Honest CPM Scope - Scheduling & the Critical Path

CPM gives exact consequences of fixed durations and precedence. It does not prove those durations are good forecasts or that resource constraints are absent in a real project. A second exact comparison changes one critical duration to show that the model must be recomputed when assumptions change.

highlighted = computed this step

Exact inputs

The computed duration is 11. Why: it follows from fixed activity durations and fixed precedence arcs. Interpretation: CPM proves a consequence of the inputs; it does not certify that the inputs are realistic.

T=11

Noncritical room

Activity B slack is 1 and activity D slack is 2. Why: not every activity sits on the longest path. This is useful operationally because it separates modeled finish drivers from activities with schedule room.

S_B=1\quad S_D=2

Second exact comparison

If activity C duration is changed to 5, the recomputed project duration becomes 12, an increase of 1. Why: changing a critical activity changes the longest path in this exact comparison.

T_{\text{comparison}}=12

Model boundary

These are exact CPM values for a pinned activity-on-node DAG with fixed durations and no resource limits; real project forecasts need measured durations, calendar constraints, and update evidence. Pixel positions are rounded for layout; every number shown is exact.

\text{exact model first, empirical fit later}