Application of the analytical hierarchy process for planning the rehabilitation of water distribution networks

Purpose – This study aims to develop a decision support tool to improve planning for the rehabilitation of water distribution networks (WDN) using the analytical hierarchy process (AHP) method and the urgency level score. Design/methodology/approach – InthispapertheAHPmethodwasusedtooutclasstheindicatorshaving astronginfluenceonthedeteriorationofthepipesandthescoreofthelevelofurgencyiscalculatedtoestablishtherehabilitationprogram(short,mediumandlongterm).TheproposedmodelwastestedforthecaseofthecityofSouk-AhrasinAlgeria. Findings – Based on the judgments of twenty-four experts, the relative weights of the three physical, operationalandenvironmentalcriteriaofthe pipelinewerecalculatedandfoundtobeequalto35.40%,55.60% and 9.00%, respectively. The two indicators, number of failures and pressure, were found to have the highest overall weights. The results of this article can be used to improve decision-making in WDN rehabilitation planning in Algeria. Research limitations/implications – The main objective of water companies is to provide citizens with good quality drinking water in sufficient quantity. However, over time, WDN age, degrade and deteriorate. This degradation leads to a drop in the performance through the degradation of water quality and an increase in loss rates. WDN rehabilitation is one of the most widely adopted solutions to address these drawbacks. Originality/value – Application of a hybrid method (AHP-Level of Emergency) for the planning of the rehabilitation of WDN in Algeria.


Introduction
Adequate access to water and sanitation services is a basic human right across the world (Al-Awar, Abdulrazzak, & Al-Weshah, 2006). Water Supply Service (WSS) managers must provide water with good quality and sufficient quantity and pressure at an affordable price to all citizens. This water is transported through water distribution networks (WDN). Over time, WDN age and degrade, resulting in higher rates of water loss, poor water quality and deterioration in the quality of service resulting in an increase in customer complaints. Decision-makers and managers of WSS are continually looking for solutions to improve this situation. One of the most widely adopted solutions worldwide is the rehabilitation of WDN (Rahman, Romali, Sufian, & Seman, 2020) in order to provide, consistently, adequate supply to consumers (Prasad, 2021). Rehabilitation consists of repairing, renewing or replacing critical pipes.
In Algeria, the rate of drinking water losses is around 50% in many cities (Boukhari, Pinto, Abida, Djebbar, & de Miras, 2020). These water losses have a negative impact on the economic viability and technical performance of WSS and constitute a relevant indicator of the inefficiency of WSS providers. These inefficiencies are exacerbated by ageing pipes and hydraulic equipment (valves, suction cups, etc.), poor infrastructure management and the quality of leakage repairs, which are among the most relevant factors for the deterioration of drinking WDN (Farley & Trow, 2003). However, rehabilitation planning by decision-makers and WSS managers needs to take into account qualitative and quantitative data and information on different elements using criteria, subcriteria and indicators that are sometimes conflicting and contradictory. To achieve this objective a documentary research (data collection) and interviews with WDN operation and maintenance managers of the local water company (ADE: Alg erienne Des Eaux), are carried out to identify and select all pertinent factors that have a direct or indirect impact on the degradation and deterioration of WDN in the city of Souk-Ahras.
Several researchers have studied different aspects of WDN rehabilitation including: (1) planning of rehabilitation, (2) strategies to improve rehabilitation practices (Hajibabaei, Nazif, & Sitzenfrei, 2019), (3) rehabilitation techniques and (4) factors influencing WDN rehabilitation. Due to the complexity of using multiple criteria to solve the rehabilitation problem and the lack of data, researchers have promoted the application of multicriteria decision making methods (MCDMs) as an effective decision support tool. MCDMs are widely used because they have a strong ability to produce sustainable and well-structured solutions to different complex decision problems (Lai, Lundie, & Ashbolt, 2008). In recent years, several researchers have applied MCDMs in water resources management (dos Santos Amorim, Bezerra, Silva, & de Sousa, 2020). The Analytical Hierarchy Process (AHP) is the most applied MCDM method in decision-making studies because it is the simplest and the most flexible in comparison to other MCDM methods (Dos Santos, Neves, Sant'Anna, de Oliveira, & Carvalho, 2019).
In this paper, a decision support tool was developed for the improvement of WDN rehabilitation planning. This is done by taking into account the fact that WDN were influenced by internal factors (length, diameter, depth, type of materials, age, location of the pipe, etc.) as well as external factors (type of soil, presence of groundwater, location of other networks, traffic, etc.). Considering all internal and external factors makes decision making very complex and requires the involvement of actors from different fields (decision makers, managers and engineers and scientists) with extensive professional and academic experience. The aim of this decision support tool is to identify pipes that should be rehabilitated in the short, medium and long term according to their level of urgency. The AHP method was applied for the classification of indicators that have a great influence on the planning of the rehabilitation of drinking WDN. The application of our model in a real case can improve the planning of WDN rehabilitation and will have lasting effects on the functional performance and quality of drinking water services.
The article is organized as follows: after this introduction, a literature review on the application of MCDMs and AHP is presented. Next, a full description of the decision support tool that has been developed in this paper is presented. Then, the main results are presented and discussed, and are followed by the conclusion section.

