A stochastic programming (SP) problem involves some or all of the parameters or variables being uncertain. Uncertainty is typically expressed as a probability distribution on the parameters. In reality, despite its precise description, uncertainty can manifest in various forms, ranging from a limited number of possible outcomes to precise joint probability distributions. In the water supply system, weather patterns (in the rainy season the rainfall is very high compared to the other seasons), water demand, and water availability are a few uncertain parameters. These uncertainties might not be sufficiently taken into account by conventional deterministic optimization techniques, resulting in less-than-ideal results. The water supply model will be enhanced in this study by SP ideas, resulting in a more stable and adaptable optimization strategy. In this research, we first analyze a 2-stage SP model by capturing more sample data and show the comparison of capturing more and less sample data. We will extend the 2-stage SP model to a 3-stage SP model by using the tree algorithm, and we will show the comparison between these two-stage and three-stage SP models.

People around the world use fresh water daily for drinking, sanitation, and washing. At the same time, they discharge wastewater into canals, which can be harmful to both human health and the ecosystem of surface water sources. A significant amount of water is consumed for washing purposes. However, it is possible to disinfect and purify this large volume of wastewater for reuse. The process of treating used wastewater is known as refinement. This study aims to develop a two-stage stochastic recourse model that refines wastewater before it is released into the environment. The goal is to ensure that the refined wastewater does not harm the ecosystem. The treated water can then be repurposed for various secondary uses. The proposed model will account for uncertainties related to the availability of water from the supplying authority. To evaluate the effectiveness of this model, we will compare the costs of the water supply system both with and without refinement. The advantages of the proposed model will be assessed through calculations of the expected value of perfect information (EVPI), the value of the stochastic solution (VSS), the recourse solution (RS), the wait-and-see solution (WS), and the expected solution based on first-stage decisions (EEV). Additionally, a risk-averse (RA) optimization model will be used to analyze the sensitivity of system costs.