Planning methodology for effective implementation of the rehabilitation policy for drinking water networks

Drinking water is transported in pipes that, over time, lose their original characteristics and are subject to deterioration. As a result, not only the pipes' hydraulic performance reduces, water losses increase and water quality deteriorates, but also customer complaints are on the rise. Today, this degradation of urban drinking water networks is a major concern for drinking water utility managers (Amaral et al., 2017). To this end, the drinking water network urban heritage is part of a rehabilitation process that is proving to be a very difficult task for managers. Therefore, rehabilitation planning requires elaborate strategies and considerable resources and should be linked to multi-criteria considerations.

In Algeria, the situation of drinking water utilities in large cities is not very encouraging. It reveals many management difficulties resulting from a combination of several factors, such as the lack of water resources (Radia et al., 2021); the anarchic expansion of towns and cities caused by the rural exodus; the poor state of the networks, with an average leakage rate of more than 50% (Abdelbaki et al., 2019). As a result, rationing is applied in most cities and the water supply is far from meeting the customers' needs. This situation puts unbearable pressure on drinking water utilities from their customers (Maiello et al., 2021). Aware of this situation, managers are attempting to improve the operation of drinking water networks and the quality of service provided to customers. To meet growing demand for water, rehabilitation is a means of reducing losses (Güngör et al., 2017), safeguarding the available resource, achieving financial savings, and improving the quality of water supply to the population. This reality has raised awareness and led the public authorities to implement a rehabilitation policy with a number of specific features. At the beginning of the 2000s, a programme was launched covering 39 cities. This rehabilitation policy is divided into two main phases. The first concerns the diagnosis of infrastructures and the creation of geographical information systems. The second concerns the implementation of rehabilitation projects. Since then, several resources have been invested at all levels to initiate diagnostic and rehabilitation studies of drinking water networks. In fact, the rehabilitation programme has been strengthened by the know-how of foreign companies specialising in network diagnostics and by a partnership with national university expertise. For this programme to be successful, managers need to be supported in making the best decisions about the rehabilitation of drinking water networks. In this perspective, the contribution of this study consists in proposing a methodological tool for better planning of rehabilitation networks.

The literature review of the decision-making support tool in the field of planning rehabilitation of drinking water networks refers to several works. In fact, there are two approaches to the problem. The first is part of a medium – or long – term approach. The second is part of ongoing rehabilitation programmes.

The first approach aims to predict the state and performance evolution of the network in order to anticipate and structure future actions. Indeed, several works have been studying predicting pipe failures issues. In this case, we find several methods used based on: survival analysis (Weeraddana et al., 2021), spatiotemporal clustering and Poisson regression (Martínez García et al., 2021), and artificial neural networks (ANNs) (Tavakoli et al., 2020).

The second approach aims to establish rules for prioritising the rehabilitation actions to be carried out under budgetary constraints. There are two aspects to this prioritisation. The first relates to the development of programming-based methods. In fact, the literature refers to a number of studies that have focused on: the optimised neural network models (Elshaboury & Marzouk, 2022), the development of an algorithm based on resilience and entropy index (Cimorelli et al., 2018), and the use of a semi-automatic method for network data reconstruction for water supply networks and simplified approach for the modelling of rehabilitation rates (Tscheikner-Gratl et al., 2016). The second aspect is based on the use of multi-criteria decision support methods. In this context, the studies carried out aim to support experts in making the best decision when solving any given problems such as selecting, sorting, ranking and describing. In these studies we observe the use of different multi-criteria methods, such as ELECTRE TRI (Elimination Et Choice Translating REality) Le Gauffre et al. (2007); ELECTRE III (Carriço et al., 2021); PROMETHEE V (Preference Ranking Organisation METHod for Enrichment Evaluations) (Fontana & Morais, 2013); ELECTRE, AHP (Analytical Hierarchy Process); WSM (Weighted Sum Model); TOPSIS (Technique for Order Preference by Similarity to Ideal Solution); PROMETHEE (Tscheikner-Gratl et al., 2017); Fuzzy Topsis (Salehi et al., 2018); and ANP (Analytic Network Process) (Așchilean & Giurca, 2018).

