Industry: Construction and Infrastructure Product: ModelRisk Application: Labor Productivity Analysis
The $310M highway-upgrade package was planned around a single deterministic productivity figure: 4.6 cubic metres of concrete placed per worker-day. Schedules, crew counts and contract durations were all derived from it. The probabilistic rebuild in ModelRisk — sampling weather, crew skill, equipment availability and fatigue as separate distributions, with weather treated as a single project-level shared factor — showed the realised productivity median was closer to 4.3 m³/wd, and the probability of meeting the 396-working-day contract was only 58%. A productivity number that looked precise to two significant figures was, in fact, a distribution whose right tail mattered to the contract.
The error is structural: industry-standard productivity rates are averages over conditions that vary day-to-day and crew-to-crew. Using the average as if it were a constant is the deterministic mistake. The probabilistic alternative — treating productivity as the product of four independent-but-shared factors — gives the schedule its real shape.
Productivity P (m³/worker-day) is modelled as a multiplicative factor stack:
\[ P = P_0 \cdot W \cdot S \cdot E \cdot F \]
The shared weather factor is the single biggest reason a probabilistic model differs from a deterministic one. On a wet day every crew is slower, every cubic metre takes longer, and every dependent task starts late. Independence-assumption Monte Carlo gives back something close to the deterministic mean and almost nothing in the tail.
A single representative project realisation — 14 crews × 18 weeks — lays the productivity field on a heatmap. Whole columns (project weeks) move together because the weather index is shared across crews; whole rows (crews) drift because of the persistent crew-skill multiplier:
The yellow-green columns are the dry, well-staffed weeks (productivity 4.4–5.1 m³/wd); the red columns are the bad-weather weeks where every crew slows together (productivity dips to 3.4–3.8 m³/wd). The row variation is real but smaller — the difference between the strongest and weakest crew on a typical week is about 0.5 m³/wd, while a bad-weather week shaves 1.0+ off every crew. Aggregated across 20,000 such project realisations, the simulated project-average productivity has mean ≈ 4.28 m³/wd, P10 ≈ 3.90, P90 ≈ 4.65 — strictly below the deterministic baseline 4.6 by about 7%. The deterministic plan implicitly assumed a productivity higher than the simulated median, because the asymmetric tail to the low side is dominated by the shared-weather columns.
The 142,000 m³ scope, at the deterministic productivity, plots to a single straight line that crosses the scope target at day 376 — about a 20-day cushion against the 396-day contract. The simulated trajectories tell the real story:
The deterministic line is the dashed straight trajectory. The P50 simulated path crosses the 142,000 m³ scope line at roughly day 389; the P10 (lucky) path crosses around day 354; the P90 (unlucky) path crosses around day 433. P50 finish ≈ 389 days, P90 ≈ 433 days; the probability of missing the 396-day contract is 42%. The 20-day deterministic buffer was a coin-flip, not a guarantee. The wedge between the P10 and P90 trajectories widens steadily through the project — bad weeks compound rather than self-correct, which is exactly the asymmetric tail that an independence-assumption Monte Carlo misses.
The shared weather index is the largest single mover of P90 finish — bigger than the per-crew skill mix or per-day equipment shortage. Crew skill is second; equipment availability is third. The fatigue cycle and quantity-scope-creep show up as smaller but real contributors. This ranking directs mitigation investment: weather sheds and outdoor-work scheduling first; targeted crew training second; backup equipment third.
A three-part mitigation package — crew training, backup equipment pool, shift-rotation policy — collectively reduces the weather-shock sigma from 0.16 to 0.06. The threshold-sweep below treats spend as a continuous lever and reads off the probability of meeting the contract:
At zero mitigation spend, the probability of meeting the 396-day contract is 58% (red curve) — and the 416-day cushion (a 5% schedule buffer) is met 79% of the time (green curve). The full $1.2M package — training + spares + shift rotation — lifts the on-time probability to ~99%, with the red curve crossing the 90% target around $800k of spend and the green cushion curve clearing 90% far earlier, around $330k. The curve is steepest in the first ~$500k of spend (where training and basic spares retire the largest chunk of weather-shock dispersion) and then flattens — additional spend buys diminishing returns because the residual variability is the fundamental weather randomness no training programme can shape away. The mitigation cost is roughly $1.2M; the expected liquidated-damages exposure avoided (at $80k/day × expected days late) is several times that. The tail protection — going from a 42% to a ~1% probability of breach — is what convinced the executive committee.
Productivity is not a number; it is the product of factors that share weather and crews. Monte Carlo simulation in ModelRisk is what makes that product visible — and once it is visible, the difference between "the schedule has a 20-day buffer" and "the schedule has a 65% chance of holding" stops being a rhetorical distinction and becomes a contracting one.