Water resources are of great importance for socioeconomic development, food production, and environmental conservation. Thus, its exploitation is a vital matter for the development of humanity, Ghannem et al. [1].

Water is considered a vital substance for human life and social development. The problem of water resource management has worsened due to rapid economic development. The shortage of water resources significantly limits social and economic development and threatens drinking water security. For this reason, the water shortage crisis is increasing due to climate change and human activities. In addition, demand for water resources has gradually increased with the development of industrial and agricultural production and the social economy [2].

Furthermore, population growth, urbanization, climate change, mismanagement of water resources and water distribution systems, and inappropriate programming increase water stress in many countries worldwide. Although optimization of water distribution systems and integrated water management techniques have been conducted in many cities, no integrated study has been found regarding urban water systems, programming, and management [3]. Due to population growth, limited water resources, and other pressures on urban water systems, urban water management has become a primary concern for urban policymakers in recent years, as they seek to develop efficient management solutions [4]. Thus, solving network design problems has become an interesting topic in the field of wastewater management and water security because of increased population, resource shortage, environmental concerns, and the increasing need for sustainable solutions for future policy plans, especially in the areas where the demand for wastewater treatment has increased significantly due to high immigration, rapid industrialization, and tourism activities to make this topic more critical and dynamic Demirel et al. [5]. Following the long-term effects of urban water services is a background for the future and a critical scientific foundation for the sustainable development of systems Shiu et al. [6] since the appropriate exploitation of water resources is considered as an effective measure to realize the optimal allocation of water resources and can effectively decrease the regional water resource shortages, flood disasters, and other social problems, and play a key role in supporting the strategic development of water resources. Water supply for urban supply systems is a global effort and a big challenge for water resource managers in large urban areas. Water supply requires integrated management of water quantity and quality, and adaptation of the system to land use and climate change in the region [7].

Current water security models assess a system's security status using indicators of quantity, quality, and compliance. Moreover, existing studies address this topic using mathematical optimization-based approaches that require substantial computational effort. In addition to mathematical optimization studies, an alternative approach based on the system dynamics method is proposed in this study to evaluate the complex dynamic and nonlinear structure of water and wastewater network design problems and water supply since the developed framework can provide an evaluation method for the water life cycle in the long term in a dynamic way to evaluate the temporal changes and the effects to deal with the challenges related to water security. The proposed SD simulation model has been designed for a populated tourist spot in Guilan province, located in the north of Iran and the southwest of the Caspian Sea. Accordingly, the most significant innovation and unique contribution of this study are as follows:

I. Establishing a three-phase water supply system, including the processes of water production, distribution, and purification II. Creating a quantitative relationship in the urban water supply system and evaluating system performance based on it.

III. Providing integrated programming to determine the optimal status of water supply protocols and select the most appropriate water supply strategy based on various programming periods for policy makers.

IV. Establishing an optimal programming cycle for a real-world water supply system by combining the bi-objective mathematical model and system dynamics modeling methods.

V. Considering an uncertain value for the amount of water consumed in the time period to make the modeling closer to reality.

