Analytical optimal hedging with explicit incorporation of reservoir release and carryover storage targets

This study analytically derives optimal hedging for a water supply reservoir considering balance between beneficial release and carryover storage value. With the reservoir operation goal expressed as a weighted sum of loss functions (i.e., normalized deviations from targets) for current release and carryover storage, the derived optimal hedging is a linear function of water availability. This analytical optimal hedging is generalized to represent two-point as well as one-point hedging. The relationship between the weighting factor and the ratio of release target to total target can be used to detect two types of two-point hedging. A factor called the inverse-weighted target ratio (composed of a weighting factor and release and carryover storage targets) is developed to simplify derived optimal hedging and distinguish these two types of hedging, which are classified as the factors less than or equal to 1 and greater than or equal to 1, respectively. One-point hedging is a special case where these two types of two-point hedging coincide and this factor equals 1. By explicitly incorporating release and carryover storage targets as well as a weighting factor and an exponent of loss functions, effects of these components on reservoir hedging can be evaluated analytically. Since reservoir release is also a linear function of reservoir inflow, analytical assessment of hedging uncertainty induced by inflow is made possible. The proposed methodology is applied to the Shihmen Reservoir in northern Taiwan to illustrate effects of derived optimal hedging on reservoir performance in terms of shortage-related indices and hedging uncertainty.