| Vose Software

Industry: Project Management
Product: Tamara
Application: Resource allocation optimization


How Many Days of Contingency Buys an 80% Chance of Finishing On Time? +242

A bridge delivery was scheduled around a single specialist crew and one heavy crane serving four work packages that, on paper, could run in parallel. They cannot: a crew can only be in one place at a time, so the packages run in series whether the bar chart admits it or not. Built the orthodox way — most-likely durations rolled through the logic network — the schedule showed a 735-day, May 2028 finish. The real question for the board was never the single date; it was how much contingency to set aside, and for what level of confidence.

Rebuilt in Tamara, Vose Software's Monte Carlo project risk tool, with the resource-serialised packages modelled as a real chain and six discrete risks on top, the contingency ladder answers that directly — pick a confidence level, read off the buffer:

Contingency ladder of buffer days beyond the 735-day plan at P50, P70, P80, P90 and P95

Each rung is days beyond the 735-day plan. P50 needs +169 days (finish 904), P70 needs +214 (949), P80 needs +242 (977), P90 needs +280 (1,015) and P95 needs +312 (1,047). The plan itself has only a 1% chance of being met, so the choice is not whether to hold contingency but how much: the P80 buffer is 242 days — roughly 7.9 months — and it lives almost entirely in the resource bottleneck.

Activity-Level Spread

The same simulation places every activity in time as a band, not a bar — and the resource-serialised crew packages stack head-to-tail rather than overlapping:

Stochastic Gantt showing resource-serialised packages with P10 to P90 finish spread

The whiskers widen downstream because each package inherits the spread of everything queued ahead of it for the crew, so handover carries the accumulated variability of the whole serialised chain. The simulated finish runs P10 803, P50 904, P90 1,015 days, mean 907 against the 735-day plan.

Where the Duration Risk Actually Lives

Tamara ranks each activity by cruciality — the rank-correlation between its duration and the project finish, i.e. how much its variability actually moves the end date:

Schedule tornado ranking activities by cruciality correlation with the finish date

Steel assembly — the welder-limited task — dominates (cruciality 0.53), ahead of pier set A (shared crew, 0.38) and soil-sensitive excavation (0.38). This is the signature of a resource-constrained schedule: the finish is governed not by the largest package but by the one that monopolises the scarce crew. Adding labour anywhere except the welder queue moves nothing; the tornado says exactly where the queue is.

Schedule Risk Is Cost Risk

Every day beyond the plan carries extended preliminaries and standing plant-hire, so the schedule distribution drives the cost distribution. Tamara let the team price the obvious de-bottlenecking move — a second specialist crew and a backup crane so the two pier sets run concurrently with steel assembly, plus a welder pre-commitment — and compare before/after on one axis:

Project cost distribution before and after de-bottlenecking against the budget

Without the second crew the cost runs to a mean of $95M and a P90 of $105M, with a 27% probability of breaching the $100M budget. De-serialising the crew packages cuts the P80 finish by 184 days (977 → 793 days) — the single largest schedule move in this study — and because schedule drives cost, the overrun probability falls from 27% to 3% and the P90 cost drops to $96M. The extra crew pays for itself many times over in avoided extended-overhead, not in the line items it touches.

The Discrete Risks That Drive the Tail

Six discrete events were modelled as Bernoulli risks, several attacking the resource-limited tasks directly. Ranking them by expected schedule impact (probability × delay) gives a clean Pareto:

Pareto of discrete risk events by expected schedule impact

Five of the six events carry ~80% of the expected discrete-event delay — a skilled-welder shortage (4.8 weeks expected), the crew being double-booked off the project (3.1), a soil/dewatering surprise (2.5), a crane breakdown (2.2) and a subcontractor M&E delay (2.1), with material-price escalation (2.0) trailing. The two largest both strike the shared resource — confirming that the resource queue, not the work content, is the exposure.

What Tamara Changed

  • The contingency decision became a confidence choice, not a guess — the ladder put a number on every rung from P50 (+169 d) to P95 (+312 d), and the board funded the P80 buffer of 242 days.
  • The bottleneck was identified by data, not intuition — steel assembly's cruciality of 0.53 named the welder queue as the governing constraint.
  • A second crew and backup crane were justified on their schedule effect — a 184-day P80 reduction, the dominant lever in the model.
  • The de-bottlenecking package cut budget-overrun probability from 27% to 3%, on extended-overhead savings rather than direct line items.

Tamara Functionality Used

  • Monte Carlo schedule simulation over a resource-serialised activity network with Beta-PERT durations.
  • Contingency-ladder analysis translating the finish distribution into a buffer-per-confidence schedule the board can fund.
  • Discrete risk-event modelling (Bernoulli occurrence × Triangular impact) targeting the resource-limited tasks.
  • Criticality and cruciality analysis isolating the shared-resource bottleneck from the largest work package.
  • Integrated cost–schedule modelling linking finish-date overruns to extended-overhead cost.
  • Scenario comparison quantifying the de-bottlenecking package's before/after impact on both the P80 finish and the overrun probability.

A resource-constrained schedule is not governed by its biggest task; it is governed by the queue for its scarcest crew. Tamara is what makes that queue visible, prices the move that clears it, and tells the board exactly how much buffer to hold.