Cost Analysis of Water Quality Assessment Using Multi-Criteria Decision-Making Approach

In modern competitive markets, cost and quality parameters are the two main factors. So, it is essential to study their relationship, especially in leading industries such as urban public service companies. Consequently, manufacturers always try to reduce production costs and improve product quality and services to consumer expectations. Also, the concerns of the new century in the field of fresh water and the reduction of its resources related to global warming have increased the costs of quality and supply of freshwater. Therefore, in this research, in order to estimate the quality costs in the field of water resources and wastewater management and identify the option that creates the most cost, in the first step, the “Prevention, Assessment, and Failure (PAF)” model was used to select cost-imposing options in organizational quality analysis. After determining the main options, appropriate criteria and sub-criteria were selected under the main study area (water and wastewater resources management). In the next step, a “Multiple-Criteria Decision-Making (MCDM) “ method based on the “Fuzzy Analytical Hierarchy Process (FAHP)” and “Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)” method was used to identify the option that creates the most cost. The results show that The highest cost of quality in the water and wastewater industry and its management are related to “Assessment Costs” and account for 36.55% of total costs. Also, The lowest cost of quality in the water and wastewater industry is related to “Preventive Costs” and accounts for only 12.18% of the total cost. In addition, the expert’s opinion shows that the effect of increasing credit with 34.01% has the greatest weight, and this criterion is the most essential in water and wastewater resources management.