Literature review
Planning the rehabilitation of WDN In recent years, several researchers have applied different models and methods for planning the rehabilitation of drinking water networks. For example, genetic algorithm (GA) based on case studies and applying multiobjective optimization models have been introduced for rehabilitation scheduling (Alvisi & Franchini, 2009;Bakri et al., 2015;Elshaboury, Attia, & Marzouk, 2020;Dell'Aira, Cancelliere, Creaco, & Pezzinga, 2021). Tabesh, Delavar, and Delkhah (2010) developed a combined geographic information system (ArcView) and hydraulic simulation software (Epanet) for the planning of pipe rehabilitation in WDN. Francisque et al. (2014) developed a decision-making tool based on a risk approach and a hybrid genetic algorithm (HGA), named Water main Replacement Risk-based Model (WARRM) to priorities the rehabilitation of drinking water pipes. Other researchers have used machine learning model (Raspati et al., 2022) while several other researchers have applied at least one of the MCDM methods for planning the rehabilitation of WDN (Scholten, Scheidegger, Reichert, Mauer, & Lienert, 2014;Caetano, Carriço, & Covas, 2022).

Multicriteria decision-making (MCDM)
MCDMs are operational research methods used to deal with complex decision problems. MCDMs allow the evaluation of several elements (criteria, subcriteria and alternatives) based on expert judgments to select the best available solutions. MCDMs have been used in several scientific and technical fields such as in energy, transport, industry, civil engineering, engineering, medicine and water resources. According to Hajkowicz and Higgins (2008), there are several MCDM methods, but the most applied in water resources management are techniques for order of preference by similarity to ideal solution (TOPSIS), AHP, elimination and choice translating reality (ELECTRE) and preference ranking and organization method for enrichment evaluation (PROMETHEE) and hybrid methods such as Fuzzy-AHP (FAHP) and AHP-TOPSIS. However, each of these approaches has different characteristics and applications.
Various researchers have applied the different techniques of MCDM to water resources management issues. Santos et al. (2016) used a hybrid method by combining AHP with TOPSIS to select the best solutions in drinking water treatment, using four evaluation criteria: financial viability, environmental sustainability, technological performance and social acceptability. Salehi, Jalili Ghazizadeh, and Tabesh (2018) developed a decision-making model called Water Distribution Systems Rehabilitation (WDSR) using a hybrid TOPSIS-Fuzzy method based on technical and nontechnical criteria to plan the rehabilitation of water networks. Ghandi and Roozbahani (2020) developed a decision support tool based on an integrated Fuzzy-PROMETHEE V method to select the best alternatives in the management of drinking water supply by choosing five criteria: reliability of water supply, simplicity of implementation, cost optimization, social satisfaction and quality of drinking water.

Study area and data collection
The city of Souk-Ahras is the capital of the wilaya (Department) of Souk-Ahras, located in the North-East of Algeria. The management of drinking water services (production and distribution) is ensured by the Algerian water company (ADE) since July 2006 (Boukhari, Djebbar, Guedri, & Guebail, 2011). The city of Souk-Ahras is supplied from Ain-Dalia dam and Taoura groundwater. The drinking water supply system is composed of a treatment plant, 18 water tanks with a total storage capacity of 33700 m 3 , 55 km of conveyance and 220 km of distribution network (Boukhari & de Miras, 2019). The WDN is composed of different materials (Polyvinyl Chloride (PVC), High-Density Polyethylene (HDPE), cement asbestos (CA), steel and cast iron) and the diameters vary between 63 and 315 mm. The distribution system of the city of Souk-Ahras suffers from several problems, the most notable of which is the lack of continuous service. The causes of this situation lie in the high rate of losses which exceeds 50% (Guebail, Djebbar, Guedri, Boukhari et al., 2020).

