Assessment of the Effectiveness of Collective Decisions for Maintenance-Rehabilitation Works of Water Pipelines Using a Qualitative Risk-based Group Decision-Making Model

Among the most important decisions in water companies are planning the Maintenance-Rehabilitation Works (MRWs) of water pipelines. Since the MRWs are costly, it is essential to use the collective decisions of an expert team for planning these works. However, the effectiveness of these group decisions is not very clear and has been less considered in previous studies. Hence, the main objective of this research is to assess the effectiveness of these collective decisions. For this purpose, the MRWs of water pipes are determined based on two methods. In the rst, the collective decision of experts is omitted, and in the second one, these decisions are considered. Finally, the results obtained from these methods are compared. The method used in this work for collective decisions is based on the nominal group technique. Furthermore, since there is deep uncertainty in water network data as well as hesitation in the group decisions, a qualitative (fuzzy) risk-based group decision-making model is developed in this research. The water pipelines studied in this work, as the case study, are addressed to pipes, which have been proposed by water companies in the six provinces of Iran. The MRWs of these pipes are determined, rst, using the collective decision of 76 experts in these water companies; and then, without this group decision making. The results of comparing these methods indicated that group decisions do not have a signicant effect on prioritizing water pipelines for the MRWs. While, in determining the renovation strategies of pipes, the viewpoints of experts could have a decisive effect on the results. Furthermore, it was found that increasing the number of decision criteria could lead to more realistic results; whereas, the number of assessed pipelines as well as the number of decision makers does not have an obvious effect on the results. group decisions do not have a decisive effect on pipes prioritization, but could be decisive for determining the MRWs strategies of the water pipelines. Furthermore, it was shown that increasing the decision criteria could make the results more realistic; nevertheless, the numbers of pipes analysed and the numbers of experts who participated, do not have a direct effect on results; While, their viewpoints could be very effective in renovation planning of the pipes. It must be mentioned that this research has been conducted in selected water companies of Iran, and the results might be changed in another country, even in other water companies of Iran. However, it seems that the results obtained from this research could be inspired for future studies in the eld of group decisions for maintenance-rehabilitation planning of the water pipeline.


Introduction
Water Distribution Networks (WDNs) are among the main infrastructure in human societies; thus, the Maintenance-Rehabilitation Works (MRWs) of these networks have always been one of the most important concerns of water companies. Hence in the last decade, many studies have been conducted in regards to MRWs of water networks (Ramos et  Hence, it is essential to consider an appropriate method for planning MRWs of water pipelines, so that, leading to improve the hydraulic-mechanical operation of these pipes.  Elshaboury et al. (2020) presented a study to determine the weight of variables affecting the water pipe failures. In this study, the Fuzzy ANP multi-criteria DMM was used, and group DMM was also considered by researchers. The GEOmetric mean (GEO) and Minimum-Maximum (Min-Max) methods were used in this research to implement group decisions. The case study of this work was related to a network in a city in Egypt. However, in this study, only the results of several group DMMs in the assessment of the condition of the pipes have been investigated; thus, the effectiveness of these methods in planning the maintenance of WDNs has not been considered. Salehi et al. (2018) have been developed a model called the WDSR model, which was a multi-attribute group DMM based on the Fuzzy TOPSIS method. This model was developed only to prioritize pipes and areas of WDNs for planning network renovation. However, in this model, the assessment of the effectiveness of group DMMs in prioritizing pipes has not been considered.
da Silva Monte et al. (2016) presented the results of a study in which the techniques for determining the weight of different decision makers in group DMM was investigated. The eld of this study was related to the maintenance of wells in WDNs, in which decision-makers consisted of 3 experts with different views. However, in this study, the maintenance of the water pipeline has not been considered and the viewpoints of a limited number of decision makers have been assessed. Choi et al. (2015) has assessed the condition of pipes in WDNs. Based on this research, they provided a method to maintain and repair the pipes in each zone of the network. Moreover, a group decision of 25 experts was used to weight different zones of the network based on their performance index; and the AHP method was applied to determine these weights. Finally, the ELECTRE method was used to prioritize network zones. However, in this study, the pipes prioritization for renovation was not considered and the effectiveness of group DMM was not assessed.
Given the most studies in the eld of WDNs renovation, it is obvious that mainly the effectiveness of group DMMs used in this eld has been less considered; while, these decisions could be useful for Maintenance-Rehabilitation Works (MRWs) of distribution networks. The e ciency of group DMMs has been recently considered in other elds (Hsieh et al. 2020); nevertheless, not has been used in the WDNs design and operation eld.
The main objective of the present study is to assess the effectiveness of collective decisions in planning the MRWs of water pipelines. In this regard, the speci c pipes proposed by the 6 water companies of Iran have been investigated; and then, using the viewpoints of 76 experts in these companies, the MRWs of the pipes were planned. Accordingly, the nominal group technique was used in this research for collective decision. In addition, to assess the effectiveness of group decisions a DMM has been developed in the present work; and then, the results of two methods including no-group DMM and group DMM were compared. Meanwhile, given the deep uncertainty involved in WDNs data (Scheidegger et  The risk-based DMM developed in this research is a new version of the RC-WDSR model, which was introduced in 2020 (Salehi et al. 2020). However, as mentioned previously, in the model of the present work, the numerical analysis of risk (quantitative) has been omitted; and as a new approach, only qualitative risk-based decision-making was considered for planning MRWs of the water pipelines. This is because that the deep uncertainty in WNDs data and hesitation in group decisions could lead to more complex analysis in the quantitative risk-based methods. The results of this work indicate that the opinions of experts do not have a signi cant effect on pipe prioritization for MRWs. However, decision-makers' viewpoints can be effective and decisive in determining pipe renovation strategies.

