This paper focuses on the capacity uncertainty in water supply chains that occurs when facilities face disruption. A combination of scenario-based two-stage stochastic programming with the min-max robust optimization approach is proposed to optimize the water supply chain network design problem. In the first stage, the decisions are made on locations and capacities of reservoirs and water-treatment plants while recourse decisions including amount of water extraction, amount of water refinement, and consequently amount of water held in reservoirs are made at the second stage. The proposed robust two-stage stochastic programming model can help decision makers consider the impacts of uncertainties and analyze trade-offs between system cost and stability. The literature reveals that most exact methods are not able to tackle the computational complexity of mixed integer non-linear two-stage stochastic problems at large scale. Another contribution of this study is to propose two metaheuristics - a particle swarm optimization (PSO) and a bat algorithm (BA) - to solve the proposed model in large-scale networks efficiently in a reasonable time. The developed model is applied to several hypothetical cases of water resources management systems to evaluate the effectiveness of the model formulation and solution algorithms. Sensitivity analyses are also carried out to analyze the behavior of the model and the robustness approach under parameters variations.

本文着眼于当设施面临破坏时发生的供水链中的容量不确定性。提出了基于情景的两阶段随机规划与最小-最大鲁棒优化方法相结合的方法，以优化供水链网络设计问题。在第一阶段中，要对水库和水处理厂的位置和容量做出决定，而在第二阶段中要做出包括取水量，水提纯量和因此储水量在内的资源决定。所提出的鲁棒的两阶段随机规划模型可以帮助决策者考虑不确定性的影响，并分析系统成本与稳定性之间的权衡。文献表明，最精确的方法无法大规模解决混合整数非线性两阶段随机问题的计算复杂性。这项研究的另一项贡献是提出了两种元启发式算法-粒子群优化（PSO）和蝙蝠算法（BA）-在合理的时间内有效地在大规模网络中解决了该模型。将开发的模型应用于水资源管理系统的几个假设案例，以评估模型制定和求解算法的有效性。还进行了敏感性分析，以分析模型的行为以及参数变化下的鲁棒性方法。这项研究的另一个贡献是提出了两种元启发式算法-粒子群优化（PSO）和蝙蝠算法（BA）-在合理的时间内有效地在大规模网络中解决了该模型。将开发的模型应用于水资源管理系统的几个假设案例，以评估模型制定和求解算法的有效性。还进行了敏感性分析，以分析模型的行为以及参数变化下的鲁棒性方法。这项研究的另一个贡献是提出了两种元启发式算法-粒子群优化（PSO）和蝙蝠算法（BA）-在合理的时间内有效地在大规模网络中解决了该模型。将开发的模型应用于水资源管理系统的几个假设案例，以评估模型制定和求解算法的有效性。还进行了敏感性分析，以分析模型的行为以及参数变化下的鲁棒性方法。