Optimal Water Supply Planning Based on Seasonal Runoff Forecasts

Suppose a commitment of water supply for the forthcoming season must be made within a prior period during which a sequence of seasonal runoff volume forecasts is available. The decision maker's dilemma is that on the average, the accuracy of forecasts increases with time, but the benefit from the supply allocation decreases as the commitment is delayed. This planning problem is modeled as a Markovian stopping process with maximization of the expected utility of outcomes as the planning criterion. The optimal decision strategy, obtained via dynamic programming, prescribes the timing of the commitment and volume of the planned supply as a function of forecasts. The strategy takes explicitly into account uncertainties in the forecasts, value of water (economic or subjective), risk attitude of the decision maker, and utility reduction factor caused by delaying the commitment. An extensive numerical example illustrates the capabilities of the model as an aid to real‐time decision making and evaluation of the economic worth of forecasts.