Cruciality: Role of Network Topology in Schedule Resilience to Delay Propagation

Construction schedules are widely modeled and analyzed as networks that consist of activities within a dependency structure of sequential and parallel paths. All future activities carry duration uncertainty that is caused by diverse risk factors. But worse, by being linked, activities can cause a "ripple effect" of delays that propagate through the remainder of a project. This paper studies this phenomenon systematically: it captures topology with the intuitive concept of reachability. It formalizes an index, cruciality, as the product of reachability and scaled covariance of any two activities within a schedule. And it simulates various test schedules with probabilistic activity durations to answer two related questions: How does schedule topology determine vulnerability to delays? And what ways can schedulers take to design more resilient schedules? It differs from research on the static critical path and forecasting the project duration; instead this work seeks to stabilize said value. Two strategies can be used to reduce the potential propagation: reduce uncertainty in high-risk activities. Or reroute, combine, or even delete links if this is technically feasible. A more parallel topology is beneficial, because it reduces potential interactions. In practice, this could be realized through strategies like modular design or task-dedicated resources.