Our study fits into the second orientation dealing with a ranking problem. In view of this situation, several studies have suggested approaches based on several elements. The approach of Yoo et al. (2014) is solely based on water pipes deterioration rate and their hydraulic importance, adding the simulation of single and multiple pipe failures. The approach of Salehi et al. (2018) is based on the development of a tool that integrates 42 criteria, which is a high number divided into two groups: technical and non-technical. However, rehabilitation strategies and economic criteria are not identified. The approach of D'Ercole et al. (2018) rests on a specific objective, which is to maximise the mechanical reliability of the network and minimise the risk of unmet water demand and pressure deficit under given economic constraints. The approach of Carriço et al. (2021) is based on the development of a multi-criteria decision support methodology that considers only three criteria: performance, cost and risk in a long-term perspective. The approach of Beker & Kansal (2023) is based on a futuristic approach to pipe and valve rehabilitation. It considers a single failure, as the failure condition of multiple connections is currently an area of research. Furthermore, the approach does not consider the physical and geometrical perspective of the network.

The studies consulted do not fit our methodology. Nevertheless, they provide interesting elements in the construction of our approach to rehabilitation. The main purpose of this study is to develop a methodology to assist managers in making the best decisions when planning rehabilitation works in a drinking water network. It aims at a global ranking of the pipes in order to rehabilitate them by order of urgency, based on a decision support tool that allows the environmental, economic, social and technical benefits of rehabilitation to be assessed. Eventually, our contribution takes into account a number of very important aspects that provide an adequate decision support tool.

In the first aspect, the selection of relevant criteria to be considered in rehabilitation projects is improved. Indeed, many criteria have been identified for rehabilitation; there has not been a comprehensive study addressing all criteria (Salehi et al., 2018). More to the point, the various studies cited do not apply to our local situation, as the different criteria influencing the prioritisation of rehabilitation works are specific to each case study. In our case, the criteria chosen should: include all environmental, economic, technical, and social parameters influencing pipe rehabilitation, reflect the local conditions of the study and ensure the availability of real practical data on the one hand. On the other hand, the number of criteria takes into account the limitations of the AHP weighting method (Gan et al., 2017).

The second aspect, on the other hand, takes into account the subjectivity and imprecision expressed by the managers of the drinking water utilities in their various judgements; for this purpose, fuzzy logic will be integrated into the AHP weighting method. The latter was chosen for its various advantages (Gan et al., 2017). In the third aspect, a decision support tool is chosen which offers a great potential for modelling decision problems and which is efficient in prioritising rehabilitation works by analysing all the different weighted criteria simultaneously.

The PROMETHEE II method was chosen because it is widely used in the multi-criteria decision support field, in particular in the water management field. It also has the advantage of being a sophisticated method that takes into account a large number of qualitative and quantitative criteria and does not need to repeat the pairwise comparison process when new alternatives are added or removed (Tscheikner-Gratl et al., 2017). In the fourth aspect, the benefits generated after the rehabilitation are evaluated and analysed in order to highlight the interest of the proposed decision support methodology for the managers of drinking water services.

The research methodology used in this paper aims to consolidate the national policy implemented by the public authorities for the rehabilitation of drinking water networks, by exploiting the know-how of foreign companies in diagnosis and skills in multi-criteria analysis. The interest of the development of this methodological tool lies, on one hand, in the construction of several criteria related to multiple and diverse objectives such as environmental protection, cost reduction, network rejuvenation, and, on the other hand, it lies in the development of a multi-criteria approach consisting in the construction of a model that captures the decision problem based on these different criteria. The explicit consideration of multiple criteria, most of which are in conflict, introduces a difficulty that does not exist in the case of a single criterion (Le Gauffre et al., 2007). This makes the decision problem more complex but goes a long way to improving decision-making. To this end, the methodology is divided into two main phases: the diagnostic phase and the planning phase. The diagnosis was carried out through a contract initiated with a specialised Portuguese company. As part of this major project, the consultant's role was to carry out studies and diagnostics in a series of missions. The purpose of these missions was to implement the necessary strategy to analyse the network situation, identify the difficulties in managing the network and find the appropriate solutions in terms of rehabilitation. To achieve this, the implementation of the contract required the exploitation of the company's know-how, the deployment of resources and the transfer of technology and knowledge. In order to carry out these tasks, the specialist company has set up a structure within the drinking water utility that specialises in collecting data on a number of relevant criteria. The foreign company's final task is to analyse and validate all the results obtained in terms of all the criteria to be taken into account in the rehabilitation plan. The aim of the planning is to prioritise the pipes to be rehabilitated from the most urgent to the least urgent ones. To this end, planning requires first of all the mobilisation of the data obtained on all the criteria during the diagnosis, and then the choice of the method for weighting the criteria, which offers an improvement in the accuracy of the judgement of the water utility managers. Finally, the choice of the appropriate multi-criteria approach, which allows the overall ranking of the pipe to be made, taking into account all the weighted criteria. This planning must provide benefits that will enable managers to understand the multiple objectives in terms of environmental, economic, social and technical aspects.