Introduction
The issue of global warming and its environmental effects on polar ice caps and depletion of water resources has made the issue of access to fresh water in the world an essential concern for policymakers in this field (Ahmed et al. 2019;Mohseni et al. 2022). Furthermore, this has created competitive markets for the freshwater supply(Abu Hasan et al. 2020;El-Sayed 2020).
Companies face various production costs in today's competitive market and must use appropriate strategies to profit and gain market share (Crespo et al. 2019;El-Gafy and Apul 2021). Quality assurance for services and products has costs the organization must bear to ensure customer satisfaction, maintain its customers, and expand its chances of living in the market (Borzuei et al. 2022;Moosavian et al. 2022a, b). Recognizing the most crucial factor that creates the Cost of Quality (COQ) and providing appropriate solutions to minimize it helps companies increase economic efficiency and, ultimately, more profit (Adimalla et al. 2018;Heddam 2016). Quality costs try to replace quality from scratch Production to prevent the creation of the poor quality product (improper service) (Cui et al. 2019). In short, the quality costing system provides the necessary platforms for better products at a lower cost (Yaghoubirad et al. 2022). Quality costs are also costs that are not definitive and are hidden in other costs.
Internal and external failure costs, evaluation, and prevention are the determinants of COQ (Hirsch et al. 2020). The company must consider the quality indicators to produce a service that satisfies the customer and has good sales (Toan 2016). Therefore, given these critical factors, cost-making options must be considered. Identify the quality and select the option that creates the most cost, to minimize them (Cian et al. 2014). Finding the most critical factor among the influential factors is another problem that decision-makers face (Gutiérrez and Magnusson 2014); Because in most service and production units, there is no purposeful plan to evaluate these costs, and the quality cost is hidden in most other costs and cannot be calculated accurately (Crawford 1992). Therefore, the essential option for cost reduction should be selected according to the essential factors for the organization and quality cost options (Shokoohi et al. 2017).
Problems of selecting and evaluating options in a situation where the decision-maker is faced with multiple options and criteria are a strategic issue that is solved using multicriteria decision models (Ho et al. 2010). In classic multi-criteria decision-making methods (MCDM), the utility and weight of the criteria are introduced as actual numbers, but factual data is not always available, and sometimes the decision-maker is faced with vague data (Dožić 2019;Ture et al. 2019). A combination of MCDM models and Fuzzy science are used (Modak et al. 2017;Sun 2010).
Limited empirical and numerical research has been conducted on the Cost of Quality. Some of these researches are described below. Brentan et al. discussed the concept of quality management, management, and quality control in a study entitled Quality Engineering Systems. His results showed that the purpose of using a quality system is to reduce overall quality costs and achieve maximum profit (Brentan et al. 2021). Chopra and Garg examined the correlation between different quality cost classes in a study entitled Behavior Patterns of Quality Cost Classes. They believe that increasing assessment and prevention efforts reduce non-compliance costs. In addition, there is a negative correlation between non-compliance costs and non-compliance costs (Chopra and Garg 2011). Omar and Murgan studied an improved model for quality costing. Their result concluded that a reduction in failure costs leads to a decrease or no increase in non-compliance costs and that the traditional accounting approach is insufficient for quality costing. Because the results largely depend on the cost of direct labor. Suppose direct labor costs only 3% of the total cost of quality (Omar and Murgan 2014).
Nowadays, due to information and data uncertainty in some areas, the Fuzzy AHP method has been used by many researchers and has been accepted as an analysis with relatively accurate results (Ishizaka and Siraj 2018). This method has been used in recent studies in various fields such as travel (Dožić et al. 2018), clothing(Moktadir et al. 2018), renewable energy (Wang et al. 2020), food industry (Kumar and Kansara 2018), and management and supply (Yadav and Desai 2017), and efficient results have been extracted from these studies.
According to the contents, Fuzzy decision methods can be effective when data and information are uncertain. Due to the importance of freshwater supply and quality cost, the criteria are first weighed using this study's fuzzy Analytic Hierarchy Process (Fuzzy AHP). Then, the options are ranked using the Technique for Order Preferences By Similarity To Ideal Solution (TOPSIS) model, and the option that imposes the most costly to the water and wastewater industry is identified.
With the economic development and the promotion of the capitalist system, cost and quality parameters are considered two fundamental factors regarding the supply of services and goods. For this reason, studying the relationship between cost and quality has received much attention, especially at the macro level and in the companies providing urban services. In the meantime, the water and wastewater industry is not exempt from this issue, and to satisfy people, they need to balance the parameters of the received cost and the quality provided. For this reason, in the present study, the most important factors of creating quality costs in the water and wastewater industry have been identified and ranked using Fuzzy AHP and Fuzzy TOPSIS algorithms. Then appropriate solutions have been presented in line with the driving factors of quality cost. Knowing the exact factors that cause quality costs and providing proper solutions to minimize these costs leads to increasing the efficiency and profit of water and wastewater companies. This issue is critical in countries like Iran, which are in economic turmoil due to political sanctions because the economic efficiency of water and wastewater companies can be increased with minor modifications in the structure of factors that cause quality costs.

Principle of Analysis
In different years, various models have been proposed to evaluate the cost of quality. What is essential in choosing a suitable model is that this selected model can well identify and explain the hidden costs in quality analysis. In this study, the "Prevention, Assessment & Failure (PAF)" model, which is very popular (Goulden and Rawlins 1995;Schiffauerova and Thomson 2006), has been used to evaluate the cost of quality. This model includes four main cost groups, as shown in Fig. 1.
Juran showed an inverse relationship between "prevention and assessment costs" and "failure costs" in the PAF model. Accordingly, more investment in both prevention and assessment will reduce failure costs (Juran and Gryna 1974). This inverse relationship indi-cates the optimal level of quality and is the basis of quality costing (Juran and De Feo 2010). Figure 2 shows the quality cost chart in terms of quality levels.
• Internal Failure Costs: Include defects identified in various stages before delivering the product or service to the customer by inspection or quality control units and action taken to eliminate them (Mahmood and Kureshi 2014;Ramdeen et al. 2007). In the present study, internal failure costs include water collection and treatment costs, water loss costs, preventive maintenance, failure analysis, wastewater recycling costs (Zyoud and Fuchs-Hanusch 2020), water distribution and maintenance of good quality, treated effluent, and the cost of grading the quality of drinking water (Zaree et al. 2019). • External Failure Costs: These are costs that are not recognizable by the customer before use and are incurred after delivery and service to customers (Cossu et al. 2003). In the present study, external failure costs include sampling water quality from customers,  customer dissatisfaction and complaints, and improving customer satisfaction (Zhou et al. 2018). • Assessment Costs: These costs are used to determine the degree to which the characteristics of the products (or services) offered to match the quality characteristics of the reference (Glogovac et al. 2019;Wu et al. 2011). In the present study, these costs include evaluation costs of subcontractors (Operating contractor), raw water inspection and testing costs, production process inspection costs, final product inspection and testing costs, quality system audit costs, equipment control costs, Inspection and measurement costs, costs of checking the quality of water stored in tanks and costs of checking the quality of water delivered to subscribers (Busico et al. 2019;Zhou et al. 2018). • Preventive Costs: These costs relate to activities spent to prevent defects and breakdowns in products (or services). Merely these costs reduce breakdowns and defects in manufactured products (or presented at different stages (Holota et al. 2016). In the present study, these costs include quality planning costs, training costs (Busico et al. 2019), process design and control costs, and reporting costs (Ziolkowska 2015).