Methodology of AHP application
As mentioned in several scientific researches, the application of the AHP method is carried out in six main steps (Kilinç, € Ozdemir, Orhan, & Firat, 2018). The first step of the AHP methodology is to define the main objective related to the problem to be solved. Then, and to achieve the defined goal, the evaluation elements (criteria, subcriteria and alternatives) must be identified. The third step can be illustrated by the creation of the hierarchical structure (a structure with several levels) of its components (Dos Santos et al., 2019). Fourth step is the composition of pairwise comparison matrix for all decision items using standard scoring values taking into account expert judgments. The selected experts were asked to compare the elements with each other according to the scale proposed by Saaty (1980). The last two steps are the calculation of the relative weights of the elements and the verification of the consistency of each comparison matrix. Figure 1 presents the methodology of the AHP application.
This methodology indicates that the elements provide a primary focus for developing decision matrices for each element. However, these matrices help determine the relative weights of each element in the same layer. Then, after calculating the relative weights of each element, the overall weight is determined for each indicator. Finally, based on the final score, the most relevant indicators for WDN rehabilitation planning are determined. The following sections detail the methodology.
(1) Step 1: Identification of the objective The first step of the AHP is the identification of the problem and the objective of the task at hand being a research or an engineering undertaking.
(2) Step 2: Selection of evaluation items Before starting the AHP procedures, elements (criteria, subcriteria and indicators) most widely applied in WDN rehabilitation planning should be selected based on the problem of the study area and the opinion of decision-makers and experts. (3) Step 3: Building the hierarchical structure The construction of the hierarchical structure involves several levels of assessment. However, the process will divide the complex decision-making into a simple hierarchical structure of all elements of this structure that are divided into independently evaluated layers to facilitate the assessment.
(4) Step 4: Establishing the decision matrices After the construction of the hierarchical structure, the next step is to establish the decision matrices of all elements for each level. The judgment applied by the experts made it possible to determine the decision matrices for each level of the hierarchical structure. For this purpose, the decision matrices were established by comparing the preference of each element to another element to determine and rank the relative and overall weights. The judgment of these experts was based on the Saaty scale (Table 1). In this step, a pairwise comparison matrix "A" was defined by the following equation (Eq. (1)): A is the decision matrix, a ij are the pairwise comparisons between elements i and j for i,j ∈ {1, 2,. . ., n} and a ii 5 1 et a ij 5 1/a ji Where n is the number of each element in the decision matrix. (5) Step 5: Calculating the priority vector for each element In this step, priority vectors (relative weights) are calculated for each of the elements (criteria, subcriteria and indicators) in the decision hierarchy. The relative weights are estimated from the comparison matrix (after the expert judgment). Next, it is necessary to check that the sum of all weights should be equal to 1.00. To calculate the relative weights, the following steps should be followed: Calculate the sum of each column of the "A" matrix Divide each element of matrix "A" by the total of the column, and this will give the normalized matrix "B".
Calculate the average of each row of matrix "B". (6) Step 6: Check the consistency ratio (CR) for each element The calculation of the CR is an important aspect in the application of the AHP method. This step is essential to check the consistency or inconsistency of the decision matrix. According to Saaty, the CR should be equal to or less than 10% (Saaty, 1980). The CR is calculated by comparing a consistency index (CI) with a random index (RI). To check the consistency of the decision matrix, the following steps are required: Calculate the eigenvalue λ max Numerical rate Definition 1 Equal importance 3 Weak importance of one over another 5 Essential or strong importance 7 Very strong importance 9 Extreme importance 2, 4, 6, 8 Intermediate values between two judgments Reciprocals of above If activity i has one of the above nonzero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i Source(s): (Saaty, 1980)  Next, the important step in calculating the AHP was to assess the consistency of the pairwise comparisons. In this step, the consistency assessment was performed based on the verification of the CR (Zyoud et al., 2016). As a general rule, CR should not exceed 10% for the decision matrix to be coherent (Saaty, 1980;Ş ener, Ş ener, Nas, & Karag€ uzel, 2010). Otherwise, if the percentage of CR is greater than 10%, the level of inconsistency should be improved by gradually reducing or increasing the most incoherent value of the decision matrix (Calizaya, Meixner, Bengtsson, & Berndtsson, 2010). According to Saaty (1980), the coherence of each matrix has been calculated from Eq. (2): where CI is the consistency index and RI is the random index.
RI is given in Table 2.
As suggested by Saaty (1980), CI is calculated using Eq. (3): λ max : the largest eigenvalue of the consistency vector, n: the number of elements in each matrix (criteria, subcriteria or indicators). (7) Step 7: Calculation of overall weights Once these steps have been completed, the AHP provides a vector of overall weights for the last level by multiplying all the relative weights of each element in all levels. (8) Step 8: Making the final decision The final step begins by summing the relative values for each set of elements at all hierarchical levels. These values are combined to establish the overall score for the indicators related to the subcriteria layer.

