Title: Probabilistic Forecasting and Optimization

Abstract: Traditional forecasting methods focus on giving an unbiased forecast and estimating the associated forecasting error. Stochastic optimization models on the other hand make a distributional assumption on the forecasted quantity and come up with an decision which is in expectation optimal. A simple example is the newsboy problem where one balances between overage and underage costs of the number of goods to purchase. If the so-called loss function is symmetric, then the unbiased forecast will be the correct optimal value in expectation. However, in many cases the loss function is not symmetric and it has been established that biased forecasts perform better than unbiased. This issue can be solved by estimating the distribution of the quantity involved. In this presentation we show several methods, both statistical and machine learning for probabilistic forecasting. The statistical methods fit a distribution to the forecast error, or they do quantile forecasting. The machine learning do either quantile forecasting or forecast the parameters of a distribution. Finally there is conformal forecasting. We state the pros and cons in terms of computation time and memory requirements. Next we show their application for several cases, such as the newsboy problem, inventory control and battery operation.