Optimising rainwater harvesting systems under uncertainty: A multi-objective stochastic approach with risk considerations

Optimising rainwater harvesting (RWH) systems’ design involves sizing the storage and catchment areas to enhance cost-effectiveness, self-sufficiency, and water quality indicators. This paper considers the design of RWH systems under long-term uncertainty in precipitation and demands. In this work, we formulate and solve a multi-objective stochastic optimisation problem that allows explicit trade-offs under uncertainty, maximising system efficiency and minimising deployment cost. We use the yield after spillage (YAS) approach to incorporate the physical and operational constraints and the big-M method to reformulate the nonlinear min\max rules of this approach as a mixed-integer linear programming (MILP) problem. By posing a risk averseness measure on efficiency as a conditional value at risk (CVaR) formulation, we guarantee the designer against the highest demand and driest weather conditions. We then exploit the lexicographic method to effectively solve the multi-objective stochastic problem as a sequence of equivalent single-objective problems. A detailed case study of a botanical garden in Amsterdam demonstrates the framework's practical application; we show significant improvements in system efficiency of up to 15.5% and 28.9% in the driest scenarios under risk-neutral and risk-averse conditions, respectively, compared to deterministic approaches. The findings highlight the importance of taking into account multiple objectives and uncertainties when designing RWH systems, allowing designers to optimise efficiency and costs based on their specific requirements without extensive parameterisation.