An Economic Evaluation of the Rural Drinking Water Fee Using the System Dynamics Method

1. Introduction

Water is a critical factor for economic growth. Providing sanitary drinking water without quality problems is a significant concern to improve living standards and promote economic activities in a region, particularly where water has become a scarce and expensive commodity. The future challenges posed by growing population demands, constrained sources of water supply, and climate change impacts are expected to require more integrated procedures for supporting water demand modeling and management (Cominola et al.2015). Due to population growth, ever-increasing demand, water scarcity, and improper management of state-owned and private water companies, the current pattern of water management cannot meet the needs for infrastructure, renewal, and modernization to reach the required level of water quality. One of the significant challenges is the drinking water pricing, which is of particular significance regarding the limitation and scarce water resources in Iran, located in the arid and semi-arid region of the world. It is, therefore, essential to focus on a modern water management strategy. Yazdandoost and Izadi (2018) reported that the accuracy degradation rate, hydraulic criticality index, and the water fee have more influence on optimal replacement time than the other input parameters.

A positive financial balance, liquidate debt repayments, and programming factors are partly dependent upon the sales price stability, provision of the services, and the uniformity of the costs. The cost estimation or final pricing is one of the critical components in legal issues such as development program laws. Water supply facilities and their maintenance, utilization, repair, and reconstruction are cost-effective practices. Therefore, estimating the final water fee based on the expenses reflected in the financial notes is a big concern for water management. Total water supply cost varies depending on geographic aspects, population, financial, regulatory laws, and social attributes of a specific region. Therefore, determining a correct and actual water fee is helpful for water and wastewater companies.

Water pricing encourages consumers to water conservation. Luby et al. (2018) analyzed the policy of public utility pricing in some of the largest urban areas in the United States. The results revealed that most cities have higher per unit water prices for low use than for high use. Wichman et al. (2016) claimed that low-income users are more water fee-sensitive. Therefore, increasing the water fee reduces the water consumed by poor users rather than wealthy customers.

Simulation and optimization models can be employed to plan and manage the water fee. Simulation models of the water distribution networks can identify the dangers and problems of an improper water management policy before its implementation and prevent undesirable effects and time dissipation (Klassert et al.2015). Regarding the role of simulation and optimization software as one of the management tools for proper decisions and programming, a comprehensive, integrated, and dynamic information system is still needed to determine the type and composition of the costs. Experts and practitioners can take serious actions to control and save costs, maintain profitability, or adjust the selling price according to marketability by comparing different scenarios over specific periods. Lopez-Nicolas et al. (2018) developed a framework for designing an urban water tariff using a hydrological simulation model to establish financial and economic sustainability.

Urban water systems involve complex ecological, social, and economic interactions (Jensen and Khalis2020). Wei et al. (2016) applied a dynamic method to simulate the interactions of urban water demand, society, economy, climate, and water conservation proceedings to manage the urban water in Macau. The key results indicated that by implementing an integrated water conservation policy and improving the water conservation culture, water demand could be reduced by 17.5% in Macau. Further, Tianhonga et al. (2019) simulated the water supply and demand in the coastal city of Shenzhen, China, using the system dynamics method. They also introduced the most effective parameters in Shenzhen’s water supply-demand chain.

Tian et al. (2020) developed a model for the management and sustainable application of water resources in Tianjin (north-eastern China) using the system dynamics method. In this research, the characteristics of the economy, population, water supply, and water demand were studied, and the modeling results were reported.

Although system dynamics is employed as a simulation strategy, various studies were conducted in which system dynamics was integrated with the optimization techniques and used to identify the optimal policies and parameters of the control systems (Schenk et al.2010). Parra et al. (2018) integrated four optimization techniques of Powell’s algorithm, simulated annealing, a genetic algorithm, and a hybrid algorithm with system dynamics in a study. They concluded that none of the optimization strategies dominates the other methods, presenting different performances in the criteria.

