Hedging Rule and Its Relevance to Decision Making in Reservoir Operation

Hedging rule for reservoir operation is used for rationing water supply. It accepts a small deficit in current supply so as to reduce the probability of a more severe water shortage. Recently, the community of water resources planning and management has started emphasizing the value of hedging rule because of growing water demand and increasing uncertainty in water sources. Although the concept is straightforward, the lack of the foresight of reservoir inflow makes it technically difficult to analyze. Uncertainty or imperfect information plays a very important role in hedging rule. However, few studies considers uncertainty in hedging rule analysis. This study develops a theoretical analysis of hedging rules for reservoir operations with consideration of uncertain reservoir inflow. Our approach is currently limited to a two-period optimization model (now and then) for a single reservoir, which is to maximize the utility over the two periods. General results have been derived for the following questions: (1) What is the timing for implementing hedging rules (when will it start and end)?, (2) When is a hedging rule trivial?, (3) What is the impact of the inflow uncertainty in the second period?, and (4) What is the impact of reservoir evaporation on the significance of a hedging rule? Moreover, a numerical model is developed to verify the conclusions from the theoretical analysis. The model specifies a certain type of utility function and represents the inflow uncertainty through a probability distribution function, and includes engineering constraints such as reservoir capacity and water withdrawal capacity. Therefore, the numerical model can be used to show more detailed analyses on price elasticity, uncertainty, and engineering capacities, which are difficult to include in the theoretical analysis.