Industry: Construction and Infrastructure Product: ModelRisk Application: Construction scheduling under uncertainty
The deterministic CPM schedule said the viaduct-and-interchange package would finish in 24 months. The board signed it. Then the planning team rebuilt the schedule in ModelRisk and discovered that the shared weather index and the shared crew-productivity multiplier — two single variables not on the CPM diagram — moved the P90 finish date by more than four months. The 24-month contract had roughly a 60% chance of being met, not the implicit 100% the deterministic Gantt suggested.
This is the central problem with deterministic construction schedules: tasks are not independent. Concrete pours, asphalt paving, MSE wall construction and trenching all suffer the same rainy week. The same field crews rotate through piling, substructure and deck work. Treat eight phases as independent triangular draws and the simulator under-states tail risk by an order of magnitude. ModelRisk solves it by sampling weather and productivity once per simulation and propagating their effect across every weather- or labor-sensitive phase.
The package has eight WBS phases — mobilization, geotechnical / piling, substructure, pre-cast girder fabrication, girder erection / deck, approach roads / MSE walls, pavement / barriers / ITS, and testing / snag / handover. Each phase carries a three-point estimate from estimating and field staff: a best case, most-likely and worst case (in days). These were entered as PERT-Beta distributions, the Vose-default for activity durations — right-skewed (true tail of bad days is longer than the tail of unusually good days), bounded, and parameterized directly by the three-point estimate.
A common alternative — a Normal around the most-likely value — was rejected for two reasons. Normal allows negative durations (a small but non-zero probability) and it understates the upside tail that delay risk lives in. LogNormal would also have been defensible; the PERT-Beta wins on interpretability for estimators.
The shared factors:
Treating those as independent per-phase noise would have hidden roughly 80 days of P90 schedule risk — exactly the kind of tail the deterministic plan suppresses.
The point-estimate CPM finish was 720 days — the contractual deadline. The simulation puts the P50 finish at roughly 690 days, the P90 at 770 days, and the P99 at 850 days. The probability of meeting the 720-day contract is about 62%. The 30-day average buffer the CPM looked to provide was, on the simulation, less than a one-in-two chance of holding.
The cost-at-risk fan is the conversation owners and lenders actually need: what cumulative spend corresponds to what month, and how wide is the P10–P90 envelope at every point along the way? The deterministic burn line plots cleanly to the $480M point estimate at month 24. The P90 envelope crosses the $540M approved budget cap around month 22 — i.e., a fifth of trajectories hit the budget cap before the planned finish, driven by the indirect cost that accumulates as the schedule stretches. The deterministic plan offered none of this visibility.
Tornado analysis ranks the seven drivers of the P90 finish:
The shared weather index is the largest single mover — bigger than any individual phase duration. The shared crew productivity multiplier is second. The single-phase drivers (substructure, girder erection) come after the two shared multipliers. Sensitivity analysis in a properly correlated model reorders the team's priorities: invest in weather-shed structures, just-in-case crew capacity, and a sheltered pre-cast yard before refining any single-phase estimate.
The tornado tells you what drives the P90; the mechanism behind it is clustering. A representative bad-but-not-extreme run stacks ordinary events — two wet weeks in piling, a storm hold in month 9, a steel-delivery lag at the substructure-to-girder handover, a crew shortfall during peak girder erection, and a pre-cast slip just before pavement start. None of these on its own is catastrophic; their clustering through the dependency network is what pushes the simulated P90 finish 50 days past the contract. The accelerated-shift mitigation moves the median earlier but barely improves the tail, because the tail is being driven by the shared weather and crew shocks, not by the median duration of any one phase. The weather-mitigation package — sheltered work-front and dry-season scheduling — tightens the weather sigma from 0.18 to 0.10 and pushes the P90 finish back to roughly 720 days at a fraction of the accelerated-labor cost. The probabilistic comparison reverses the rank order the deterministic mean would have given.
In construction, "the plan" is not a date — it is a distribution. ModelRisk is what makes that distribution visible, and once it is visible the steering committee can argue about contingency in the language of probability rather than the language of single dates.