Knowing the dynamic interactions and feedback loop between the related hydrological, social, and economic factors is vital to successful strategic planning and water resources management. The complexity and uncertainty of nonlinearity, multiple interactions, and dynamic feedback between these factors make it challenging to predict the results of decisions (Kotir et al.2016). The lack of mental and organizational frameworks in traditional linear causal thinking and mechanistic models hinders their ability to address complexity as they consider the dynamics of sub-systems in isolation. Consequently, the root causes of the problems are not fully understood, which prevents the creation of strategic water management policies (Phan et al.2021). The complexity of water and wastewater systems is not reflected in the current decision-support tools used for their management.

System dynamics (SD) modeling is a tool that helps to recognize the multiple interactions between the various but linked sub-systems that drive the dynamic behavior of the system as a whole (Sterman2000). Consideration of the combined effects of system dynamics can improve management decisions and reduce the possibility of adverse side effects and unintended consequences from policy decisions (Sterman2000; Phan et al.2021). Subsequently, many authors have suggested that SD modeling produces a comprehensive perception of the degree of complex dynamics, feedback processes and interconnections between hydrological, social, economic and ecological processes for decision-making in water resource management systems (Bakhshianlamouki et al.2020).

To the best of our knowledge, no study combines a comprehensive model of simulation and optimization for the modeling of the financial system of a water and wastewater company to examine the side effects of implementing a decision over time.

Therefore, the main aims of this inquiry are as follows:

(A)	Identification of the parameters influencing the water fee at the Rural Water and Wastewater Company of Hamedan province.
(B)	Simulation of the financial balance of the company by system dynamics method.
(C)	Sensitivity analysis of the important parameters of the financial system of the company under the influence of water fees.
(D)	Determination of the water fee and study of its impact on the system parameters to prevent the financial losses of the Water and Wastewater Company.

2. Materials and Methods

2.1. System dynamics method

A system comprises components and elements that cooperate to achieve a desired outcome. Systems may be categorized as (a) open systems and (b) feedback systems. In open systems, the output is defined by the input, and the output has no impact on the input. Feedback systems, however, are a type of closed-loop system in which the inputs are directly affected by the outputs (Bavandpour et al.2021).

System dynamics modeling is based on the cause-effect relationships between components, and the model is most powerful when these relationships are combined to create a feedback loop. Taking a systems dynamics approach yields two major advantages. The cause-and-effect relationships between the components of the system are easily observable. As a result, the actual cause of the behavior can be discovered. The other advantage is that it is possible to determine which structures or parameters should be changed to promote better behavior (Azar2012).

Current research aims to provide a computer-based model by the system dynamic analysis to evaluate the technical and economic factors affecting the water fee. Without a need to describe the complex equations, the system dynamic method examines the behavior of complex systems with more efficient performance than other so-called simulation methods.

In this study, Vensim system dynamics software was used, providing a fully integrated simulation system to simulate the models of dynamic systems.

2.2. The causal loop diagrams (CLDs)

The basis of the system dynamics method relies on the hypothesis of feedback processes in which past and future behavior of the system affect the simulation results (Nozari and Liaghat2014). CLDs are used to display the behavior of cause and effect from a system’s standpoint. The relationship between variables is expressed by using the “$+$” or “−” signs through an arrow. The positive and negative signs indicate that the two variables change in the same and opposite directions. In positive loops, an increase (or decrease) of any variable in the loop results in an increase (or decrease) of the same variable. A negative loop exists when an increase (or decrease) of any variable in the loop results in a decrease (or increase) of the same variable. Positive and negative feedback loops are also called reinforcing and balancing feedback loops. A positive or reinforcing loop is denoted with an “R”. However, a negative or balancing loop is denoted with a “B”. The CLD (Figure 1) is presented to simulate the water supply network and determine the water fee. These feedback loops are described as follows:

Reinforcing loop R1 involves water fee, water consumption, income organization, and funds balance. As water fee increase, water consumption decreases inversely because of the proportion of the cost of water. The income organization is directly correlated to its water consumption, so a decrease in water use leads to a decrease in income, thus reducing the amount of the fund balance. If the fund balance is in decline, one method of improving it could be to raise the water fee.

