Water-energy nexus under uncertainty: Development of a hierarchical decision-making model

In this study, an interval stochastic bi-level programming (ISBP) method is developed for planning the water-energy nexus (WEN) system. In ISBP, interval-parameter programming (IPP) and two-stage stochastic programming (TSP) are introduced into a bi-level programming (BP) framework. ISBP can tackle dual uncertainties expressed as probability distributions and interval values as well as balance the tradeoff between two-level decision makers. An ISBP-WEN model is then formulated for planning the WEN system of Jinan (the capital of Shandong province, China), in which the upper-level model aims to maximize system benefit and the lower-level model aims to minimize the electricity consumed for water allocation. Major findings are: (i) dual uncertainties can affect the city's water-allocation pattern and lead to different amounts of water shortage and electricity consumption; (ii) [25.5, 31.3]% of water-allocation target cannot be satisfied under the low water-flow level, implying that the city would face serious water shortage; (iii) compared with surface water and reclaimed water, groundwater is the scarcest source for the city and the proportion of groundwater deficit would be [41.2, 49.9]% under the low water-flow level; (iv) compared with the traditional single-level model, electricity consumption from ISBP-WEN would be reduced by [3.9, 5.1]%. These findings can help managers to identify the desired strategy between different stakeholders and provide numerical information for planning the WEN system under dual uncertainties.