Methodology
Considering that the primary purpose of this research is to evaluate the costs of quality (finding the option that has the highest cost) in the field of water resources management, the present study in the group of development studies with a descriptive approach (describing the conditions in the study Case) is placed. Figure 3 provides a schematic of the conceptual model of the present study.
Since the current research is investigating a practical issue and a real challenge in Iran's water and wastewater industry, relying on real and available information instead of simulation software, which requires many assumptions, will be a more reliable option. Therefore, to achieve the research goals, the knowledge of experts in this field has been used. It should be mentioned that a list of experts and senior decision-makers in this field was prepared to select experts in the water and wastewater resource management field. Then, prioritization was done according to the specialties of these people and their field of study. In the next step, these people were contacted, and the people who agreed to participate in this project were included in the final list. In the last step, the experts more suitable for this research based on different criteria were selected as the final options. The selection criteria were chosen based on the research objectives and tried to cover the appropriate comprehensiveness of the country's experts.
Due to the lack of a proper quality costing system, there is no accurate data on quality costs, and the available data is vague and inaccurate; Therefore, fuzzy logic has been used to decide and choose the option that imposes the most cost (Banihabib and Shabestari 2017). Four criteria of cost imposed (cost), final profit (profit), increase of credit (credit), and strategy focus time (strategy), and four options of internal failure costs, external failure costs, assessment costs, and preventive costs are considered and for the opinion of ten experts decision-maker used.
The Analytic Hierarchy Process (AHP)is used to examine and weigh experts' opinions (usually 2 to 10 people) with paired questionnaires and, depending on the question-er's opinion and the review of incompatibility coefficients, the accuracy of the answers is evaluated (He et al. 2020). Here, weighting is done according to the appropriate incompatibility coefficient for each of the ten selected specialists. It should be noted that all calculations have been done in MATLAB software.
The reason for integrating the AHP model with fuzzy logic is that the fuzzy hierarchical analysis process (FAHP) is the fuzzification of the classic AHP method using fuzzy numbers and calculations. When preferences show uncertainty and imprecision, definite and precise numbers are not very suitable for showing time judgment. In order to deal with ambiguity, triangular fuzzy numbers and AHP have been integrated into the fuzzy method to solve decision-making problems.

