PERT & Three-Point Estimate Calculator (with Monte Carlo)

About the PERT & Three-Point Estimate Calculator (with Monte Carlo)

Give each task an optimistic, a most likely and a pessimistic estimate — of its duration or of its cost — and the tasks it waits for. The calculator works out each task’s PERT mean (O + 4M + P) ÷ 6 and standard deviation (P − O) ÷ 6, finds the critical path, the expected total along it and the floats of the other tasks, and gives the chance of finishing by a target date or duration, or within a budget.

A Monte Carlo simulation then runs the project 10,000 times with each estimate drawn from a beta-PERT or a triangular distribution: it gives the P50, P80 and P90 totals (and dates, with a start date and your working week), the chance of meeting the target when the other paths are counted too, and how often each task is on the critical path. Estimates that are out of order (an optimistic value above the most likely) are caught. The free preview shows the expected total and watermarked charts; the percentiles, probabilities and the schedule table, and its CSV for Gantt tools, need a Pro pass.

The formulas

PERT, the Program Evaluation and Review Technique, comes from the US Navy’s Polaris programme (Malcolm, Roseboom, Clark & Fazar):

• Mean of a task: (O + 4M + P) ÷ 6, which weighs the most likely estimate four times.
• Standard deviation: (P − O) ÷ 6, so the range from optimistic to pessimistic covers about six standard deviations; the variance is its square.
• Project total: for a schedule, the longest path through the network of means (the critical path), worked out with a forward and a backward pass; for costs, the sum of the means.
• Its spread: the square root of the summed variances of the critical tasks (or of every cost item), treating the estimates as independent.
• Chance of meeting a target T: Φ((T − total) ÷ standard deviation), the normal distribution’s value for that z; and the total for a chance p is total + z(p) × standard deviation.

Why the simulation often says later than PERT

PERT’s formula looks only at the critical path. When another path is almost as long, it becomes the longest one in many runs, and the project always waits for the later of its paths, so the real chance of finishing on time is lower than the formula says. The simulation counts every path in every run: that is why its average and its P80 are often above the PERT figures, and why a task with float can still be on the critical path in a share of the runs — the table shows how often.

Beta-PERT or triangular?

Beta-PERT draws each estimate from a beta distribution between O and P with its peak at M and the PERT mean (O + 4M + P) ÷ 6, so the simulation matches the formula. Triangular draws from a triangle with the same three corners: its mean, (O + M + P) ÷ 3, gives the pessimistic estimate more weight, so a skewed estimate (P far above M) gives a later total. Use triangular when the pessimistic case is as believable as the others; otherwise beta-PERT.

Dates, links and task lists

• With a start date, durations in working days skip your weekend and the holidays you list; one working day starts and ends on the start day. Calendar days and weeks count every day.
• Links are finish-to-start without lag: a task starts when all the tasks it comes after have finished. Model a waiting time as a task of its own.
• A list from the WBS maker, a spreadsheet or a scheduling tool can be pasted with its header row; the Schedule (CSV) has ID, Task, Duration and Predecessors columns first, as Gantt and spreadsheet tools read them.

Limitations

• Estimates are treated as independent. If tasks run late for the same reason (one supplier, one team), the real spread is wider than both PERT and the simulation show.
• Only finish-to-start links without lag, and no resource limits: two tasks the same person must do can overlap in the schedule.
• The figures are only as good as the three estimates: ask the people who will do the work, and keep the pessimistic case honest.
• At most 300 tasks; the simulation always runs 10,000 trials.

Privacy

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