Beyond Deterministic Scheduling: Revealing Hidden Critical Paths under Stochastic Time Variability through Monte Carlo Simulation and Hierarchical Clustering

In many Engineer-to-Order (ETO) companies, each one-of-a-kind product is effectively treated as a separate project, making the critical path a central tool for scheduling tasks and allocating resources. However, relying solely on deterministic durations may fail to capture the variability typical of real-world operations, leading to potentially inaccurate project timelines. Despite this challenge, the literature rarely explores how variable activity durations can lead to different critical paths, with significant implications for both project duration and resource allocation. This study tackles this gap by integrating optimistic and pessimistic duration estimates within a Monte Carlo Simulation (MCS), systematically recording and analyzing all the critical paths actually observed. By quantifying how frequently each activity appears among these paths, a hierarchical clustering method is employed to detect recurring patterns and correlations. From the results, it emerges that the deterministic critical path can diverge from the one that arises under variable conditions, highlighting which tasks require greater attention to prevent delays. Consequently, the proposed framework offers a comprehensive basis for resource allocation in ETO environments, illuminating those activities most susceptible to time deviations. This approach is particularly valuable for project managers and engineers operating under high uncertainty, enabling proactive risk management and reducing potential bottlenecks.