System Description
Improving management conditions in the field of water and wastewater is a national challenge, so the framework of the studied system should also be defined at the national level.
Iran, as one of the political poles of the Middle East, has experienced severe water crises in recent years. Problems such as global warming (Moosavian,Zahedi, et al. 2022), which has covered the whole world, as well as the decrease in the level of water reserves and the drought of rivers and lakes in Iran, have spread social concerns caused by water. Therefore, the purpose of this research is to examine practical solutions for evaluating quality costs and choosing the right option to reduce costs and provide sustainable water supply at the national level. Since the management of water and wastewater in Iran is provincial, therefore, the selection of experts should be done in such a way that the selected representatives cover the prevailing conditions of the country's regions.
This study is comprehensive and based on the information available in the last 5 years. The reason for choosing this time frame is to create extensive changes in water and wastewater resource management. These developments, which were created after the spread of social concerns caused by the quality of supply and the resulting costs, have significantly affected the improvement of the country's conditions. Still, various factors continue to make the improvement of water and wastewater resources management one of the main national challenges.

Model Description
In this research, first, the "Fuzzy Analytic Hierarchy Process (FAHP)" method is used to weight the criteria, and then the "Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)" is used to rank the options, which is briefly presented below.

Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP), one of the most common multi-criteria decisionmaking methods, was first proposed by Thomas Saati in 1980(Saaty 1988. The application of this decision-making method is based on several different parameters and criteria (quantitative or qualitative). Since the classical AHP method is based on human resource judgment (decision-makers) and human judgment and perception are always associated with uncertainty, the present study uses the fuzzy AHP method (Chang 1996). The fuzzy AHP method is often used in uncertainty and amplitude of variation to rank a criterion (Kahraman et al. 2003). Considering the choice of the fuzzy AHP method as the main algorithm, it is necessary to describe its steps. Various methods have been proposed in different references for fuzzy AHP (Jaiswal et al. 2015), but since Chang's developed algorithm has more uncomplicated steps than others, this algorithm is used in the present study. In this method, fuzzy numbers are displayed as a two-dimensional array with format (m 1 /m 2 , m 2 /m 3 ) or a three-dimensional array with the format (m 1 , m 2 , m 3 ). These values represent the smallest, most probable, and most significant possible values and the m 2 is between m 1 and m 3 (Sun 2010). In Fig. 4, a triangular fuzzy number M = (l, m, u) is presented. Also, the membership function of this fuzzy number is defined according to Eq. 1, and the basic concepts of algebraic operations are used to follow the principles of fuzzy algebra (Modak et al. 2017).
The AHP model is similar to human thinking and turns complex decisions into more straightforward problems, thus reducing the complexity of difficult decisions. The main steps of AHP are as follows: • Organize the problem hierarchically: In the first stage, the problem is represented in the form of a tree in which, at its highest level, general objectives and at the lowest level, options, and between these two levels, criteria and sub-criteria are placed (Fig. 3).
• Calculate the internal pairwise matrices: Several methods have been developed to derive the weights of criteria from paired matrices, some of which are: the eigenvector method, least logarithmic least squares method, and least weighted squares method, and fuzzy programming method (Modak et al. 2017). • Criteria ranking: The last step is to rank the options according to the final weight of each of them. The weights of each criterion are obtained by multiplying the internal weights of the sub-criteria of each level by each other and the sum of the final weights, and then the priorities are determined (Chang 1996).

Technique For Order Preferences By Similarity To Ideal Solution (TOPSIS).
According to TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), (m) options are evaluated by (n) indices, and each problem can be considered as a geometric system containing (m) points in n-dimensional space (Sun 2010).
This model has the concept that "the selected option should have the shortest distance from the positive ideal solution (best possible caseA + i ) and the longest distance from the negative ideal solution (worst possible caseA − i )". This method is done in 6 steps as follows: • Convert the initial decision matrix (D) to a non-scale matrix (ND) using the Euclidean norm (Zaree et al. 2019). • Calculation of unbalanced weight matrix (V) by multiplying the weighted unbalanced matrix (ND) by the index coefficient matrix (WJ). • Determine the positive ideal solution (A + i ) and the negative ideal solution (A − i ) for all options according to Eq. 3.
• Determine the Euclidean norm distance according to Eq. 4.
• Calculate the relative distance (A i ) to the ideal answer (C i ). In this case, the closer the option (A i ) is to the ideal solution, the closer its value (C i ) is to one. (Eq. 5) Ranking options based on the relative distance (A i ) to the ideal answer (C i ) in descending or ascending order.

