Industry: Construction and Infrastructure Product: ModelRisk Application: Project Delays — Probabilistic Schedule Risk
A $780M bridge project was bid on a 36-month duration that ran the critical path through 14 activities. Pulling those same activities into a Monte Carlo schedule gave a P50 of 41.9 months and a P90 of 46.0 months — a 10-month spread above the bid date the deterministic Gantt could not see, and a daily liquidated-damages clause of $85,000 that turned the spread into a real number on the balance sheet.
The contractor adopted ModelRisk to do what critical-path scheduling cannot: tell you the probability of finishing on each date, not just the date implied by stacking modal durations.
The swimlane above lays out a representative trajectory — one of the 30,000 Monte Carlo paths whose finish lands at the simulated P50 (42 months). The critical-path row shows the 11 sequential activities. The marine-permit row catches the 8% backlog event that consumes months 3–6.5 and pushes the caisson start later than the deterministic CPM predicted. The weather-cluster row shows three storm clusters firing at moments that drag the deck-erection and approach-viaduct activities. The precast / supply row shows the small slip events that compound — each tiny on its own, none catastrophic, but together responsible for half the bias between the deterministic 36-month bid and the realised 42-month median. The CPM bar-chart cannot draw any of this because the CPM does not know what month it is.
Stacking modal task durations to get a project duration is a known statistical fallacy. The sum of right-skewed durations is itself right-skewed; the modal sum is always less than the median sum, which is always less than the mean sum. On this project, that gap was 6 months — exactly the gap between the bid date and the P50.
Three structural effects compound the bias:
max(predecessor finishes)
The schedule had 47 tasks, all assigned PERT distributions with (min, mode, max) triplets calibrated from a company database of 31 prior major-bridge projects:
(min, mode, max)
Tasks on the marine side and the land side were linked by a Gaussian copula with ρ = 0.4 on weather (storms hit both sides at once) and ρ = 0.3 on the labour pool. Independent durations would have under-stated P90 by 4–5 months.
Running 30,000 iterations and plotting P(finish on time) against the candidate milestone gives a clean buffer trade-curve:
The baseline curve crosses 1% at the 36-month bid, 50% at month 42 (the P50), 80% at roughly month 45, and 90% at month 46 (the P90). Bidding 36 months on a project with this risk profile was equivalent to betting that 99% of the schedule tail would not realise — an enormous concentration of LD risk on the contractor. The deterministic bid had a $5.2M liquidated-damages reserve, equivalent to ~60 days of slip. At $85k/day, the expected LD exposure from the simulation was $13.6M, and the P90 LD exposure was $30M. The mitigation curve (front-load permit + parallel precast + split caissons) shifts left across the entire range — the 80% line is now reached at month 43, not month 45, and the probability of meeting the original 36-month milestone rises from 1% to 13%. The buffer sweep makes the buffer-for-confidence trade negotiable rather than rhetorical.
The sensitivity ranking told the project director where to spend management attention.
The biggest mover was the precast segment delivery cycle: a 30-day shift in the fabrication-line ramp moved P90 by 19 days. Second was the marine-permit windows — the 8% chance of a 120-day regulator backlog was the single largest discrete risk on the project. Third was caisson-sinking duration variance, and fourth was the weather-day clustering parameter. Subcontractor productivity, despite being talked about constantly in management reviews, ranked sixth — its actual spread was narrow on this project type.
This redirected three concrete decisions. The marine-permit application was front-loaded by 6 months (cutting the 120-day backlog tail by half). A second precast yard was contracted as parallel capacity (compressing the fabrication-line risk). The caisson scope was split into two parallel rigs (variance on the max of two is lower than variance of one). After re-simulation:
A bar-chart Gantt showing only modal durations hid the activities with the longest whisker, which are where management attention pays back most. The probabilistic Gantt reordered the team's risk register.
The precast-segment activity and the deck-erection cycle had narrow median bars but enormous whiskers; the river-crossing pile cap had a wide bar but a tight whisker (well-understood scope). The contractor agreed a "fast-track precast" clause with the subcontractor based directly on this chart — paying a 4% premium for delivery guarantees that cut the precast P90 by 22 days.
The project was re-bid with a 41-month base programme and an LD reserve of $14M (the simulated mean exposure). The project finished in month 39.8 — inside the simulated P25, $9M below the recalibrated LD reserve, and 6 months earlier than the simulated P90 of the original schedule. None of those decisions would have been possible if the schedule had remained a deterministic Gantt.
In project management, "the schedule" is a probability distribution. Monte Carlo simulation is what makes that statement actionable instead of philosophical.