Reinforcing loop R2 involves water fee, water consumption, income organization, funds balance, network reconstruction, network performance, and burden acceptability.

This feedback loop represents the interaction between funds balance and burden acceptability: the larger the funds balance, the larger the network reconstruction, and the better the network performance. increasing the network performance (better the network performance) decreases the burden on consumer households.

Considering that there is a relationship between burden acceptability and water fee, as network performance rises, the willingness to pay for water decreases, and water consumption increases (MacDonald et al., 2003). Therefore, a rise in water use leads to a growth in income, enlarging the fund balance.

Reinforcing loop R3 involves fund balance, network reconstruction, repair and maintenance, and costs. Decreasing the fund balance decreases the network reconstruction and raises the repair and maintenance cost, thus reducing the amount of the fund balance.

Balancing loop B1 involves funds balance, water fee, water consumption, and power and energy cost. This negative feedback loop represents the interaction between funds balance, and power and energy cost: the lower the funds balance, the larger the water fee, and the lower the water consumption and power and energy cost, which in turn increase the funds balance.

Balancing loop B2 involves funds balance, water fee, water consumption, and chemical cleaner cost. This negative feedback loop represents the interaction between funds balance, and chemical cleaner cost: reducing water consumption reduces the required disinfectants (chemical cleaner), thus decreasing the costs. Reducing costs will, in turn, increase the fund balance.

Balancing loop B3 involves funds balance, water fee, water consumption, and purchased water cost. This negative feedback loop represents the interaction between funds balance, and purchased water cost: reducing water consumption diminishes the demand for water from the Water and Wastewater Company (purchased water cost), thus decreasing the costs. Reducing costs will, in turn, increase the fund balance.

Balancing loop B4 involves funds balance, network reconstruction, and cost. The fund balance of the company is directly associated with the renovation of the water supply network. Therefore, increasing the fund balance will increase the renovation costs, reducing the fund balance.

It should be noted that the government manages the urban water supply and wastewater collection systems in Iran. The amount paid by the customers for water and wastewater services is not as much as the costs required to provide these services. Therefore, the government pays part of the water consumption expenses through subsidies to reduce the financial burden on customers and the water fee.

2.3. The stock and flow structure

The state and flow, along with the feedback, are the basic concepts of the theory of system dynamics analysis. States are the system accumulation and the principle of decisions indicating the system’s state. Figure 2 depicts an example of the state and flow structure in this study. It is noted that the fund balance of the company and the water demand are defined as the state variables, while company capitals and the expenses of each sector are defined as the flow states. Others are considered as auxiliary variables.

When the fund balance of the company becomes negative, the water fee increases. In this case, customers reduce their water consumption due to an increased water fee. Therefore, the water fee must be changed so that all customers can cover the least of their water demand. According to Eq. (1), demand (D) is a function of the water fee calculated from the integral of the price elasticity function (E) of demand at the initial price point $p_0$ to the new price $p^{\prime }$ (SH22017).

To determine the fluctuations in demand, the price elasticity of demand is defined according to the fluctuations in water fees, and it is described as follows (Sloman2006):

where P is the price of goods ($), $E_d$ is the Elasticity of demand (Dimensionless), t is the time (Year), and $Q_d$ is the demand quantity (Cubic meter).

On the other hand, the ability of the company to improve the water supply network is increased by increasing the fund balance. If the network performance improves, the customers tend to pay more for the water, so the water fee decreases. According to Eq. (5), if the network performance is low, consumers tend to increase the water fee to raise the service levels and water quality (Lobasenko2017).

where v is the function of expenditures, P is the water fee, y is the income, WTP is the willingness to pay for water, and q_0 and q_1 are the initial and final quality of the drinking water, respectively.