Fuzzy Logic
The foundation of fuzzy logic is based on the theory of fuzzy sets. This theory is a generalization of the classical theory of mathematical sets. In classical set theory, an element is either a member of the set or not (there is no third case) (Chang 1996). The membership of the elements follows a zero and one (binary) pattern. In contrast, fuzzy set theory introduces the concept of graded membership. In this way, an element can be a member of a set to some extent (not wholly) (Liu et al. 2020). The membership of the members of a set in fuzzy logic is determined by the function u (x), where x represents a definite member, and u is a fuzzy function that determines the degree of membership of x in the set and its value is between zero and one (Eq. 6).
In other words, u (x) maps x values with possible numerical values between zero and one. The function u (x) may be a set of discrete or continuous values. When (u) is a discrete value, only a small number of discrete values between zero and one are in the answer set; Whereas when the set of values (u) is continuous, a continuous curve of decimal numbers between zero and one is formed in the set of fuzzy numbers (Liu et al. 2020). An example of fuzzy numbers defined in the fuzzy Analytic Hierarchy Process (AHP) is presented in Table 1.
In each of the matrices, each of the cells above the main diagonal of a matrix indicates the degree of importance of the row elements relative to the column elements, and each of the lower cells of the main diagonal of a matrix indicates the degree of importance of the column elements to the row elements. They are the inverse of the value of the above main diagonal of a matrix. For each cell, the average weights determined by the experts were obtained using MATLAB software (Table 5), and finally, the weights of the criteria were obtained according to Fig. 6. The Buckley method has been used to calculate the criteria's weight. In this method, after determining the Pairwise Comparison Matrix (PCM) with the help of relative importance scales, the geometric mean of the row criteria is used to calculate the fuzzy weight vector. Finally, each criterion's fuzzy weight is obtained, and the final weight of the criterion is obtained by defuzzification (and normalizing if needed).
According to Fig. 6, it can be seen that the effect of increasing credit has the greatest weight. In fact, from the point of view of experts, this criterion is the most essential in water and wastewater resources management.

Strategy FocusTime
(2/3,1,2) (2/3,1,2) (1/3,2/5,1/2) (1,1,1) In the following, the opinion of experts in the water and wastewater industry will be examined to examine the options. Since their analysis is a linguistic variable, fuzzy triangular numbers are used. In order to rank the options (with the model similar to fuzzy ideal options), defining fuzzy numbers are necessary. So fuzzy numbers, according to Table 6, have been used to convert experts' opinions about options. Fair (F) (5,7,9) Relatively good (RG) (7,9,10) Good (G) (9,10,10) Very good (VG) At this stage, the decision matrix was formed following experts' opinions. Tables 7, 8  and 9 show three examples of this matrix Fig. 6 The weight of the criteria obtained by the method of FAHP In the next step, the average weights determined by the decision-makers are calculated. Two examples of them are presented according to Tables 10, 11 and 12.
In the following, considering that the opinion of every ten experts is considered equal, their average opinion is presented in Table 13. The two criteria of Cost Imposed and strategy focus time are cost and are considered negative. The two criteria of Final Profit and increase of credit are profit and are considered positive.
The final results presented for the main research criteria in Table 13 are the same as the final weights calculated in Fig. 6. The importance of credit is indicated in the results of this table. Finally, by analyzing this data in MATLAB software, the ranking of the options is obtained according to Fig. 7.
The results of Fig. 7 show that the most influential role in the cost of quality in water and wastewater resource management is related to the Assessment option. This issue can be related to several parameters that play a role in the field of evaluation. Therefore, the Assessment cost is the most crucial parameter in water resources management to improve the COQ.  (7,9,10) (0,1,3) (0,0,1) (0,1,3)