Material And Methods
The main objective of this research is to assess the effectiveness of collective decisions for planning MRWs of the water pipelines in WDNs. For this purpose, a qualitative risk-based model was developed using a multi-criteria group DMM. Figure 1 illustrates the analytic steps of this model. for rehabilitation. In the present study, the criteria affecting the priority of pipes for MRWs were developed to 50; and were divided into two categories of criteria and sub-criteria. Figure 2 shows the criteria and sub-criteria effective in the prioritization of pipe for MRWs. The model developed in this research is well-established, which can analyse any network with any number of criteria as well as any number of pipes. Furthermore, it is possible to assess network data with uncertainty using this model. Therefore, even networks with 1 or 2 criteria (accurate or imprecise) and with any number of pipes can be assessed by this model.

Step 2. Selecting the case studies
In this step, the case studies of research were selected. For this purpose, to consider a wide range of different regions of Iran, WDNs from the six provinces were chosen. Furthermore, for selecting these provinces, the various combinations of the numbers of decision makers/pipes/criteria were considered. Finally, a total of 76 decision-makers participated in these provinces. The dispersion of these six provinces and the numbers of decision makers/pipes/criteria in their water companies are shown in Figure 3. The number of pipes studied in this work was proposed by each water company. In addition, the numbers of criteria were determined based on data available in water companies. In this work, the selection of decision makers was based on their knowledge and work experience and was completely voluntary. The educational degrees and work experiences of these decision makers are presented in Table 1 in percentage. In this study, to determine the pipe risk, the Pipe Failure Probability (PFP) and Pipe Failure Consequence (PFC) were assessed based on criteria determined in step 1. The method used for risk assessment in this research was based on analytic steps of the RC-WDSR model, which has been introduced in Salehi et al.
(2020). For this purpose, in each case study, the conditions of the water pipelines were investigated in regards to 50 criteria. However, it should be noted that all criteria do not have the same role in pipe failure. Indeed, as shown in Table 2, some of these criteria are effective in PFP and others affect PFC. While, some of these criteria have a simultaneously in uence on the probability and consequence of pipe failures ( Table 2). The major information in Table 2 is obtained from Salehi et al. (2020).  In this table, each criterion was divided into seven categories. This categorization was not based on numerical classi cation, but on linguistic-fuzzy division.
The condition of each pipe in relation to each criterion was determined based on the available eld data as well as the knowledge and experience of the network operator who lled the form ( Table 3) μÃ(x) = 0x ≤ x min x -x min