According to the United States Environmental Protection Agency (US EPA), the threshold for water bill payments is 2% of the customer’s total income (Water Infrastructure Network2000). It means that low-income customers cannot afford the water bills if the water bill is more than 2% of the household income. Accordingly, the Burden Acceptability parameter is assumed to change, as shown in Figure 3 (Rehan2011).

Equation (6) was utilized as an exponential model to forecast the pipe failure rate in terms of network pipe age (Kanakoudis and Tolikas2001) :

where $N(t)$ is the number of failures per year t (Number of breaks per km), $t_0$ is the base year of analysis, and k is the growth rate coefficient (1/year), which varies between 0.05 and 0.15 regarding the pipe material and diameter.

It is to be noted that the model is simplified by assuming that the renewal fraction, the price elasticity of demand, and the growth rate coefficient (k) values are constant in time. Another assumption of the model is that the annual income of households in the whole region was considered average. In addition, the water charges are set at the same price for all customers in the area.

2.4. Sensitivity analysis

The method of one-variable sensitivity analysis is used to investigate the factors affecting the water fee. According to Eq. (7), the given parameters are considered a time function by assuming that the rest parameters are constant (Guo et al.2001).

where $Y_t$ and $X_t$ are the dependent and independent variables of the system at time t, ${dY}_t$ is the rate of the changes in the variable Y at time t, and ${dX}_t$ is the rate of changes in the independent variable X at time t.

2.5. Optimization

In this study, Vensim system dynamics software was used, providing a fully integrated simulation system to simulate the models of dynamic systems. Ventana Company (Ventana Systems Inc.2015) developed Powell’s method as an optimization algorithm in Vensim software, and several researchers confirmed its accuracy (Parra et al.2018; Barati et al.2020). In discontinuous problems in which objective-based derivatives cannot be optimized, the Powell method is employed to solve the unpredictable optimization problems (Vierhaus et al.2014). The Powell method is a direct optimization strategy and is one of the most efficient solutions. Due to searching for a fast gradient in all algorithmic repetitions, the method approaches the final solution faster than the probabilistic demographic methods such as the genetic algorithm. One of the advantages of the classic Powell method is that there is no need for an explicit calculation of the function gradient. It searches for the function value in different directions and finds the least function value. Figure 4 shows a conjugate gradient scheme that is based on the Powell optimization algorithm (Kramer2010).

The main objective of the present research was to determine the actual water fee to prevent financial losses for the company. Therefore, the objective function was defined in such a way that the fund balance of the company remained constant from 2010 (equal to 16265778136 below zero) (Eq. (8)).

where ${\mathrm{\text{Fund Balance}}}_{2010}$ is the financial statements of the company in 2010 (the reference base year for cumulative fund balance), and the ${\mathrm{\text{Fund Balance}}}_i$ is the financial statements of the company in ith year.

Water fee is the decision variable, and it is non-negative :

The amount of water allocated to each customer should be greater than the minimum water demand (350L/day) : The amount of water consumption should be no more than the total available water : According to the United States Environmental Protection Agency, the threshold for water bill payments is 2% of the customer’s total income. Therefore : The general steps for developing the model framework are shown in Figure 5. In Step 1, to run the model, primarily primary necessary data are gathered and categorized. In Step 2, the causal loop diagram between variables is found. Then, to perform a more detailed quantitative analysis, the causal loop diagram is transformed into a stock and flow diagram in VENSIM. In Step 3, we will use our data and the model to investigate the factors affecting the water fee. In this step, we would improve the model’s ability to predict the actual water fee in water and wastewater companies. In Step 4, we will determine the objective function and constraints to determine the actual water fee and prevent the financial losses of the Water and Wastewater Company by using Powell’s algorithm.

