Criteria Analysis, weight and Priority for Handling Bridges in Kudus District using AHP and Promethee II methods

To determine the criteria for selecting bridges, the ideal support method was required to assist the decision makers. This study was based in the Kudus district and the object of this research was 20 proposals from the Public Works Office for the 2019 bridge handling. From the visual assessment: severe bridge damage (10 bridges), minor bridge damage (3 bridges), medium bridge damage (6 bridges) and bridges in good condition (1 bridge). An imbalance exists between the bridges that need to be maintained and the capacity that can. Depend on existing data, the objective of this study is to analyze the ideal weight main criteria and priority for handling the bridge using the AHP and Promethee II method. A total of 10 respondents were involved in assessing the criteria for The AHP method. A more consistent weighting criteria were produced with a value of 0.31, the ADT weight was 0.19, the number of public and social facilities weight was 0.12, the population weight was 0.15, the area weight was 0.05, the bridge length weight was 0.05, and the bridge width weight was 0.13. The weight of the ideal main criteria is approximately 0.40. Furthermore, the Promethee II method makes the process of priority weighting more dynamic and easier by reducing questionnaire from the AHP method. The main priority was the 8 severely damaged. The highest weight priority was the Klaling – Tanjungrejo 05 bridge.


Introduction
Bridges are major transportation facilities that must be properly managed to avoid incurring disasters. Bridge management and rehabilitation should be conducted all year-round. Furthermore, there is a need to maintain the condition of the road network to maintain the functionality of the bridges. The performance of a bridge will decrease along with the time of service so that increasing age, the level of damaged needs more maintenance like routine maintenance, periodic maintenance and rehabilitation. The bridges are very important transportation infrastructures in Kudus District. This study was based in Kudus District Public Works Office for the 2019 bridge handling. An imbalance exists between the bridges that need to be maintained and the capacity that can be maintained. Hence, a comprehensive consideration is required to determine the priority of the bridge to be handled.
Currently, determining the priority of bridge handling is based on the condition and functionality. However, several other criteria are to be considered during bridge selection. The criteria used are: the value of conditions, Average Daily Traffic (ADT), population, number of public and social facilities, area, the length and width of the bridge. The objective of this study to analyse the ideal weight main 1.1. AHP The Multi Criteria Decision Making (MCDM) is a strategy for making credible decisions. The best alternative I choosen from the available numbers based on several specified criteria [1]. One of the weighting techniques used in MCDM is the Analytic Hierarchy Process (AHP) The AHP method gives room for policy makers to argue, make judgments, or make measurements of inter-criteria attachments [2]. AHP is a method in the decision making system which provides space for perception, preference, experience, and intuition. Developed in the 1980s by Saaty, this method allows decision makers to model complex problems in a hierarchical structure. The structure shows the relationship between the objectives, influencing criteria, and available alternatives. The AHP method does not provide any statistical interpretation [3], so it is not limited by the sample size in the analysis. Initially, this method was created to enable a single person to make alternative decisions. The AHP not only supports decision makers by allowing them to develop complex assessment exercises, but it also allows them to combine objective and subjective considerations in the AHP decision process.

Promethee
The Promethee is a method of determining priority weights which focuses on simplicity, clarity, and stability [4]. The major criterion in the Promethee method is the value of the outranking relationship. In this method, all parameters stated here have real influence [5]. If the decision maker wants a complete solution to the problem, he should use the Promethee II throughout the ranking because it compares all emerging alternatives [6]. Promethee II presented six criteria preference functions (Brans et al., 1986), namely: usual criterion -type I, quasi criterion -type II, linear preference criterion -type III, level criterion -type IV, linear preference criterion and different areas -type V, gaussian criteriontype VI. By using the Promethee II method, much questionnaire can reduce from AHP method.

Research Methods
Looking for the 2018 secondary data existing condition in Kudus District that follows bridge handling and level questionnaire is the first steps for this study. The main priority for handling bridges is the assessment of the condition which is based on Attachment I of the Regulation of the Minister of Public Works and Public Housing of the Republic of Indonesia Number 33/ PRT/M/2016. This concerns the Implementation of Special Allocation Funds for Infrastructure.
The importance level questionnaire criteria for the AHP method and the preference criteria for Promethee II involves 10 respondents from several related agencies and policy makers. The criteria used are the value of conditions, Average Daily Traffic (ADT), population, number of public and social facilities, area, the length and width of the bridge.