Rehabilitation is aimed at improving the functioning of a drinking water network. This is achieved via interventions that include the renovation of existing pipes, the replacement of some pipes with new ones, or the installation of new pipes to meet the demand of new consumers (Le Gauffre et al., 2007). For this purpose, managers must define the appropriate intervention for each pipe in order to optimise the necessary rehabilitation work. But how are we going to rehabilitate the network? In our case, the rehabilitation is done by ranking the pipes from the most urgent to the least urgent ones. This choice is motivated by the assumption that this rehabilitation, which focuses on the weakest network elements, can quickly improve the operation of the network and effectively support the rehabilitation over time. However, it is not easy to achieve an ideal overall ranking. Certainly, the difficulty lies in the choice of the elements and tools to be taken into account in this methodology, allowing a faithful description of the existing interactions between the network and the city with its environment. To succeed in this bet, it is, therefore, necessary to adopt a methodology that integrates a set of relevant measurable criteria to take into account the constraints, interactions, needs, and expectations of rehabilitation. Then, the multiple nature of these criteria calls for a multi-criteria analysis that requires the expertise and judgement of managers to assess the importance of each criterion in relation to the others, and finally, the choice of an efficient decision support tool with a very high modelling potential that allows the global pipe ranking to be rehabilitated by simultaneously analysing all the different weighted criteria.

The criteria to be taken into account when planning the rehabilitation of the networks were identified on the basis of the documents relating to the water problem in Algeria, the technical work on the rehabilitation of the drinking water networks and the results of the diagnosis carried out by the foreign company. The criteria that contribute to the improvement of rehabilitation are very diverse in order to analyse the drinking water network from its different aspects. The criteria chosen must take into account all the environmental, economic, technical and social parameters that influence the rehabilitation of the pipes. These criteria should reflect the local conditions of the study and should also ensure the availability of real-world data. In this respect, the diagnosis carried out by the foreign company was a great help. Through their missions, many measures were taken according to relevant criteria.

The criteria weighting is calculated from the judgements of experts in the field. However, it is quite difficult for the experts to give specific and objective scores. In order to make the best use of the information provided by the experts, two approaches, AHP and Fuzzy Logic, are combined.

The weighting of the criteria is calculated using extent analysis on Fuzzy AHP method.

• – Fuzzy Analytical Hierarchy Process method (Fuzzy-AHP): Fuzzy-AHP is a combination of two concepts: Fuzzy set theory and AHP method. This choice is motivated by two aspects; the first one is related to the AHP method. It has several advantages (Gan et al., 2017). In fact, it has the advantage of being a widely used method, especially in the water sector (Hamchaoui et al., 2015; Bouchraki et al., 2021). It allows a good organisation of the decision problem under a hierarchical structure with several levels. In the AHP method, the verification of the consistency of the judgements is mandatory. It is first obtained by calculating the consistency index (CI) as follows:

  

  (1)

RI is the random index depending on the size of the matrix. If CR ≥ 0.10, the judgement should be revised and improved to reduce inconsistencies. Moreover, in the AHP method, judgements are represented by an exact value; these judgements are expressed by experts who evaluate the importance of the criteria taken two by two according to a scale. The second aspect aims to overcome the disadvantage of the AHP method. The Fuzzy-AHP method expresses individuals' subjective judgements in more specific and informative forms than the AHP method. The AHP method cannot capture the intangible intuition or hesitation in the decision-making process, whereas it can be measured in the Fuzzy-AHP method (Chen et al., 2022). Therefore, the integration of the Fuzzy set theory concept proves to be necessary. This concept represents an effective solution to improve the accuracy of the judgements found in the analysis of multi-criteria problems. For this, verbal judgements are no longer expressed by an exact value, but by a triangular function. The fuzzy judgements method proposed by Laarhoven is based on the concept of Zadeh's fuzzy sets. This method is resting on pairwise comparisons of triangular fuzzy numbers (Van Laarhoven & Pedrycz, 1983). The triangular fuzzy number can be described by M=(l, m, u) where l≤m≤u; l and u are the lower and the upper values of M and m is the modal value. The construction of the fuzzy judgement matrices requires the use of a scale. In fact, there are several scales of Fuzzy-AHP in the literature. In this study, Saaty's fuzzy triangular is used scale (Table 1), taken from the paper of Söyler & Pirim (2014).

• – Chang's extent analysis method: the weight vector is calculated using the formulas of Chang's extent analysis method as well as the basic notions of triangular fuzzy numbers. The main formulas of Chang's extent analysis method are summarised in Chang (1996).