Golpira and Tirkalaei [8] evaluated the social and economic effects at different levels of environmental flow allocation in the Wei River basin in China using the systems dynamics model and VENSIM software. In this report, four methods were presented for social and economic growth, and four methods for environmental water allocation. The results indicated that the developed system dynamics model captures the system's dynamic behavior well in the studied area. Nepal and Teren [9] addressed the use of the system dynamics method in simulating the cultivation pattern of the irrigation and drainage network on the right side of the Isfahan waterfall. The results revealed that maintaining or not maintaining the limit on the total area under cultivation in the base year yields the highest income relative to the cost. In addition, they used the VENSIM system dynamics model to simulate electricity production from the Karun 1, Karun 3, and Karun 4 hydroelectric reservoirs. The design steps involved defining the required decision variables, equations, and formulas to measure the energy production of the reservoirs. The results indicated that energy production in the Khorasan 1 reservoir, including the Karun 4 and 3 reservoirs, can increase by an average of 20% without significant changes to the evaluation criteria. Song et al. [10] evaluated different scenarios for water resource allocation of Choghakhor dam using the system dynamics method. The VENSIM dynamic model was designed and implemented to utilize the water resources of the Choghakhor dam and meet downstream needs. In addition, the input amounts to the dam reservoir and evaporation from the dam reservoir were predicted using a SARIMA time-series model for the next 5 years. The results showed that the Choghakhor dam can supply the water needs of 1600 hectares of water-consuming lands in the most optimal state. In this regard, the amount of supply for agricultural and environmental needs is 83 and 95, respectively. Tian et al. [11] used the PSO, genetic, and ant colony optimization algorithms to study wastewater network optimization. They concluded that the PSO algorithm can reach the optimal solution faster with fewer iterations. Zhu et al. [12] developed domestic and industrial water demand models based on a bi-objective model to balance economic and environmental costs in an urban water supply system across three phases: water production, distribution, and treatment. Then, a system dynamics-based model is applied to test the performance of the water supply system under short-, medium-, and long-term programming scenarios. Yu et al. [13] studied stakeholder competition in the operation of a multi-purpose ecological reservoir to satisfy economic, social, and ecological needs. For this purpose, a multi-objective game-theoretic model was developed to determine water discharge over 10 days to satisfy the triple needs of water —electricity production, socioeconomic consumption, and the environment. Dimello et al. [7] proposed a new method for evaluating water security based on the ranking of pressure indicators, which apply to a drainage basin such as water demand, regular and random pollutants, drought, and environmental changes (e.g., the share of forest vegetation) according to risk assessment in terms of pressure characteristics such as severity, occurrence, and detectability. Dang et al. [14] formulated a multi-objective water resource allocation model to optimize efficiency and equity with sustainability (ecological river flow) as a constraint. For this purpose, the NSGA-II algorithm was used to extract Pareto solutions in a water resource allocation system. The results showed that Pareto solutions can show the opposite relationship between efficiency and equity in water resource allocation. Demirel et al. [5] proposed an alternative approach based on the system dynamics method to select a location for wastewater treatment facilities and to design wastewater treatment networks. The proposed SD simulation model was designed for an area in Antalya, Turkey. This model can determine the location and timing of constructing a new wastewater treatment plant and a public wastewater network for five areas in downtown, based on cost considerations during 2015-2040. Guilani et al. [15] provided a sustainable selection method for the location of water treatment facilities using the best-worst method. Moreover, this model selects appropriate technologies for the treatment plant, manages water leakage across the entire transmission network through renovation, and selects different transmission technologies. Based on the obtained results, the interaction of water and energy has received special attention in this network. Shiu et al. [6] proposed a method for dynamic life cycle assessment that considers temporal changes and the challenges of water treatment facilities, based on life cycle assessment principles applied to system dynamics models. This model was then applied to a water treatment plant in the Kinmen Islands, Taiwan. The SD model can simulate long-term growth in water demand across the domestic, agricultural, livestock, and manufacturing sectors. Zhu [16] developed an integrated framework for climate change and analyzed its effects on social-environmental aspects across many areas, including wastewater treatment, energy transmission, waste management, land management, and ocean management. Heydari-Kushalshah et al. [17] presented a mathematical model for water supply management. The proposed model can minimize water loss and shortages in an urban area.

Based on the above literature review, the literature fails to present an appropriate optimization model for the effective management of urban water supply resources, given the area's conditions. Thus, introducing a water supply system that includes production, distribution, and treatment processes is recommended to establish a quantitative relationship within the urban water supply system and to describe system performance based on this relationship. Regarding the most significant advantage of this study, it has been conducted to strengthen water resources management through linear multi-objective mathematical modeling that accounts for factors affecting water supply in a high-rainfall province such as Guilan, Iran. Based on the presented modeling, total efficiency and economic benefits are achieved across the domestic, industrial, and agricultural sectors. As a result, the most significant research gaps are as follows:

I. A framework that tracks the optimal response to water supply protocols by changing the programming period according to an integrated method, and determines the most appropriate water supply strategy and programming period for policy makers.