AHP procedure steps
The AHP solution process outlines steps [7] which follow: a. Model construction and problem structuring The problem must be stated and entered into a rational system, such as the network format in figure 1 below:   The correlation matrix is arranged based on ratio scale 1-9. The paired comparisons scale and perception information [8] can be seen in table 1 below : One element is slightly more important than the other 5 One element is more important than the other 7 One element is absolutely essential to the other 9 One element is clearly more important than the other 2,4, 6,8 Values between two close consideration values  When an assessment is carried out for a pair, automatic mutual values are assigned to the opposite comparison matrix. If the number of respondents is more than one person, then the calculation of the geomean/geometric average is done. The formula used to calculate geometric averages with equation (1) as follows : c. The next step is to calculate the eigen value by dividing the value of each element in the geomean matrix by the total value of each column, next, the weight is calculated by adding the eigen value of each element in a row and dividing it by the number of elements, hence, the average eigen value of the equation is achieved ( 2) as follows: d. In the assessment process, problems occur in the consistency of paired comparisons. Hence, consistency ratios are calculated using the following steps:  The first step is the division of the value of the result of the matrix multiplication with the eigen value in equation (3) as follows :  The second step averages the results achieved in the first step which is called the consistency vector value (λ). As in equation (4) as follows :  Next is the calculation of the consistency ratio value with equation (6) as follows: If the calculated ratio is less than 0.10, then consistency is considered acceptable.

Promethee II procedure steps a. Criteria evaluation
 Figure 2 shows the visual method [9] of determining the bridge condition on the district/city road segment.

Figure 2. Scheme for determining bridge conditions
To determine the bridge handling programs for the district/city roads, the following regulations should be considered: a. If the value of the condition is 0 and 1 (if categorized as good condition, a routine maintenance program is needed.   Determine the type of analysis and threshold of Promethee II. The preference threshold (p) is the smallest or the biggest deviation that is considered sufficient to generate full preference.  Make an evaluation table.
The results of criterion data analysis, criterion weight, threshold and Promethee II types are made in one table as in the example table 3 as follows:

Results and Discussion
This study was observed with a questionnaire and the 2018 secondary existing data for the 2019 bridge handling.

The Result of the AHP method
From the AHP method, the values are according to the stages of the study as follows: a. Test data consistency is done by calculating the consistency vector values in table 4 below:    From the data of the criteria value, the threshold value (p) can be determined as follows: •

Results of Promethee II method
Promethee II method make the process of weighting priority more easier with only a few level questionnaire. From this case with 20 alternatives, 200 questionnaire needed to answer by using the AHP method only. By using the Promethee II method, it can 28 questionnaires needed to answer. The main priority is the 8 severely damaged bridges. The highest weight priority is Klaling -Tanjung rejo 05 Bridge. However, two severely damaged bridges were not included in the top 10 list of damaged bridges. The two bridge alternatives should still be in priority even though the value of the other criteria is not high. Studying the configuration of all criteria weights produced by the AHP method, including the condition of the bridge with 0.31 weight, it appears that the condition of the weight is less than half of the total weight of other criteria. Hence, even though having the biggest weight value is not a major factor considered because other criteria weights are also important, this could be why the 2 severely damaged bridges were not included in the top priority list. The next possible scenario is the criteria being too small which prevent the alternative bridge from receiving the absolute value for the criteria. With the existing scenario, the maximum value of the priority weight of the bridge criteria is just 0.23, while the total value of the other criteria weight is 0.67, so, these exclude the alternative bridges from inclusion into the top priority list for handling bridges in Kudus district.
From the calculation of the weight criteria, the biggest weight measured is 0.31 which is shown in the results of the paired questionnaires, and it is considered as the main weight for determining the priority weights. Other studies with the same AHP method also mentions these criteria has the greatest weight compared to others. This report received 0.3793 of the criteria weights condition, and this is the highest weight of the 3 criteria used [10]. Another report also shows a similar value with 0.491 [11]. In the study, it explains that the weight criterion condition is the highest weight of the 6 criterions and has a value of about 0.367 [12]. From the three studies, the weight of the ideal criteria is approximately 0.40. Hence, the condition criteria weight is 0.31 which is the highest weight of the 7 criterion used in