PRΟΜΕΤΗΕΕ (Preference Ranking Organisation Methods for Enrichment Evaluations) belongs to the family of outranking relations methods and supports multi-criteria decision analysis. PROMETHEE II is the most widely applied complete ranking method, as it follows a transparent and easy-to-understand calculation procedure. Its main advantage is the possibility to evaluate alternatives that are in fact difficult to compare due to some existing trade-off relation between valuation standards, and non-comparable alternatives (Thakkar & Thakkar, 2021). Add to this, the PROMETHEE II method is related to the fact that it generates preference indices in the interval [−1, 1], which means that there is a real zero point that provides a measure of separation for the studied locations, distinguishing them in two classes. Those with a positive net preference flow indicate outranking capacity and those with a negative outranking represent outranked locations (Vavatsikos et al., 2022).

Other advantages include the completeness of the ranking, the high degree of flexibility in defining preference and indifference thresholds for each criterion, and the use of free downloadable software that allows the results to be presented in an orderly fashion.

The PROMETHEE II method requires information for its application, which must be clear and comprehensive between experts and decision-makers (Ishizaka & Nemery, 2013). These pieces of information are:

• – Information between the criteria: they express the relative importance of each criterion through the weight. PROMETHEE does not have a tool to calculate the weight. In our case, the weight is calculated by extent analysis on the Fuzzy-AHP method.

• – Information within each criterion: they express the difference between the evaluation of two actions a and b with regard to a particular criterion into a preference degree ranging from 0 to 1. These pieces of information are called preferences. For each criterion, a preference function is associated with it. It is expressed as follows (Ishizaka & Nemery, 2013):

  

  (3)

  where and for which ⁠.

F_j is a non-decreasing function of the observed deviation (d) between ⁠. A is a finite set of action is a set of criteria evaluation.

There are six types of preference functions, for each function no more than two parameters are to be set.

The PROMETHEE II method is based on the following formulas (Ishizaka & Nemery, 2013):

• – Preference index:

  

  (6)

Such as: implies a low preference of a over b, however, implies a strong preference of a over b.

• – Outranking flows: the two outranking flows are expressed as follows:

  

  (7)

  

  (8)
• – Net outranking flow:

  

  (9)

The highest value of the net outranking flow is assigned to the best action.

In the following section, the description of the Fouka drinking water network is first presented, followed by the results obtained from the application of the methodology concerning the final ranking of the pipes and the benefits generated after rehabilitation.

The synthesis obtained during the diagnosis is structured according to three important points: the identification of relevant criteria, the collection of data on different aspects and the validation of the data obtained.

Identification of relevant criteria: the results of the diagnosis refer to 13 relevant criteria that reflect: the description of the network characteristics, its condition, its performance, customer satisfaction, the assessment of the rehabilitation costs and the appropriate solution to be implemented for each pipe. These criteria are as follows: material, ruptures, type of seal, complaints, overlap, rehabilitation technique, age, linear leakage index, linear loss index, size, yield, length, and rehabilitation cost.

Collection of data: the means used to measure the various criteria mentioned above made it possible to reach information with a certain degree of precision at the scale of each pipe section and to obtain measured values for a number of criteria reflecting national specificities, such as the linear loss index. The diagnosis also allowed the appropriate rehabilitation technique to be identified for each pipe, taking into account national specificities.

Validation of data: the measurements carried out throughout the sector have enabled us to collect a great deal of data on the criteria identified, at the scale of each section of pipe. The obtained values are therefore measured in the field. These values are verified by the Portuguese company, which not only participated in the measurement but also in the validation of the data. To this end, we have found these values to be acceptable and it will be useful to consider the 13 criteria. Our decision to include all criteria is therefore motivated by their availability, representativeness, and relevance.

The results of the diagnosis will be used in the planning phase. Consequently, the use of all the measured and available data in the analysis of the prioritisation will allow a better pipe ranking.

The different criteria selected are described in the following:

Material: this criterion is based on pipes that require a change in material type. High-density poly ethylene (HDPE) and ductile iron pipes are the most commonly used due to the various technical and economic advantages they offer. The most sensitive pipes to be rehabilitated are those with a material other than HDPE and ductile iron (HDPE = 1, ductile iron = 2, other materials = 3). Knowing that the highest value of the evaluation is given to the priority pipe, this principle is followed to give the different criteria evaluations.

Ruptures: this criterion is based on the treatment of pipe rupture if required. The most sensitive pipes to be rehabilitated are those with ruptures (no ruptured = 1, ruptured = 2).