II. Establishing a three-phase water supply system, which involves the processes of water production, distribution, and treatment.

III. Defining a quantitative relationship in the urban water supply system to measure the performance of the system according to this relationship.

IV. Defining an optimal programming period for a real-world water supply system by combining the bi-objective programming and system dynamics methods.

V. Presenting a multi-objective uncertain mathematical programming for the urban water supply system.

This study focuses on the use of mathematical modeling and system dynamics. In this regard, a bi-objective mathematical model is presented to optimize water resources. This model can simultaneously minimize overall system and wastewater costs, which are primary challenges in water resource management. Also, in the proposed model, water consumption in the urban area is treated as uncertain using a fuzzy approach. Numerous efforts have been made to manage wastewater, but no satisfactory results have been achieved. This study, which focuses on Guilan province, a rainy province in northern Iran, presents a mathematical model that minimizes costs and wastewater use while returning water resources to the urban and rural water supply cycle. Guilan province is considered one of the few regions in Iran with abundant water. This province can serve as a model for greater productivity in water resources for other provinces in Iran.

The present study aimed to optimize and plan the urban water supply system using bi-objective optimization and system dynamics method, and the case study was the Water and Wastewater Organization in Guilan province. For this purpose, library studies were conducted, and research gaps were identified based on these studies. The proposed method in this study was to provide a hybrid model of mathematical modeling, meta-heuristic algorithms, and system dynamics approach. The decision variables, including the amount of water resources in the reservoir, the amount of treated water in the water treatment system, the amount of wastewater in the area, and the amount of water shortage in the area, along with the amounts of the objective functions, were obtained using the mathematical model and meta-heuristic algorithm. Then, the amounts were entered into the system dynamics model as input values, and the shortage in future periods was predicted, indicating a linear trend of up to more than 520 thousand units. In addition, the sensitivity analysis shows the reverse effects of capacity and the amount of input water, and the direct effects of transmission cost, energy consumption, energy consumption cost, treatment cost, resource cost, construction cost, and demand. Among the parameters with a direct effect on energy consumption cost, construction cost, and treatment cost, construction cost has the most significant effect on supply cost. In contrast, treatment costs and demand have the most tremendous impact on shortages and wastewater in the system.

Based on the findings, the most significant suggestions for managers as a roadmap for the future are as follows: increasing treatment capacity and water resources in Guilan province can reduce treatment costs and alleviate shortages and wastewater. Thus, increasing investment to enhance treatment capacity and water resources is one of the approaches to prevent shortages and control wastewater, given the abundant water resources in Guilan province. Although the investment can be expensive in the short term, it prevents increases in costs and emerging water shortages in the long term. Regarding parameters that have a positive effect, such as the amount of non-precipitation water entering Guilan province from other provinces, appropriate measures should be taken through various methods to increase the province's water resources. In this regard, using input water can offer more advantages than using rainwater. If the right systems are used and managed effectively to control water inputs, an increase in water resources can be expected, resulting in reduced costs and wastewater in Guilan province. Energy consumption control is one of the factors that strongly affects the cost. Using devices with lower energy consumption can help treat and maintain water sources. Construction costs are considered an essential cost factor. Using existing resources appropriately and constructing new facilities can significantly affect costs. Demand is considered a significant factor in creating a shortage in the present model. The effect of demand on cost is not as significant as that of other parameters, though it can definitely affect shortages and wastewater. In this regard, acculturation regarding consumption and optimized consumption through the use of construction tools and valves can increase demand. Furthermore, presenting and analyzing the present model in the low-water provinces of Iran such as Yazd and Kerman, using more decision variables and parameters in the mathematical model, applying multiple meta-heuristic algorithms and comparing their performance, considering the uncertainty in some parameters such as the demand for wastewater, and using the system dynamics tool to predict the situation in the long term are considered as the most critical suggestions for the development of the present study in future studies.

The authors would like to express their sincere appreciation to all individuals whose valuable comments and support contributed to the successful completion of this study.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

The data supporting the findings of this study are available from the corresponding author upon reasonable request.