The uncertainty of demand in water supply optimization models
1999
Guhl, F. | Brémond, Bernard | Gilbert, Denis
For several years, we have been working on methods of minimizing water production and transport costs in drinking water networks. This paper deals with the demand prediction of water supply and, in order to improve the performance of the commonly used linear programming model, how we take into account the stochastic character of demand. First, we constructed a model to predict the demand in the coming hour. To optimize a drinking water network, we need to know the demand over several consecutive hours. Ideally, the models to be constructed should be able to predict the demand over 24 hours, which corresponds to the optimization period we are using. Our optimization starts at 06h00 with full reservoirs. This later fact allows us to make a reliable demand forecasting a bit later on the day without loosing any information related the quality of prediction : 12 timesteps, from 13h00 to 24h00. These models use neural networks techniques based only on calendar variables (hours, date) and past demand as inputs data. The obtained results seem to confirm the interest of this choice and appear to be a Gaussian distribution. In a second step, we integrate in the optimization model the Gaussian distribution average value and its standard deviation. The stochastic linear programming method proposed in this paper, allows us to add probability in the tanks stock constraints. This method seems to be welcomed by networks managers because they can better control risks in optimization management.
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