Type of seal: this criterion is based on the change of defective seals. The most sensitive pipes to be rehabilitated are those with defective seals (non-defective seals = 1, defective seals = 2).

Complaints: this criterion is based on the rehabilitation of pipes where there are complaints from customers. Complaints are due to different types of inconvenience caused by a malfunction in the drinking water network. For this reason, the most sensitive pipes to be rehabilitated are those that have caused more complaints (no complaints = 1, complaints = 2).

Overlap: this criterion is based on the rehabilitation of overlapping pipes. These overlaps are the result of the drinking water network crossing various networks: gas, sewerage, electricity, telephone, etc. The most sensitive pipes to be rehabilitated are those with overlaps with other networks (no overlap = 1, overlap = 2).

Rehabilitation technique: this criterion is based on the use of the least resource-intensive pipe rehabilitation technique. The most sensitive pipes to be rehabilitated are those requiring rehabilitation techniques with fewer resources (replacement = 1, extension = 2, maintenance = 3).

Age: the oldest pipes are the most susceptible to deterioration. This criterion is based on the rehabilitation of the oldest pipes (Age = pipe age (year)).

Linear leakage index: it is defined as the number of leaks observed in a pipe of known length over a given reference period. This criterion is based on the pipe rehabilitation that has recorded more leaks (Linear leakage index = pipe linear leakage index (leakage number/km/year)).

Linear loss index: it evaluates the volume of water loss over a pipe of known length and over a given reference period. This criterion is based on the rehabilitation of pipes with higher water losses (linear loss index = pipe linear loss index (m³/day/km)).

Size: a large size carries a large flow and supplies more people than a small size. This criterion is therefore based on the rehabilitation of larger size pipes (size = pipe size (mm)).

Yield: this refers to the ratio between the water volume consumed by users and the public service and the volume of drinking water injected into the distribution network. This criterion is based on the rehabilitation of low yield pipes (yield = pipe yield (%)).

Length: long length can also be the cause of pipe damage. This criterion is based on the rehabilitation of pipes with longer lengths (length = pipe length (m)).

Rehabilitation cost: this criterion is based on pipe rehabilitation at minimum cost (Rehabilitation cost = cost of pipe rehabilitation (€)).

• – Construction of the pairwise comparison matrix of the criteria: it is developed from the answers to a questionnaire addressed to managers of drinking water utilities. The Fuzzy-AHP method and the fuzzy triangular preference scale are used. The summary of the answers given is presented in Table 2.

• – Consistency of judgements study: this study requires the calculation of the eigenvalue (λ_max). The latter is obtained from the defuzzified matrix containing the Crisp values (λ_max=14.8518).

• The consistency index: ⁠. The consistency ratio:

• The CR value is less than 0.1. Therefore, the matrix of fuzzy judgements is coherent.

• – Calculation of the weight vector: it is obtained by using the formulas of extent analysis on Fuzzy-AHP method described in the methodology section.

PROMETHEE II is used to determine the complete order of priority for the rehabilitation of the 204 pipes. Before this can be done, it is necessary to collect the various pieces of information that express the evaluation of each pipe in relation to each criterion. An appropriate choice of preference functions and preference and indifference thresholds is then made for each criterion (Table 3). This choice is made between the expert and the decision-maker. The latter must agree on the value of the different thresholds: p (preference threshold), q (indifference threshold), and s (the intermediate value between the preference and indifference threshold) of each function.

The PROMETHEE II method is executed using the Visual PROMETHEE software. The pipes are ranked in order of priority as follows:

