A Cost-Agnostic Model to Identify Infrastructure Projects to Improve Rain-flow Allocations in a Growing Demand Environment

Climate change has led to the redistribution of water resources in many regions due to changes in global and regional water cycles. Sustainable water management is essential to ensure further socioeconomic development in the fastest-growing megalopolitan region, such as the Greater Bay Area (GBA) in China. Although optimal water allocation policies for various jurisdictions, provinces, cities, and areas in the GBA have been widely explored, most studies have focused on solutions within the context of existing infrastructure. Optimizing allocation on such a regional scale is a significant challenge due to differences in objectives, decision-makers, long-term contracts, trade deals, and other factors that are difficult to model or that make obtaining reliable data difficult. The presented study is part of a 3-year collaborative efforts among experts in climate change, water resources and operation research funded by the Hong Kong government (CRF Ref. No. C6032-21GF). And instead of focusing on determining optimal allocation, we intend to investigate the sustainability of the current scheme in line with the area’s rapid development under intensified climate variability and provide supportive information on the alleviation of system stress and bottlenecks over time.

We start with developing an aggregate rain-flow allocation model over a relevant time horizon to minimize shortage and overage costs. The model is infrastructure cost-agnostic and focuses on the marginal value of added storage capacity and network connectivity. We use the dual variables of the optimization problem, aggregated over different demand and supply scenarios, to identify infrastructure projects that can best improve the performance of the system based on projected but uncertain demand growth. Specifically, we first obtain the allowable range that can be solved by a linear programming based on the dual problem and subsequent problem reformulation for a single project. Then we introduce the approximated allowable range by aggregating over multiple scenarios to improve accuracy and computational efficiency. Combined with the aggregated marginal value, these features are used to create a list of the most promising projects in terms of their ability to improve the matching of supply and demand. The model can use feedback from decision makers to eliminate from consideration projects that are too expensive to build. The analysis can be used recurrently to obtain further improvements leading to a feedback loop with a finite number of rounds. This feedback loop can save significant time and effort compared to cost-based models that require obtaining cost data for many projects that will never be built. Based on our current results, we find that this process is quite efficient, and the feedback loop will basically end in a few rounds. These results can be extended in several directions including the discounting of cash flows. Moreover, we identify pairs of projects that have positive synergies making one more effective in the presence of the other.

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