Determining Forecast and Decision Horizons for Reservoir Operations under Hedging Policies

Hedging policies for reservoir operations accept a small deficit in current supply to reduce the probability of a severe water shortage in the future. Although the concept of hedging is straightforward, the lack of foresight of reservoir inflow makes it technically difficult to analyze. One of the critical questions for hedging research is how long one can hedge given the forecast of an uncertainty input. Decision makers always hope to look further to the future, but the longer the forecast period, the more uncertainty and less reliable information to be involved, which will have a diminishing influence on decision making. In a multi-period reservoir operation optimization problem, it is usually the release (the decision) in the first or first few periods that are of immediate importance to the reservoir manager. These imminent release decisions depend in general upon inflow forecasts for subsequent periods. Forecasts of inflow further into the future are expensive and/or less reliable. It is therefore, of utmost interest to quantify the diminishing effect, if any, of future data on the initial decisions in order to know if distant forecasts have negligible impact on initial decisions. For dynamic reservoir operation optimization models, when it happens that the decisions in the initial few periods are not affected by future data beyond a certain period, the period is known as "forecast horizon" and the number of the initial periods is known as the "decision horizon." This paper will examine the existence of "forecast horizon" and "decision horizon," determine the associated conditions for dynamic reservoir operation problems; and use the horizon theory to consolidate the numerical modeling of dynamic reservoir operation problems under hedging policies. A theoretical framework for horizon identification with reservoir operation problems will be established; a numerical model will be developed to explicitly incorporate the general principles on forecast and decision horizon.