Industry: Construction and Infrastructure Product: ModelRisk Application: Managing and Mitigating Cost Overruns in Large-Scale Infrastructure Projects
The deterministic estimate said $500M. The owner added 8% contingency for an approved budget of $540M. The probabilistic rebuild in ModelRisk showed the mean simulated cost at roughly $544M, the P90 at $604M, and a 51% probability that the project would breach the $540M budget. Eight percent is the construction-industry default. On this project, with this risk profile, the right number was closer to 16%.
Cost-overrun analysis in infrastructure is not really about cost. It is about correlation. Steel, fuel and equipment costs do not drift independently — they move together when oil prices spike. Material costs and labor costs are linked through schedule extension. Treat the cost stack as nine independent triangular distributions and Monte Carlo will give the right mean and badly under-state the tail.
The bottom-up estimate decomposes into ten cost lines:
The cost-component distributions are LogNormal, not Normal. The reason is simple: a cement cost cannot go below zero; the upside (a 20% price shock) is observed more often and is larger than the downside (a 10% drop). LogNormal captures both. Normal allows negative costs and symmetric tails that the industry data refuses to give back.
The two single biggest moving parts — steel and equipment & fuel — also carry a 6% probability of a 25–40% price shock event (a supplier failure, a geopolitical fuel-price jump, a strike). A shock-augmented LogNormal captures what a plain LogNormal would smooth out.
The classic in-house cost model treats every line as independent. The real world has clear correlation structure:
ModelRisk's Gaussian-copula construction lets the team specify these as rank correlations that hold across the entire joint distribution — most importantly in the tail. Independence would have given an annual mean of $544M with a much tighter spread. The copula widens the P90 by roughly $32M, because in years where steel is up, fuel is usually up too. That is exactly the kind of compounding risk single-point cost estimators do not see.
The deterministic S-curve plots cleanly to $500M at month 36. The simulated P10–P90 envelope tells the real story: by month 20 it already straddles the approved $540M budget cap, and by month 36 the P90 trajectory is around $604M — $64M above the budget line. The fan widens through construction because every monthly draw of steel, fuel and labor compounds the gap. An owner setting contingency by industry rule-of-thumb (8% on top of the point estimate) is implicitly betting that the P50 trajectory holds — and the simulation says the P50 trajectory sits essentially on the budget cap, with a 51% chance of finishing above it.
The contingency-sweep curve plots P(total cost ≤ budget) directly against the contingency percentage, for both the unhedged baseline and the hedged variant — letting the board read off the confidence level for any candidate number:
Reading off the unhedged curve: an 8% contingency ($540M) buys ~49% confidence, a 20% contingency ($600M) buys ~89% confidence, and a 21% contingency ($604M) clears the 90% line. The 80% probability-of-meeting-budget target — the standard owner board-approval threshold — needs roughly 16%, not 8%. The hedged curve sits visibly above the unhedged one at every contingency level, with the gap widening above 15%: the hedging program buys more probability than it costs everywhere, but the marginal value of hedging is highest exactly where the unhedged curve is still climbing through the high-stakes 70–85% confidence band.
The top three contributors to total cost variability are change orders, direct labor and steel & rebar. Change orders — modeled as a Beta scaled to 20% of contract value, mean 8% — is the single line the owner most directly controls (through design freezes and scope discipline). The team's mitigation priorities follow the tornado, not the deterministic spreadsheet's largest absolute line items.
Cost overrun and schedule extension are not independent draws — they share the copula factors (steel / fuel / labor) and are linked structurally through the per-month extension charge. The joint-density chart makes the dependence visible:
The joint quadrant — total cost above $540M and schedule more than 6 months over plan — is roughly 2–3× more likely than independence would predict. That is the trial where everything goes wrong together: commodity shock, labor squeeze, schedule extension, idle equipment, LD exposure. An owner who books contingency for cost overrun and a separate reserve for schedule extension is double-paying for the marginal trials and severely under-providing for the joint trials. The copula-aware view says: book a single reserve sized to the joint quadrant, not two independent ones.
Cost overrun is not a number. It is a distribution that depends as much on what moves together as on what moves. Monte Carlo simulation in ModelRisk is what makes both visible — and once they are visible, contingency stops being a percentage rule-of-thumb and starts being a defensible confidence level.