P4 – P59 – P5– P2 – P5 – P140 – P44 – P55 – P1 – P75 – P56 – P3 – P13 – P115 – P135 – P47 – P19 – P52 – P177 – P110 – P20 – P14 – P46 – P139 – P62 – P203 – P120 – P45 – P161 – P48 – P66 – P103 – P22 – P42 – P96 – P58 – P32 – P152 – P132 – P6 – P95 – P116 – P76 – P176 – P187 – P49 – P80 – P159 – P43 – P33 – P160 – P23 – P119 – P137 – P174 – P24 – P111 – P109 – P170 – P191 – P153 – P141 – P71 – P196 – P117 – P78 – P54 – P53 – P112 – P126 – P113 – P101 – P102 – P158 – P25 – P130 – P17 – P188 – P128 – P193 – P142 – P64 – P16 – P18 – P38 – P69 – P50 – P67 – P60 – P106 – P154 – P151 – P165 – P183 – P184 – P134 – P65 – P131 – P185 – P166 – P40 – P72 – P68 – P12 – P39 – P51 – P107 – P118 – P194 – P26 – P172 – P36 – P167 – P150 – P15 – P143 – P169 – P144 – P35 – P70 – P31 – P79 – P198 – P195 – P61 – P30 – P138 – P197 – P87 – P9 – P90 – P133 – P85 – P173 – P114 – P201 – P81 – P199 – P21 – P98 – P8 – P175 – P63 – P155 – P77 – P74 – P186 – P88 – P37 – P136 – P162 – P89 – P190 – P163 – P157 – P123 – P164 – P84 – P94 – P73 – P189 – P86 – P147 – P178 – P204 – P180 – P10 – P82 – P27 – P92 – P168 – P148 – P104 – P149 – P179 – P129 – P182 – P41 – P105 – P125 – P99 – P124 – P121 – P97 – P91 – P29 – P34 – P146 – P100 – P11 – P108 – P145 – P93 – P83 – P171 – P28 – P156 – P181 – P122 – P192 – P200 – P127 – P202 – P7.

The final priority ranking of the 204 pipes, ranked from the most urgent to the least urgent, follows the descending order of the net flow values. The obtained results place the P4 pipe in the first position, recording the highest value of = 0.6104, its = 0.6454 and = 0.0351; P59 comes second and P7 last, recording the lowest value of = -0.3974 its =0.0062 and = 0.4037.

The P4 pipe has the highest priority for rehabilitation; due to the critical situation of the first four most decisive criteria. In fact, C9 and C8 are very important, of the order of 697.96 (m³/day/Km) and 0.051 (leakage number/km/year), respectively; at the criterion C4 several complaints are recorded; C11 is very low, it is of the order of 48%. On the other hand, P7 is the last pipe to be rehabilitated because it is in very good condition compared to the others. In particular, C9 and C8 are very low, in the order of 2.106 (m³/day/km) and 0.0001 (leakage number/km/year), respectively; at the level of C4 no complaint is recorded and C11 is very considerable, it is of the order of 83%.

This part focuses on the analysis of the benefits generated after the rehabilitation of the drinking water network in the Fouka sector. From the final pipe ranking, a series of analyses are carried out on the environmental, economic, social and technical parameters represented by the following five criteria:

Recovered water volumes (m³/year): this involves quantifying the gain in volumes of water not lost.

Recovered costs (€/year): represents the costs of water volumes recovered.

Investment costs (€): corresponds to the investments necessary for the rehabilitation project.

Avoided complaints (complaints): means the effect of rehabilitation on the avoidance of customer complaints.

Average age after rehabilitation (year): reflects the effect of rehabilitation on the rejuvenation of the network.

Environmental parameter (Recovered water volume): the water loss assessment quantified the volumes of water that can be recovered by rehabilitating the drinking water network (Figure 3(a.1)). These huge volumes of water recovered are of the order of 361,643.75 m³/year. The recovery of these large amounts of water is a perfect response to the desired solution, which is in line with the national context, as our country suffers from a lack of water. It can be seen that the curve of recovered water volumes follows a curvilinear movement, indicating a much greater recovery of water volumes during the first rehabilitated pipes than those of the last rehabilitated pipes. Indeed, 49.36% of water volumes recovered is reached at only 20% of the rehabilitated pipes and 90.07% of water volumes recovered is reached at only 70% of the rehabilitated pipes. Also, the volumes of water recovered are much greater in the first 60% of the rehabilitated pipes; the remaining 40% present recoverable volumes but are less significant.

Economic parameters (recovered costs and investment costs): the recovered water volumes have a direct impact on the recovered costs; for this purpose, the curve of recovered costs (Figure 3(a.2)) is identical to the curve of recovered water volumes. Figure 3(b) shows a comparison between the recovered costs (Figure 3(b.1)) and the required investment costs (Figure 3(b.2)). We can see that the investment costs are constantly increasing and are higher than the costs recovered; these investments costs are recoverable within 3 years after a complete rehabilitation of the network. Rehabilitation requires a lot of financial resources; therefore, increasing the rate of progress of rehabilitation work requires greater financial investment.

Social and technical parameters (complaints and average age): in terms of complaints and an average age of the network, both decrease with the rate of implementation of rehabilitation works. We note that the average age follows a linear movement with an average reduction of 5 years for every 10% of pipes rehabilitated (Figure 3(c.1)). On the other hand, the complaints follow a curvilinear movement and reach the average value of 0 after 70% of the pipes have been rehabilitated (Figure 3(c.2)).

