Water treatment is traditionally seen as an "end-of-pipe" solution to deal with contaminated water satisfying discharge regulations at a minimum expense. However, the reuse of treated water as regenerated water is a promising strategy to counteract water scarcity. This approach to transform waste into resources is motivated by the circular economy paradigm. This study presents a mathematical programming approach to target both the environmental and economic benefits of water systems by introducing additional regeneration units to close the loop. In addition to water users and authorities, the approach also considers operators and dealers, which are revealed as key stakeholders. Hence, the feasible region of the regeneration units design specifications is determined and visualized through a multi-objective optimization approach targeting the systems operating cost and freshwater consumption. Its application is demonstrated on a benchmark case study from the literature, revealing a potential economic benefit of 37.5% and a freshwater reduction of 80.9% over the case without regeneration units. Furthermore, we show that a cooperative exchange strategy leads to higher benefits compared to the solutions presented in the literature. Finally, we demonstrate how the barrier plots introduced in this work can be used by different stakeholders in the water market to support their decision-making.

传统上，水处理被视为一种“管道末端”解决方案，可以以最低的费用处理满足排放法规的受污染水。然而，将处理过的水作为再生水再利用是解决缺水问题的一个很有前景的策略。这种将废物转化为资源的方法是由循环经济范式推动的。本研究提出了一种数学规划方法，通过引入额外的再生单元来关闭循环，从而实现水系统的环境和经济效益。除了用水者和当局，该方法还考虑了运营商和经销商，他们被揭示为关键利益相关者。因此，通过针对系统运行成本和淡水消耗的多目标优化方法，确定并可视化再生单元设计规范的可行区域。它的应用在文献中的基准案例研究中得到了证明，与没有再生装置的情况相比，潜在的经济效益为 37.5%，淡水减少了 80.9%。此外，我们表明，与文献中提出的解决方案相比，合作交换策略会带来更高的收益。最后，我们展示了这项工作中引入的障碍图如何被水市场中的不同利益相关者用来支持他们的决策。与没有再生装置的情况相比，潜在的经济效益为 37.5%，淡水减少了 80.9%。此外，我们表明，与文献中提出的解决方案相比，合作交换策略会带来更高的收益。最后，我们展示了这项工作中引入的障碍图如何被水市场中的不同利益相关者用来支持他们的决策。与没有再生装置的情况相比，潜在的经济效益为 37.5%，淡水减少了 80.9%。此外，我们表明，与文献中提出的解决方案相比，合作交换策略会带来更高的收益。最后，我们展示了这项工作中引入的障碍图如何被水市场中的不同利益相关者用来支持他们的决策。