Industry: Project Management
Product: ModelRisk
Application: Resource Planning

Planning for the P80, Not the Plug Number: Probabilistic Resource Planning

PMI benchmarks put cost overruns on large infrastructure programmes at 10–30%, schedule overruns at 20–50%, and contingency reserves typically set somewhere between 5% and 25% — yet the resource plan that drives the budget is still, in most firms, a single column of hours and unit rates with no probability attached. When a $180M renewable-energy program priced its labor plan deterministically at $134M of total installed cost, the simulation showed that figure was the P32, not the median — the probability of finishing within the deterministic budget was just 32%, not the 50% the team assumed. The chart below is the labor-hour engine underneath that cost: a full distribution where the deterministic 1.42M-hour plug is no longer a single answer but a point on a curve.

The owner moved its baseline from "the deterministic plan plus a flat 15% contingency" to "the P80 of the simulated cost," with the gap between P50 and P80 made explicit. ModelRisk was the engine.

What goes uncertain, and how

A resource plan has three layers of uncertainty that compound: how many hours each task will need, how productive each hour will be, and how much each hour costs. Each was given a distribution defensible against historical data, and none was modeled as Normal where it shouldn't be.

Task hour requirements. Each WBS-3 task got a PERT distribution from the project controls historian — for the turbine-pad concrete pours, for example, optimistic 1,800 hr / most-likely 2,400 hr / pessimistic 3,800 hr per pad, with the long right tail driven by re-work and weather windows.

Labor productivity. Modeled as a Beta(8, 2) distribution on the range [0.65, 1.20] of nominal, mean ≈ 1.09, calibrated against the firm's last 12 wind farms. Productivity is bounded — a 1.5× crew is not a real outcome — and Beta carries that constraint where Normal would not. (A mean above 1.0 is why the simulated hour count lands slightly below the deterministic plug even as cost runs over.)

Material lead time. LogNormal with mean = 22 days, σ_log = 0.55 (P90 ≈ 39 d, P99 ≈ 64 d) — the standard skewed shape of overseas component logistics; a single port strike or vessel-schedule slip is in the right tail.

Hourly composite labor rate. Truncated Normal at $74/hr ± $6/hr, clipped at $60 and $95; rate floors and ceilings are real because of master labor agreements.

Cross-task correlation. Weather-sensitive tasks share a 0.45 rank-correlation on duration; the Wilson-EOQ-style assumption that task durations are independent is wrong on every construction job in history, and ModelRisk's correlation matrix handles it directly.

The deterministic plan and what it hid

The plug numbers in the cost script summed to 1.42M labor hours and $134M total installed cost. The simulation:

The instructive part is the disagreement between the two rows. On labor hours, the 1.42M plug is actually a touch conservative — it sits around the P67, because the productivity factor (which the team calibrated optimistically high) pulls the hour count down in most iterations. Yet the cost plug of $134M is the P32: a moderately optimistic figure with only a 32% chance of being met. The plan was under-counting cost while over-counting hours, because the dollar tail is driven by the composite-rate and material-lead-time distributions, not by hours alone. Calling a single number "the estimate" hides exactly this kind of cross-cancellation — and a probability distribution on each output is the only way to surface it before the steel is on order.

Cost vs. hours: which inputs move which output

Resource planning lives in two output dimensions, and the drivers of one are not the drivers of the other. A sensitivity ranking on total installed cost put labor productivity at the top:

Productivity dominates because it multiplies across every task. Material lead times rank second because they trigger demobilization-remobilization charges and idle-crew overhead — a non-linearity the deterministic plan compounds badly. Composite hourly rate ranks third; component price is far down the list because the contract is partly fixed-price. This ranking told the team where to spend its risk-reduction dollars: a productivity-tracking incentive structure (worth ~$3.4M at expected value) beat any further wage-negotiation effort.

Two resource strategies, two cost curves

The team compared the baseline crewing plan against an alternative "smooth crewing" plan that limited peak-month headcount to 165 (vs. unconstrained peak ~210) by stretching three non-critical work packages. Re-running the simulation under both plans:

The smooth plan added 11 days to the P50 finish but, by levelling the crew, avoided most of the demobilisation-remobilisation and idle-crew charges that pile up on the worst iterations. The net effect was a small, broad improvement: roughly $0.3M off the P50 and the mean, and about $0.6M off the P95. The two CDFs sit almost on top of each other, which is itself the finding — at this programme's cost structure the dollar tail is driven far more by the composite rate and material-lead-time distributions than by crew profile, so headcount smoothing buys schedule stability and a modest tail trim rather than a dramatic cost cut. The model didn't pick; it showed that the case for smoothing here rests on cash-flow and schedule grounds, not on a large P95 saving.

What changed

• Baseline budget reset from $134M (plug) to $154M (P80) with the $20M gap shown to the steering committee as the true contingency for the plan, not a flat 15% on top of an underestimate.
• Peak-month crewing capped at 165 under the smooth plan, trimming the demob/idle-crew tail and stabilising cash flow — a modest P95 cost reduction of roughly $0.6M, chosen mainly for the schedule and phasing benefits rather than headline savings.
• A WBS-3 resource histogram that finance can use as the basis for cash-flow phasing, replacing the prior static S-curve that assumed perfectly even draws.

ModelRisk Functionality Used

• PERT distributions for ~140 WBS-3 task hour requirements fitted against the project controls historian using the distribution-fitting dialog.
• Beta(8, 2) productivity factor on [0.65, 1.20] applied as a multiplier across all craft tasks — keeping the variable bounded where Normal would have allowed nonsensical >150% outcomes.
• Rank-correlation matrix (ρ = 0.45) linking weather-sensitive task durations so storm shocks compound; LogNormal(μ = log(22), σ = 0.55) for material lead times.
• Tornado over total installed cost that selected productivity tracking (~$3.4M EV) as the highest-return mitigation rather than wage re-negotiation.
• Scenario re-simulation comparing baseline vs. smooth-crewing strategies, producing the P50/P80/P95 contrast that selected the smooth plan for the fixed-price wrap.

Resource planning is not "what is the most likely hour requirement" — it is "what does my organisation need to commit to so that I am 80% confident of staying within plan." Monte Carlo simulation in ModelRisk turns that second question from a guess into a number with a chart underneath it.