Reliable water supply system design under uncertainty

Given the natural variability and uncertainties in long-term predictions, reliability is a critical design factor for water supply systems. However, the large scale of the problem and the correlated nature of the involved uncertainties result in models that are often intractable. In this paper, we consider a municipal water supply system over a 15-year planning period with initial infrastructure and possibility of construction and expansion during the first and sixth year on the planning horizon. Correlated uncertainties in water demand and supply are applied on the form of the robust optimization approach of Bertsimas and Sim to design a reliable water supply system. Robust optimization aims to find a solution that remains feasible under data uncertainty. Such a system can be too conservative and costly. In the Bertsimas and Sim approach, it is possible to vary the degree of conservatism to allow for a decision maker to understand the tradeoff between system reliability and economic feasibility/cost. The degree of conservatism is incorporated in the probability bound for constraint violation. As a result, the total cost increases as the degree of conservatism (and reliability) is increased. In the water supply system application, a tradeoff exists between the level of conservatism and imported water purchase. It was found that the robust optimization approach addresses parameter uncertainty without excessively affecting the system. While we applied our methodology to hypothetical conditions, extensions to real-world systems with similar structure are straightforward. Therefore, our study shows that this approach is a useful tool in water supply system design that prevents system failure at a certain level of risk.