Results and discussion
This section illustrates the process of applying the AHP methodology to the decision-making problem for the planning of the rehabilitation of the drinking WDN of the city of Souk-Ahras,

Selection of assessment items
The AHP method starts with the identification of the problem and the objective of the project. In our case, the main objective is to rank the indicators that have major influence on the planning of the rehabilitation of drinking WDN. Then, the elements are selected by decision-makers, WSS managers and experts. In conclusion, three decision criteria (physical, operational and pipe environment), seventeen evaluation subcriteria and fifty-six indicators were considered for the decision-making of WDN rehabilitation planning (Table 3).
Developing the hierarchical structure The hierarchical structure makes it possible to identify the contribution of each element to the final decision. In the case of our study, four levels are considered in the AHP process: the first level is dedicated to the evaluation objective, while the other three levels are assigned to the three elements (criteria, subcriteria and indicators). The hierarchical structure developed in this paper is presented in Figure 2. For the criteria level (Cr), three decision criteria are considered: (Cr 1 ) physical, (Cr 2 ) operational and (Cr 3 ) pipeline environment. At the subcriteria level, a total of 17 subcriteria (SC) were applied for the evaluation of the upper-level criteria, six subcriteria SC 1 -SC 6 were selected for Cr 1 respectively, five subcriteria SC 7 -SC 11 were selected for Cr 2 and six subcriteria SC 12 -SC 17 were favored for Cr 3 . Then, two to five Indicators (I) related to each subcriterion are selected based on scientific literature, expert experience and local conditions. For example, for the subcriterion "Types of materials" (SC 2 ), the indicators chosen are CA I 1.

Establishing the decision matrix
To establish the decision matrix, twenty-four experts (eight university researchers who have published scientific articles in the field of water management, eight decision-makers from the water resources directorate and eight WSS managers from the Souk-Ahras ADE unit) were selected to carry out the judgment (pair-wise comparison) according to the Saaty comparison scale. These experts were chosen according to their professional and scientific experience; they have wide knowledge in WDN management. For this purpose, decision matrices were developed for three levels: (1) The M1 matrix represents the evaluation of three decision criteria; (2) The three matrices M2.1ÀM2.3 represent the 17 evaluation subcriteria; (3) The matrices M3.1ÀM3.17 represent the performance of the 56 Indicators.
After establishing the decision matrices, the AHP will be applied to calculate the relative weights at each level, and the consistency of the results will be checked. (2) Determine the value of the random index (RI)
(3) Calculate the coherence index (CI) The CR value for this matrix is 0.776 (7.76%), which is less than 10%. Therefore, the matrix is considered to be consistent. The results of the calculation of the relative weights of the criteria matrix [M1] are shown in Figure 3, the criterion "operational" plays the most important role with a relative weight of 55.6% followed by the criterion "physical" (35.4%), and the criterion "pipe environment" (9.0%). In general, operational and physical criteria such as the high age of pipes, repair of leaks and decrease in high operating pressure of WDN have a great influence on failures of drinking water pipes.
Pairwise comparison of the subcriteria CR 5 9.99% < 10% → consistency is verified. Pressure (34.8%) and the number of failures (32.5%) are the two subcriteria that have high influence on the criterion "Operation". According to experts' judgments and for the case of Souk-Ahras city, the subcriterion "water quality" does not have a great effect on the functioning of the WDN. The subcriteria, type of traffic (31.9%), laying bed (26.5%) and type of soil (18.5%), play an important role in the criterion "pipeline environment".  The pairwise comparison process for the Indicator layer is the same as for the criteria and subcriteria. For this purpose, the priority vectors are calculated in the same way as for the other levels. The "diameter over 300mm" indicator has the highest weight for the subcriterion (diameters) with a rate of 54.5%. The results of all the other indicators are presented in Table 3.