To significantly improve the quality of the drinking water utility, the ideal would be to rehabilitate all the water pipes.

This requires political will in order to make the necessary investments. However, if the available funds are not sufficient, it will be essential to reach at least 60% of the rehabilitated pipes. In fact, at this level, the network is classified as well-maintained and provides 85.44% of the recovered water volumes (Figure 3(a)) and has less than 15% water loss. This value is well accepted by the water utility managers. Complaints are also close to zero, and the average age of the network is reduced from 50.95 years to 17.85 years.

The following section discusses the role of the criteria and their sensitivity analysis. It is concluded with a discussion of the results obtained and of the approach proposed, as well as its limitations.

The selected criteria play different roles in the pipe ranking. The role of each criterion is expressed by the weight assigned to it. An analysis of the weights shows that the four criteria C4 ‘Complaints’, C8 ‘Linear leakage index’, C9 ‘Linear loss index’, and C11 ‘Yield’ each have a weight greater than 0.150. Their total weight is 0.648 for an overall weight equal to 1.Criteria C4, C8, C9 and C11 are therefore the most important for the prioritisation of rehabilitation work. Then, the criteria C2 ‘Ruptures’, C3 ‘Type of seal’ and C7 ‘Age’ have a weight between 0.05 and 0.150. The other criteria C1 ‘Material’, C5 ‘Overlap’, C6 ‘Rehabilitation technique’, C10 ‘Size’, C12 ‘Length’, and C13 ‘Rehabilitation cost’ have weightings of less than 0.05.

The weighting of these criteria will lead to a final ranking of the pipes. This ranking must have a certain stability and changes in the weights (input parameters) must not have an effect on the final result (pipe ranking). In order to strengthen the treatment of the multi-criteria decision support problem, the sensitivity analysis study of the criteria is carried out on the weight of the criteria. The aim of this analysis is to determine the influence of criteria weighting on the stability of the final pipe ranking. It is performed using the visual stability intervals window in the visual PROMETHEE software. Table 4 summarises the weight stability intervals for each criterion.

The analysis of the amplitudes of the stability intervals shows three levels of amplitude, criteria with a small amplitude of the stability intervals (0–10%), criteria with a medium amplitude of the stability intervals (10–20%) and criteria with a large amplitude of the stability intervals (>20%).

The first level, with small amplitude stability intervals, is represented by two criteria, C6 and C11, with values of 2.79 and 5.41%, respectively.

The second level, with medium amplitude stability intervals, is represented by nine criteria C2, C1, C5, C8, C3, C13, C4, C7, and C9 with values ranging from 10.66 to 19.69%.

The third level, with large amplitude stability intervals, is represented by two criteria, C10 and C12, with values of 30.85 and 72.3%, respectively.

Therefore, the influence on the change of the pipe ranking is much greater for criteria with a small amplitude of the stability intervals (first level). A small change in the weighting values will result in a complete change in the pipe ranking. On the other hand, criteria with a large amplitude of stability intervals (third level) have no effect on the final ranking; a large change in weight values will have no effect on the final result.

The national context in which the rehabilitation approach is being developed is one of constraint and urgency, exacerbated by water scarcity. The challenge was met by developing a proactive rehabilitation approach, which was applied in a selected sector. This enabled effective interventions to be made to reduce water losses, protect the resource, and provide a better service. The degradation of urban infrastructure requires rehabilitation (Ferreira & Carriço, 2019), which is a major challenge in developing countries (Minaei et al., 2019), leading to effective and efficient management of water distribution systems (D'Ercole et al., 2018).

Diagnosis is a key part of our approach. Several tasks are carried out during this major operation. It allowed us to identify the various qualitative and quantitative criteria that characterise and describe the network, and to specify the necessary rehabilitation techniques. The importance of diagnosis is approved by a number of researchers, as it also enables comparative analysis of situations and evaluation of performance in relation to the objectives set (Ferreira & Carriço, 2019; Carriço et al., 2021).

The choice of criteria varies from one case study to another. In the case of Carriço et al., (2021) and Salehi et al., (2018), the choice of criteria is in accordance with the objectives of the study. In our case, the criteria used are the result of a diagnosis taking into account all available criteria. The simultaneous integration of several criteria makes the prioritisation of rehabilitation works a complex task. It makes use of the decision support tool, which is constantly evolving (Wątróbski et al., 2019).

The choice of decision support tools takes account of this constant evolution, which offers a number of advantages. In fact, a better weighting of the criteria is possible through the integration of fuzzy logic. This observation is shared by Salehi et al., (2018), who favour using fuzzy logic for several reasons. In addition, the use of the decision support tool presented in this study is flexible and not limited by the number of pipes. It can also be modified by adding or subtracting criteria to adapt it to the specific situation of a given network.