Preventive
Quality planning (5,7,9) (1,3,5) (0,1,3) (7,9,10) Education (0,0,1) (7,9,10) (0,1,3) (3,5,7) Field investigations show that Assessment costs, especially in developing countries, include a large part of quality costs. Among Assessment costs, "subcontractor Assessment cost" and "audit and quality system creation cost" have the largest share. On the other hand, considering the current conditions of Iran and the existence of political sanctions, and the impossibility of exporting oil, economic development depends on the reduction of basic costs, including COQ. The results obtained from this research show that Assessment costs constitute 37% of the total quality costs of water and wastewater industries. For this reason, by reducing these costs, economic growth can be provided under the conditions of sanctions. Regarding the evaluation cost of subcontractors, which includes most of the Assessment costs, the following solutions are suggested: • Providing a platform for the fair holding of subcontracting tenders and fighting against big rents and local cooperative companies. • Preventing government employees from interfering in the private sector and subcontracting companies.

Cost Imposed
Final Profit

Cost Imposed
Final Profit
In developing countries, the private-sector contractors' evaluation process has many flaws. However, by following the suggestions, a fairer platform can be provided for the evaluation and selection of subcontractors, and the costs of contractor evaluation can be reduced. By reducing these costs, Assessment costs will be reduced, and as a result, a more significant  42,8.28,9.42) (6.71,8.42,9.42) (4.28,6.14,7.57) Preventive (2.5,3.5,5) (2.5,4,6) (5,7,9) (7,9,10) share of quality costs will be reduced, and the economic efficiency of water and wastewater industries will increase.

Conclusion
Evaluating quality costs and managing them is one of the main challenges in various industries. The water and wastewater industry is considered one of the mother industries of every country and annually imposes a high cost on the government treasury. Evaluating quality costs and reducing them can increase economic productivity at the macro level. On the other hand, countries like Iran, which are in financial turmoil (due to political sanctions), are looking for a solution to reduce large expenses. In the field of economic management of these countries, quality cost management is very important and can reduce adverse economic effects such as inflation.
In the present study, in order to estimate the quality costs in the field of water and wastewater industries and identify the option that creates the most cost, in the first step, the "Prevention, Assessment, and Failure (PAF)" model was used to select cost-imposing options in organizational quality analysis. After determining the main options, appropriate criteria and sub-criteria were selected under the main study area (water and wastewater resources management). In the next step, a "Multiple-Criteria Decision-Making (MCDM) "method based on "Fuzzy Analytical Hierarchy Process (FAHP)" and "Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)" methods were used to identify the option that creates the most cost.
In this regard, the main areas of cost imposition (decision options) were selected under the headings ((Preventive Costs, Assessment Costs, Internal Failure Costs, and External Failure Costs)) and the main criteria were selected as ((Cost Imposed, Final Profit, Increase of Credit and Strategy Focus Time)).
Finally, the outlines of the results are presented as follows: • The highest cost of quality in the water and wastewater industry and its management are related to "Assessment Costs" and account for 36.55% of total costs. • The lowest cost of quality in the water and wastewater industry is related to "Preventive Costs" and accounts for only 12.18% of the total cost. • Areas " External Failure Costs " and " Internal Failure Costs " are in second and third place with 28.98 and 22.30% of the total cost. • A fair assessment of subcontractors and prohibition of intervention of government employees in the private sector and contractors will make tenders more appropriate and, as a result, reduce "Assessment Costs".
Quality costs account for a significant percentage of industry costs, while most managers and experts do not pay attention. This increases the cost of quality in the "Assessment and External Failure "areas. With more emphasis on investing in preventative activities such as staff training, careful design of management charts, and troubleshooting of monitoring systems, in addition to reducing the cost of error and producing a defective product, the assessment costs are also reduced. Funding No funding resources were used in this study.
Availability of data and materials All data, models, and code generated or used during the study appear in the submitted article.

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