Step 4. Planning the maintenance-rehabilitation works of pipes
In this study, lling the form of the pipes' qualitative risk (Table 3) by the network operator, the priority and renovation strategy of pipes were determined. To analyse this form, a multi-criteria decision model was developed based on the TOPSIS method, which has been introduced rstly by Yoon and Hwang (1981).
The reason for using this method is its signi cant ability in planning the design and rehabilitation of water and sewer networks   (4) These best and worse pipes are calculated only to measure the distances of real water pipelines from them for determining the pipes' priorities/strategies for MRWs. Indeed, these pipes are theoretical and do not exist in real WDNs.
In the next stage, the distance of each water pipeline was measured from the pipes with the highest and least risks. This distance was determined using the below formula: Distance of water pipeline from the pipes with the highest/least risk={\text{S}}_{\text{m}}^{ \pm }{\text{S}}_{\text{m}}^{\text{ }\pm } = \sum This index is a number between zero and one, which the closer it is to the number 1, the higher the priority of the water pipeline for MRWs.
In addition, to determine the strategy of MRWs for each water pipeline two other indices were determined using the same formula of number 6 as follows:   Table 2 shows the form used in this study for weighting the criteria. It should be mentioned that since the main objective in this research is assessing the effect of collective decision for planning the MRWs of the water pipelines, the weighting of experts is omitted for a correct judgment of the effect of expert viewpoints.  As shown in Table 4, each of the linguistic values is related to a trapezoidal fuzzy number. Accordingly, the weight obtained for each criterion would be a fuzzy value. This value was achieved using the following formula: In the second method of this research, analytic steps of Fuzzy TOPSIS were performed without using group decision making. Finally, the results of two methods including group DMM and no-group DMM were compared.

Results & Discussion
The results obtained from this research are presented in Figure 5 and Tables 5 and 6. The discussion of these results is as follows:   Figure 5, the results of the two methods in determining the MRWs strategies of pipes is more than 60% in 3 water companies (Sarbaz, Ferdos and Shahr-e-Kord). While, compared to other cities (Ardabil, Marivan and Mashhad), this similarity for pipe priorities is less in these water companies.
On the other hand, as shown in Figure 3, the criteria studied in water companies of Sarbaz and Shahr-e-Kord is less than other companies. Therefore, considering Figures 3 and 5, it seems that reducing the number of criteria studied can almost lead to the reversal of the results. Accordingly, regarding to the viewpoints of network operators and the results presented in previous paragraphs, it can be generally said that reducing the number of decision criteria can have an adverse effect on the accuracy of the results of group decisions.
4. The least similarity of the results is related to the MRWs strategy of the pipes in Mashhad and Marivan. It means that the most effective group decision on determining the strategy of pipe renovation is related to the water companies of these two cities. However, the number of pipes in these two cities was signi cantly different. Hence, the number of pipes studied in Mashhad was equal to 13, whereas, in Marivan was equal to 5. This result indicates that the number of pipes does not affect the obtained results. Thus, the model developed in this study can be robust, and provides accurate results with any number of pipes. 5. As represented in Figure 3, it is clear that the most number of decision makers are related to water companies of Khorasan Razavi (Mashhad), Chaharmahal and Bakhtiari (Shahr-e-Kord), and Sistan and Baluchestan (Sarbaz). However, considering the results presented in Figure 5, it is obvious that the viewpoints of decision makers are signi cantly different in these companies. In addition, the results of Ardabil are very close to Shahr-e-Kord and, the results of Mashhad are close to Marivan. While, the number of decision makers in Ardabil province was 9, and for Chaharmahal and Bakhtiari province (Shahr-e-Kord), the 14 experts were volunteers. There is also a signi cant difference between the number of decision makers in Khorasan Razavi (Mashhad) and Kurdistan (Marivan) provinces. Hence, 23 decision makers participated in the Water Company of Khorasan Razavi, whereas, 9 experts were proposed in Kurdistan Province for this research. Accordingly, it can be concluded that increasing the number of decision makers does not necessarily make the results to be better or worse; and the viewpoints of decision makers are more important than their number. The criteria and sub-criteria considered in this research Figure 3 Page 17/17 The number of decision makers/pipes/criteria in water companies studied in this research The similarity of the results of Group and No-Group DMMs