Cost-Aware Project Scheduling with Activity Uncertainty

In this work, we introduce a general cost-aware project scheduling model that incorporates probabilistic activity outcomes into the optimization of time-critical processes. The framework addresses settings in which each activity is characterized by a duration, a cost, and a success probability, and where delays may have severe consequences. To capture these features, we model the problem of determining the optimal ordering and timing of tasks, so as to minimize expected total cost while ensuring completion within strict deadlines, as a Mixed Integer Linear Programming model.

Moreover, to assess the practical relevance of this approach, we apply the model to the pre-transplant assessment phase of the heart donation process, a context where multiple diagnostic tasks must be scheduled under strict time constraints and uncertain donor suitability outcomes.  In this case study, the durations of several clinical activities are themselves uncertain, adding an additional layer of complexity that further amplifies the value of explicitly incorporating uncertainty into the scheduling process. The application illustrates how modeling both probabilistic outcomes and stochastic durations can prevent inefficient task ordering and costly delays, thereby supporting more informed decision making in high stakes clinical settings. Beyond this application, the proposed framework is broadly applicable to project scheduling problems with uncertainty, cost considerations, and strict time requirements.

Joint work with Alessandro Agnetis, Arianna Freda, Piero Ghersi, Andrea Pacifici, Marco Pranzo