2.6. Statistical analysis

The performance of the simulation model was evaluated by the correlation coefficient ($R^2$) and normalized root mean square error.

where n is the number of data within the study period, $Y_i^O$ is the measured values, $Y_i^S$ is the simulated value using the model, ${Ȳ}_i^O$ is the mean of the measured data, and ${Ȳ}_i^S$ is the average of the simulated values, ${\sigma }_O$ is the observed standard deviation and ${\sigma }_S$ is the simulated standard deviation.

2.7. Case Study

Hamedan province, with an area of 20172m², covers a total of 2.1% of Iran. The province is between $49^{\circ }35^{\prime }$ and $59^{\circ }33^{\prime }$ north latitude and $34^{\circ }47^{\prime }$ to $34^{\circ }49^{\prime }$ east and includes nine cities, 25 districts, 30 towns, 73 villages, and 1120 rural districts. According to the official data from the national statistics center of Iran for 2016, Hamedan’s population has reached around 1,812,026. About 62% of the population lives in urban areas, and the rest (38%) live in rural areas. The geographical location of Hamedan province and its subsections is demonstrated in Figure 6.

Rural Water and Wastewater Company of Hamedan started its official activity in 1998. The following items are listed among the company activities: (a) Study and implement the plans to develop the facilities of supply, transfer, and distribution of the drinking water in villages; (b) Study and implementation of the rural wastewater disposal schemes, including collecting, transferring, and purification, (c) Drinking water supplementation in the rural networks by approved standards within the Ministry of Energy plans and approvals framework, and d. Make necessary arrangements to develop NGO participation in rural water and sanitation. The company is currently working on the establishment of an executive structure for the rural water and wastewater in the cities of Nahavand, Bahar, Asadabad, Malayer, Famenin, Razan, Tuyserkan, Kabudarahang, and Hamedan to provide appropriate services to the villagers. According to the annual report of the company’s financial status, the number of customers, consumption, and water fee for various applications in 2011–2016 are presented in Table 1. In this study, information about the company’s costs is collected from the annual report of the Rural Water and Wastewater Company of Hamedan (Table 2).

In Iran, a minimum service charge is included in the water bill, and water is a highly subsidized commodity, leading to the inefficient use of the already scarce resource.

3. Results and Discussion

3.1. Automated calibration

After ensuring the correctness of the simulation results, calibration of the model can proceed to fit the model to the observed data. Vensim’s optimizer performs the calibration automatically. Vensim adjusts constants parameters to match simulation and observation data sets best. In this software, the calibration process occurs by maximizing the payoff function. The payoff function that automated calibration tools maximize is :

where $\theta$ is a parameter that will be estimated, $w_t$ is the weight of the payoff function (it is typically 1/(standard error of measurement)), and $e_t(\theta )$ is error term at time t.

In this section, the results of the simulation model were evaluated using the statistical indices and information on the financial statements and explanatory notes of the Rural Water and Wastewater Company of Hamedan province, including the balance sheet, profit, and burden accounts from 29 March 2011 to 30 March 2016. The input parameters of the model included net sales, water fees, sales expenses, and non-operating costs. The accumulated fund balance at the year’s end was considered a controllable output parameter. The company has a negative fund balance every year in the study period.

After calibration, the values for parameters of the renewal fraction, the price elasticity of demand, and the growth rate coefficient are 0.2, 0.35, and 0.1, respectively. Replacing the original parameters with the calibrated values reveals the result shown in Figure 7. In this figure, the simulation of the cumulative negative fund balance of the company was plotted against actual data. Noticeably, there is an acceptable agreement between the observation and simulation results. In this case, the statistical indices of R² and NRMSE were 0.99% and 4%, respectively.

Despite an increase in the water fee in recent years, the fund balance of the company is still negative. The accumulated burden of the company varied from 11.4 million US dollars in 2011 to 26.9 million US dollars in 2016. Therefore, decisions should be made to increase the company’s profitability and make the financial balance positive.