Generally, the ranking approaches are based on an unequal weighting of the criteria. More broadly, Yoo et al., (2014) use five different criteria weighting methods, leading to relatively similar ranking results. In our case, the weighting of criteria is carried out with effective and up-to-date tools in combination with other approaches, and the consistency of judgements is checked with the AHP method (Gan et al., 2017; Beker & Kansal, 2023). On the other hand, in some studies, the weighting is based on nominal or cardinal scales, which are simply used to rank the criteria (Carriço et al., 2021) and do not check the consistency of the judgements. Therefore, the choice of AHP offers an advantage through the validation test, which makes it possible to approve the weights of the criteria and to detect any inconsistencies in the comparison of the criteria. It is one of the determining factors in the use of the AHP method. In fact, it is the most widely used method in publications related to the water sector (Beker & Kansal, 2023).

The rehabilitation approach is applied using PROMETHEE visual software, which is free to download and easy to use. This is in contrast to other studies (Yoo et al., 2014; Carriço et al., 2021), which require experience and special programmes or programming skills. In addition, the PROMETHEE software provides a sensitivity analysis of the criteria weights and their influence on the final pipe ranking. This analysis is recommended in ranking problems (Carriço et al., 2021).

The sixth goal of sustainable development calls for action by governments and companies. In order to take action, our approach is geared towards planning that meets the concept of sustainable development and constitutes a significant advantage over other studies. Indeed, the rehabilitation approach developed generates benefits based on environmental, economic, social, and technical aspects. Unlike the studies by Yoo et al. (2014), D'Ercole et al. (2018), Salehi et al. (2018) and Carriço et al. (2021), which did not carry out a benefits analysis, the Beker & Kansal (2023) study focused solely on the benefits of minimising maintenance time and costs and optimising repair and maintenance resources.

Each of the studies carried out on rehabilitation has its own specificities, linked in particular to the criteria used. This leads to limitations, which in our case can be summarised as follows. The first limitation relates to the selection of criteria, as it is not easy to reach a consensus on the nature and number of criteria. Indeed, we find that the type and number of criteria chosen vary from one case study to another. The second limitation relates to the weighting of the criteria. In fact, this limitation is related to the first one, since each time the number or nature of the criteria changes, it is necessary to review the weighting of the criteria, which is likely to change. The third limitation concerns the experts consulted. Indeed, the evaluation of criteria may differ between local and international experts for the same criteria. This leads to differences in the weighting of the criteria.

This paper presents a case study of prioritisation of pipe rehabilitation, from the most urgent to the least urgent, applied to the Fouka sector, located in Bejaia city. For this purpose, a decision support tool was proposed using the Fuzzy-AHP and PROMETHEE II methods.

The rehabilitation planning is analysed on the basis of 13 decision criteria that are material, failures, type of seal, complaints, overlap, rehabilitation technique, age, linear leakage index, linear loss index, size, yield, length, as well as rehabilitation cost.

On the basis of the priority ranking of the 204 pipes in the Fouka sector, an assessment of the benefits to be gained after rehabilitation is made in terms of environmental, economic, social and technical parameters. The results demonstrate that the water recovery rate is higher in the first 60% of the pipe rehabilitation; the investment costs will be recovered within 3 years after a complete rehabilitation of the network; the average age of the network is reduced by 5 years for every 10% of pipes rehabilitated; complaints reach a value of 0 after 70% of the rehabilitated pipes.

The final ranking of the pipes and the benefits generated are of great interest to the managers of drinking water utilities. The solution represents the best strategy to adopt within the rehabilitation policy. The methodology is therefore perfectly suited to the needs of drinking water utility managers. This encourages the application of the methodology to other sectors or cities and will contribute to the success of the national strategy for the rehabilitation of drinking water networks.

The proposed decision support tool is flexible, as it allows the introduction or subtraction of criteria, and is not limited by the number of pipes. Therefore, the decision support tool can be adapted to the specific situation of a given network.

In perspective and with a view to generalisation, it would be interesting for drinking water utilities to organise national and international meetings with stakeholders to develop a common set of criteria for rehabilitation.

We would like to acknowledge the support and assistance received from the managers of the water utility (Algérienne Des Eaux: ADE), unity of Bejaia. At this opportunity, we would like to thank the Director of this unity as well as all those who responded positively to our questions and questionnaire and we are grateful for their help and for the data they made available to us.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.