Calculation of global weights
The overall weight of the indicators is calculated by multiplying its local priority vector by the corresponding local weight of the criterion and subcriteria. The overall indicator weights are synthesized to establish the overall priorities for the selection of indicators that have a high influence on the malfunctioning of drinking water pipes. The results of the global indicator weights are shown in Figure 4. According to Figure 4, the global weights of the indicators, which have a great influence on the rehabilitation of WDN, are the number of failures exceeding 3 leaks in the same place (I.2.3.3) and the pressure, which exceeds 6 bars (I.2.1.3), and if age of the pipe is over 50 (I.1.4.4) with the following respective percentages 12.38%, 10.98% and 5.70%.
Calculating of the level of urgency Before a final decision is made, the urgency level must be calculated to enable the classification of pipes that are to be rehabilitated in the short, medium and long term. To perform this task, the model has to be applied to a real case with real data. The 1700 dwelling district, city of Souk-Ahras, was chosen due to the high number of leakage repairs in recent years. The distribution network of the 1700 dwelling district has a length of 12860 m. It includes 90 pipes of different materials ( Figure 5) and diameters ( Figure 6).
The pipes diameters range from 40 to 300 mm. Lengths material types and diameters are reported in the table below. HDPE is the most used material, with a percentage of 40.41% of the total network length followed by PVC with a percentage of 39.64%.

Global Weight
Indicators Figure 5.

Overall weights of indicators
After calculating the overall weight of each indicator using the AHP method, it is necessary to rank and map the sections in order of importance (priority order) for the planning of the rehabilitation of the WNDs. This task produce a table containing the results related to each pipe in our case study by adding up all values of selected indicators (Appendix 1). The urgency level attached to each pipe is then calculated (Figure 7). The values of the urgency level obtained ranged from 0.1261 to 0.4816. Subsequently, the pipes were grouped into four classes of urgency levels: (1) 1st level: urgency level > 0.3000 (2) 2nd level: 0.2300 < urgency level ≤ 0.3000 (3) 3rd level: 0.1500 < urgency level ≤ 0.2300 (4) 4th level: urgency level ≤ 0.1500 The final step is to classify the pipes according to the four-time groups (e.g. the first level equals T1), this will allow building a rehabilitation program. As a result of this step: 14 pipes need rehabilitation before 5 years (T1), 31 pipes between 5 -10 years (T2), 36 pipes between 10 -15 years (T3) and 9 pipes after 15 years (T4). The results obtained are illustrated in Figure 8.
The scheme for establishing the rehabilitation program is shown in Figure 9, with: In the first period (T1 ≤ 5 years): the length of the pipes to be changed is 3394 m. In this period, the steel pipes will be replaced by cast iron and the PVC by HDPE. Additionally, a pressure regulator will be installed to decrease the pressure in this sector; Second period (5 < T2 ≤ 10 years): in this period, 3501 m of PVC pipes will be changed to HDPE; Third period (10 < T3 ≤ 15 years): in the third stage, 4854 m of pipe will be rehabilitated; Fourth period (T4 > 15 years): in the last phase, 1111 m of pipe will be targeted for rehabilitation.

Conclusions and recommendations
In this article, a decision support tool has been developed based on a hybrid method that integrates the AHP and the calculation of the level of urgency to establish a rehabilitation Histogram of pipes to be rehabilitated versus time Figure 9. Graphical interpretation of a rehabilitation program program for WDN. The AHP method was used to prioritize the indicators having a strong influence on the dysfunctioning of the WDN. On the other hand, the calculation of the level of urgency was applied to classify the pipes to be rehabilitated. When developing the model, three criteria, physical, operational and pipeline environment, were taken into account. The decision matrices were calculated based on the opinions of 18 experts. A decomposition of the problem into a hierarchical structure of elements was necessary. In the case of this study, four levels are considered in the AHP process: the first level is dedicated to the evaluation objective, while the other three levels are assigned to the three elements: criteria, subcriteria and indicators. According to the results of this model, it is considered with high risk of new damage and failures in the existing WDN pipes with high ages and high pressures. Before a final decision is taken, the level of urgency must be calculated to allow the classification of pipelines to be rehabilitated in the short, medium and long term. The model developed was applied to the district of 1700 housing units in the city of Souk-Ahras. The study area was chosen because of its high number of leak repairs in recent years.