Optimal Hedging Rules for Water Supply Reservoir Operations under Forecast Uncertainty and Conditional Value-at-Risk Criterion

Abstract

Hedging rules for water supply reservoir operations provide guidelines for balancing the consequences of competing water allocations. When inflow forecast uncertainty is addressed, hedging acts as insurances for offsetting the negative influence of water shortage in the future, especially when drought is anticipated. This study used a risk-averse criterion, the conditional value-at-risk (CVaR), rather than the expected value (EV) criterion, to rationalize water delivery for overcoming the shortcomings of risk-neutral hedging rules in minimizing water shortage impacts in unfavorable realizations, in which actual inflow is less than anticipated. A two-period hedging model with the objective of maximizing the CVaR of total benefits from water delivery and water storage is established, and the optimal hedging rules using first-order optimality condition are analytically derived. Differences in hedging rules under the two criteria are highlighted by theoretical analysis and numerical experiments. The methods are applied to guide the operations of a water supply reservoir, and results show that: (1) the hedging rules under the EV criterion are special cases under the CVaR criterion; (2) water delivery in the current period would be greatly curtailed under the high influence of forecast uncertainty or the significant risk-averse attitude of decision makers; (3) hedging to maximize the CVaR of total benefit is at the cost of reducing the EV of total benefit; and (4) in real-time operations, compared with the hedging policies under the EV criterion, the hedging policies under the CVaR criterion would be more effective when applied to dry and extremely dry hydrological conditions, especially when inflow is overestimated. These implications provide new insights into rationing water supply and risk aversion.