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This thesis develops new methods to generate probabilistic forecasts and applies these methods to solve operations problems in practice. The first chapter introduces a new product life cycle model, the tilted-Gompertz model, which can predict the distribution of period sales and cumulative sales over a product's life cycle. The tilted-Gompertz model is developed by exponential tilting the Gompertz model, which has been widely applied in modelling human mortality. Due to the tilting parameter, this new model is flexible and capable of describing a wider range of shapes compared to existing life cycle models. In two empirical studies, one on the adoption of new products and the other on search interest in social networking websites, I find that the tilted-Gompertz model performs well on quantile forecasting and point forecasting, when compared to other leading life-cycle models. In the second chapter, I develop a new exponential smoothing model that can capture life-cycle trends. This new exponential smoothing model can also be viewed as a tilted-Gompertz model with time-varying parameters. The model can adapt to local changes in the time series due to the smoothing parameters in the exponential smoothing formulation. When estimating the parameters, prior information is included in the regularization terms of the model. In the empirical studies, the new exponential smoothing model outperforms several leading benchmark models in predicting quantiles on a rolling basis. In the final chapter, I develop a predictive system that predicts distributions of passengers' connection times and transfer passenger flows at an airport using machine learning methods. The predictive system is based on regression trees and copula-based simulations. London Heathrow airport currently uses this proposed system and has reported significant accuracy improvements over their legacy systems.