capable of meeting the objectives in decision-making. The principle used was the principle of preparing the hierarchy, the setting priorities, and logical consistency. The AHP core was the weighting and scoring. The weighting was obtained from the pair-wise comparison matrix as a result of the respondent's perception (questionnaire). The scoring in this study used the Linear Model equation.

Priority scale determination with the analytic hierarchy process (ahp)
Based on 30 respondents and the observed six criteria (A-F), the respondent's answers were varied, ranging from 1-9, aligned with the following meanings: 1) Equally important; 2) Between equally important and more important; 3) More important; 4) Between more important and important; 5) Important; 6) Between important and very important; 7) Very important; 8) Between the very important values is very important; and 9) Very important.
The weighting obtained was assessed using a criteria comparison scale. The value of the initial matrix criteria was obtained from the average comparison value by dividing the cumulative number of comparison scales by the number of respondents, simplified to calculate the vector values (Xi) and eigenvalues (λi).

Results of the weighting criteria (2 nd level) and sub criteria (3 rd level)
After the interviews and calculations by using AHP method were conducted, the results obtained were shown to have weighted levels that were recapitulated based on the criteria and levels as shown in Tables 7 and 8.

Proposed road maintenance works
After determining and assessing the level of damage, the category of maintenance work was determined with the values listed in Table 9.
Each segment's assessment was grouped into the handling that it required, including routine maintenance, periodic maintenance, improvement or development work. The weighting was obtained by dividing the sub-criteria value into the existing road conditions by four (4). For example, the condition of there being a road hole (x1) on the segment Simpang Lampu Merah Pandan -Tanjung Paku road (033) was 2. The weight of the subcriteria of the hole was therefore 2/4 = 0.50, as shown in Table 14  The traffic volume data in Table 11 was obtained from the average survey results: 2 x 24 hours on the market days and non-market days. Weighting the LHR of each type of vehicle was done by comparing the LHR with the highest LHR of the same kind of handling group. For example, the truck traffic (x7) on the Simpang Lampu Merah Pandan -Tanjung Paku Road (033) was 148, divided by the highest LHR with the same handling group, which was a motorcycle (incidentally the same section), which were 9923. Therefore the weight of the sub-criteria of the truck was 148/9923 = 0.015, as in Table 14, column b. The value of the benefits toward the road conditions was gain from the total of the equivalent LHR road user value, found in the LHR survey results using the Traffic Data Analysis Sheet form (A2) SK 77/KPTS/Db/1990. The weighting of the economic benefits based on the traffic data were obtained by comparing the value of the benefits with the highest benefit value of the same type of handling group (see Table 14, column c).
Road handling costs for routine/ periodic maintenance and improvement were taken from the standardization of the DAK 2018 activities and then adjusted to the road conditions that are to be handled. The weighting estimated costs were found by comparing the estimated costs associated with the highest estimated costs of the same type of handling group. If the road was proposed, then it was given a value of one (1). If it was not proposed, then it was given a value of zero (0).
Regarding the land use factor, the same assessment was also carried out. That is if the construction of a road would affect the productivity of that type of land use, such as agricultural/ trade/ education and social-cultural factors. These were marked by giving it a value of one (1). However, if the road built would not affect the products directly, then it was given a zero value (0). For more details, see Table 14, column E. The drainage condition was divided into five (5) assessments, starting from zero (0) to five (5). Thus an evaluation could be given based on the condition of the existing road drainage, as exposed in Table 13. The assessment of the sidewalk condition was divided into three (3), namely good condition -1 point, medium condition -2 points, and if there were no sidewalks on the road, then the specified point was 3. For the assessment of the street lights, an evaluation was made that if there was a street light on the section, then 1 was given, whereas if there was no street light, then zero points were given (0). For more details, see Table 14, column F.   3014 We then calculated the amount of Y using formula from Brodjonegoro [3] or Eq. 7: Y = weight criteria x (sub criteria weight x secondary analysis weight), or Y=A (a1.x1 + a2.x2 + a3.x3 + a4.x4 + a5.x5 + a6.x6) + B (b1.x7 + b2.x8 + b3.x9 + b4.x10 + b5.x11) + C (c1.x12 + c2.x13) + D (d1.x14 + d2.x15 + d3.x16 + d4.x17) + E (e1.x18 + e2.x19 + e3.x20 + e4.x21) + F (f1.x22 + f2.x23 + f3.x24) In order to get the value of each segment (Y), the value of the criteria in the 2 nd level ( Table 7) was multiplied by each sub-criteria value in the 3 rd level (Table 8). This data had been multiplied and added to the value of the secondary data criteria (Table 14). The value obtained would determine the order of the top priorities for handling.

Proposed road maintenance worksthe analysis using the AHP method
The first priority road for the secondary arterial and collector roads in Solok City was the Sigege Junction -Ampang Kualo Road section (0.907), with the type of handling being road improvement. The second priority was SMP 1 Damar Junction Road (0.602), to the kind of handling being periodic maintenance while the last priority was BRI Junction -Tanjung Paku Junction Road (of 0.427), and the type of road handling was routine maintenance, as shown in Table 15.

Conclusions
From this study, the following conclusions can be drawn. The priority for road handling was determined using the AHP method, considering specific aspects/criteria and combining various criteria and sub-criteria carried out by weighting based on the level of importance. AHP consolidates broad and unstructured problems into a model that is flexible and easy to understand. Consider logical consistency in the assessment. In this case, for the criteria, the level 2 Road Condition Factor got the highest rating in road handling with a weight of 31.46%. The Traffic Volume Factor had the second priority place, with a weight of 21.89%. In the top three in the priority list for road handling was Sigege Junction -Ampang Kualo Road section (0.907), and the type of handling was road improvement. The second priority was SMP 1 Damar Junction Road (0.602), and the kind of handling was periodic maintenance while the last priority was BRI Junction-Tanjung Paku Junction Road (0.427), and the type of road handling was routine maintenance.