SC QUALITY GUILDActivity network, critical path and PERT
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Enter the activities, what each one waits for, and how long it takes. Get the earliest and latest start and finish of each, the slack, the critical path, and with three-point estimates the chance of finishing by a target.
ON THE EXAM · CQPA II.D.1, II.D.2, CQE V.B.7, CSSBB IV.D.5 · FREE · NOTHING YOU TYPE LEAVES YOUR BROWSER
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The activity network
An activity network diagram shows the activities of a project and the order they must happen in. Here each activity is a box (activity on node) and each arrow says "this must finish before that can start". It is one of the seven management and planning tools, and the basis of the critical path method (CPM) and of PERT.
The forward and backward pass
- Forward pass. An activity's earliest start (ES) is the latest earliest finish (EF) among the activities before it. EF = ES + duration. The largest EF is the project duration.
- Backward pass. Working back from the end, an activity's latest finish (LF) is the smallest latest start (LS) among the activities after it. LS = LF − duration.
- Slack (float) = LS − ES = LF − EF. It is how long an activity can slip without delaying the project.
The critical path is the chain of activities with zero slack. It is the longest path through the network, and it sets the project duration. Any delay on it delays the project; time saved off it does not shorten the project.
PERT: three estimates
PERT (program evaluation and review technique) treats each duration as uncertain. With an optimistic time a, a most likely time m and a pessimistic time b:
- expected time te = (a + 4m + b) / 6
- standard deviation σ = (b − a) / 6, so variance = ((b − a) / 6)2
Add the expected times along the critical path for the expected project duration, and add the variances (not the standard deviations) for its variance. The chance of finishing by a target T is then read from the normal distribution with z = (T − expected duration) / σpath.
The figure is usually optimistic. It ignores the other paths, and a path that is nearly critical but very uncertain can finish last. Watch the near-critical activities as well as the critical ones.
Crashing and fast tracking
To finish sooner, shorten activities on the critical path, by adding resources (crashing) or by overlapping activities that were in sequence (fast tracking). As the critical path shortens, another path may become critical; recalculate after each change.
Gantt chart or network?
A Gantt chart shows when each task happens on a calendar and is easier to read. The network shows why: which activities drive the finish date. Most projects use both.
On the exam
CQPA lists activity network diagrams among the quality management tools (II.D.1) and PERT and the critical path method among the project management tools (II.D.2). CQE (V.B.7) and CSSBB (IV.D.5) include activity network diagrams. Expect to find the critical path, compute slack, and calculate a PERT expected time and standard deviation by hand.