Probabilistic Audience Forecasting and Campaign Optimization

The fragmentation of linear television and radio audiences has increased the complexity of advertising planning, requiring integrated predictive and optimization approaches. This paper proposes a probabilistic predictive–prescriptive framework that combines slot-level audience forecasting with Gross Rating Points(GRP)-constrained campaign optimization under realistic operational constraints. The forecasting module produces calibrated quantile predictions (P10/ P50/P90) using gradient boosting models with hierarchical back-off mechanisms, explicitly modeling uncertainty. These forecasts are translated into expected GRP contributions and embedded into a mixed-integer programming formulation that minimizes cost or maximizes GRP subject to budget, separation, caps, channel mix, and flighting constraints. The proposed architecture establishes a unified decision-support pipeline linking probabilistic forecasting and mathematical optimization. An evaluation framework is defined to assess predictive accuracy, calibration, and planning robustness in real broadcast environments. The integration of uncertainty-aware forecasting with constraint-rich optimization provides a structured foundation for robust campaign allocation in traditional media contexts