Construction Schedule Risk

What is modelled

A project is a network of stages that cannot start before their predecessors finish. The critical path method finds the longest chain, which fixes the project length, and the spare time (float) of every other stage. When durations are uncertain, many random projects are simulated: the finish is the latest of several uncertain finish times, so the chance of meeting a plan built on average durations is lower than it looks.

Equations

• Forward pass ESi = max EFpred, EFi = ESi + di; backward pass LFi = min LSsucc; float TF = LS − ES.
• Triangular durations (0.75 d, d, 1.5 d) for 25 per cent uncertainty, mean (a + m + b)/3.
• Crane-lifted stages scale as d / (1 − downtime); steel delay adds days to the lower frame.
• Probability of finishing by day t is the fraction of simulations with finish ≤ t.

Checks run in the page

• Zero-float chain and the project length.
• Brute-force enumeration of every path.
• The triangular sampler against its mean, variance and mode probability.
• The mean of the simulation against the critical path of the mean durations (merge bias).

Honest simplifications

The network has ten generic stages with invented durations, the crane is not a shared resource that serialises stages (it only adds downtime), triangular distributions are assumed independent and the same relative width for every stage, there are no weather seasons or cost, and the 3,000 simulations use a fixed seed so results are repeatable but still carry a statistical error of about a day.

• Press Windy site, late steel and watch the chance of meeting the deadline drop sharply.
• Press Extra MEP crew and see which stage leaves the critical path.
• Press High uncertainty and compare the planned finish with the 80 per cent finish.