3.2. Verification of the results

The model was validated using an extreme condition test. An extreme condition test evaluates the model’s responses under extreme input values. The validity of a model’s equations in extreme conditions is tested by examining the reasonableness of the outcomes produced by the model equations with what is known about what would occur in a similar situation in reality. The extreme-conditions test requires a thorough inspection of the policy within a model, tracking the auxiliary equations all the way back to the state variables, and assessing the implications of imaginary values of the state variables and their combinations on the rate equation. Forrester and Senge (1980) state that it is an effective analysis for identifying shortcomings in the model structure. Many proposed formulations seem workable until subjected to extreme conditions. In this study, for extreme conditions, the water fee has been increased by 1.5 times yearly. As a result of increasing the water fee, the water demand should decrease progressively, which the model properly represented (Figure 8). The results show that customers respond to higher water fees by reducing the water demand when the water fee reaches 0.035 US $. Water demand reached its minimum value (350L/day) in 2013 to 2016 for each customer, indicating a significant reduction in the water demand relative to the approved state. Rezaee and Shojaa (2021) state that as the tariff of water increases, the demand for it will decrease.

3.3. Sensitivity analysis

To analyze the system sensitivity, variables with the most uncertainty level was selected. The variables being examined include burden acceptability, fund balance, willingness to pay for water, and water consumption. To examine sensitivity degree of these variables, the water fee is increased by 10% every year for the study period of 2011–2016. Based on Eq. (7), six sensitivity degree values can be obtained for each variable. Their average represents the general sensitivity degree of the variable to the water fee. The sensitivity degree analysis has been presented in Table 3. It is shown that the fund balance and the water consumption respond to the water fee with high sensitivity. Conversely, the burden acceptability and the willingness to pay demonstrate low sensitivity to the water fee.

Table 4 presents the average sensitivity of the parameters, namely burden acceptability, fund balance, willingness to pay for the water, and water consumption, which were affected by a 10% change in the water fee, population, price elasticity of demand, time of price elasticity of demand, consumer services pricing, targeted subsidies, household income, and rate of pipe failure.

The results show that the burden acceptability is dependent upon the water fee and household income. In this way, with the growth in the water fee, the burden acceptability is reduced, and conversely, with the growth in household income, the burden acceptability is increased.

The fund balance of the company is more dependent upon the water fee, population, and targeted subsidies. The fund balance will rise in relation to an increase in these parameters.

By increasing the rate of pipe failure (network failure rate), the customer’s willingness to pay for the water increases. In general, the willingness to pay for water services has been used as a criterion for setting water prices in many countries and cities. Wang et al. (2010) showed that when water service is diminished, the willingness to pay to improve the water service increases. In addition, the higher the household income is, the higher the willingness to pay for improved water services.

The water consumption is more dependent upon the water fee, and population. With the growth in the water fee, the water consumption is reduced, and conversely, with the growth in population, the water consumption is increased. Soto Rios et al. (2018) showed that water pricing has the potential to positively trigger water security and can help ensure a sustainable water future.

3.4. Optimization

Water fee was the only decision variable used to minimize the function. Therefore, after model implementation, the lowest water fee was suggested to prevent a negative fund balance in the company for the study period (Table 5). Looking at Table 5, the approved water fee per year is lower than the optimal, which is the cause of the negative fund balance and excessive burden for the government.

The model is designed so that fluctuations in the price-dependent parameters are observable after the decision. The cumulative fund balance of the company, burden of the water bills on customers, burden acceptability, and the water demand is demonstrated in Figure 9 for the approved water fee by the company and the optimal fee proposed by the model.

In Iran, the minimum service charge is included in the water bill, and water is a highly subsidized commodity paid for by the government. Therefore, the government pays the amount of the company’s budget deficit, and because of the very low water fee and the high consumption of customers, the company is always making losses.

