Scenario Generation The Forecasting Module

Stochastic models assume that probability distributions governing the uncertain factors are known or can be estimated. The aforementioned fact and the computational effort required to obtain solutions are the main drawbacks of this approach. In this section, a methodology based on forecasting techniques which can be utilized for the scenario generation is presented. 

The parameters that the proposed methodology requires from a forecasting module are the mean forecast (6) and the forecast error distribution for each uncertain parameter that is considered in the predictive model. 

Future uncertain parameters in period t ( t) can be expressed as depicted in Eq.(7.56), where the uncertain parameter for scenario hi is computed as the 

The forecast errors distributions depend on previous errors (e ) and on how many periods ahead the forecast is being done. If the correct forecasting model has been chosen, and if the statistical procedure used to estimate parameters in the model yields unbiased estimates, then the expected forecast error will be zero. When the forecasting error (e) is assumed to be normally distributed (7V(0, Tj)), of forecasting error for the period ahead can be calculated by means of Eq. (7.57). This approximation holds even for non-normally distributed errors. For more details about estimation of forecast errors, please refer to Montgomery et al. (1990). 

Consequently, a Monte Carlo sampling to generate (e ) assuming that this parameter is governed by a N 0, probability distribution and Eq.(7.56) can be utilized to create the scenarios required in stochastic mathematical models, as shown in Fig. 7.5. 

---