Proactive scheduling creates robust offline schedules that optimize resource utilization and minimize job flow times. This work addresses scheduling challenges in business processes, often encountered in service systems, which differ from traditional applications like manufacturing due to inherent uncertainties in activity durations, and human resource availability. We model the business process scheduling problem (BPSP) as a variation of stochastic resource-constrained multi-project scheduling (RCMPSP), and apply process mining to infer unknown parameter values from historical event data. To overcome the randomness in activity durations, we transform the problem into its deterministic counterpart, and prove that the latter provides a lower bound on the Makespan of the stochastic problem. Our approach integrates data-driven Monte Carlo simulation with constraint programming to generate proactive schedules that guarantee, with high probability, that the Makespan remains below a predefined threshold. We evaluate our approach using synthetic datasets with varying levels of uncertainty and size. In addition, we apply the approach to a real-world dataset from an outpatient cancer hospital, demonstrating its effectiveness in optimizing the process Makespan by an average of 5% to 14%.