As it can be seen in Figure 9, the company’s cumulative fund balance is declining for the approved water fee. Therefore, it induces a significant financial burden on the company. In contrast, for the optimized water fee, the cumulative fund balance of the company has been stable since 2011, and the fee fluctuation is zero. In other words, if the optimized water fee was applied by customers, no excessive financial burden was imposed on the company during the study period from 2011 to 2016.

Water fee increment induces a burden on customers. Because of the increment in water fee in the optimized situation, customers will have a higher financial burden than the approved water fee for all years. In other words, by increasing the water fee, the annual household water bill will be increased, and the water bill burden will be increased during the simulation (Eq. (17)). Rehan (2011) mentioned that financial burden acceptability diminishes by increasing the water fee.

According to Figure 3, as the water bill burden increases, the willingness to pay (burden acceptability) decreases. Therefore, it can be seen in Figure 9 that, in optimal conditions, because of the increase in water bill burden, the burden acceptability has decreased for all years.

If the model proposed water fee was employed, the burden acceptability increased by 2% in 2013 and 2016. On the other hand, due to the increase in the water fee, water demand decreased during the research period compared to the approved water fee. Water demand reached its minimum value (350L/day) in 2013 and 2016 for each customer, indicating a significant reduction in the water demand relative to the approved state.

4. Conclusion

In this research, we combined a comprehensive model of simulation and optimization for the modeling of the financial system of a water and wastewater company, and the following results were obtained:

•	The financial system of the Water and Wastewater Company was complex, and the system dynamics method efficiently simulated the complexities.
•	The calibration process occurs by maximizing the payoff function. For this purpose, the forecasted cumulative burden of the Rural Water and Wastewater Company in Hamedan was compared with the fund balance sheets and financial statements from 2011 to 2016. The results showed that values of the statistical indices of $R^2$ and NRMSE were 0.99% and 4%, respectively.
•	The sensitivity of the financial system was analyzed relative to the parameters, which had more uncertainty levels. The key results showed that the fund balance of the company, water consumption, and burden acceptability was more water fee-sensitive.
•	The sensitivity level of the fund balance of the company to the burden was 15.13, 13.91, and 12.87, respectively, which indicates the financial dependency of the company on the parameters.
•	Among the system parameters, the burden acceptability of the water bill is influenced by the water fee and customers’ income. The sensitivity level of the willingness to pay for the water increases up to 90% by 10% increase in the failure rate of the network pipes. Water consumption is more affected by the number of customers and the water fee.
•	Despite the increasing water fee in recent years, the fund balance of the company was still negative, and the slope of the relevant chart and burden has increased over time. Therefore, to avoid excessive losses, the actual water fee was determined by the Powell optimization method within the study period. Nevertheless, forecasting an optimal price resulted in a rise in the burden on customers, especially in 2013 and 2016, and the burden acceptability dropped by 2% in these years. Therefore, water consumption reduced significantly within the mentioned period.
•	One of the benefits of the developed model is the visibility of the fluctuations in each system parameter after optimizing the water fee over time.
•	Besides the visibility of the changes in all system parameters over time, fast model generation, simplicity, modification of the model structure in response to the system changes, optimization, sensitivity analysis, and time dissipation are categorized among the advantages of the system dynamics method. Therefore, experts and practitioners can use the model as a management tool for decision-making and planning purposes.
•	However, the developed SD model has several limitations. This study’s available case study data was insufficient, and more data are required to evaluate the models’ accuracy. The model was calibrated at an annual time step. The model could not evaluate the impact of the other management policies (i.e., climate and weather variability) on reducing the water demand. Using stochastic models to forecast the model inputs is also suggested, then running the developed model for sustainable water demand management.

Acknowledgments

The authors would like to thank the Rural Water and Wastewater Company of Hamedan Province for their financial support and for providing the necessary statistics and information. We also thank Mr. Seyyed Mostafa Hashemi, the managing director, and Ms. Elham Shahbazi, the Head of the Research and Productivity Department of the Company, for their valuable support and cooperation.