The Critical Path

The Critical Path

The critical path is the zero-slack longest path through the project DAG. In this example, the marked activities determine the project duration. The lesson connects the table interpretation to the graph: zero slack in the schedule becomes a critical route through the dependency network.

highlighted = computed this step

Critical activities

There are 4 critical activities. Why: each has zero slack in the recomputed schedule. Interpretation: these are the activities that currently control the modeled finish.

critical activities=4\text{critical activities}=4
critical path graphABCDEF

Zero slack path

The slack values on A, C, E, and F are all 0. Why: delaying any one of them delays the project finish. Their zero slack is the schedule signal, not a theme or drawing convention.

SA=SC=SE=SF=0S_A=S_C=S_E=S_F=0
critical path graphABCDEF

Critical path duration

The critical path duration is 11. Why: it matches the project duration from the forward pass. Interpretation: the longest path is the reason the whole modeled project cannot finish earlier.

T=11T=11
critical path graphABCDEF

Diagram note

The graph marks the recomputed critical tasks and critical precedence arcs by role. The same exact schedule table determines those marks, so the diagram is evidence rather than decoration. Pixel positions are rounded for layout; every number shown is exact.

critical path is a longest path in the DAG\text{critical path is a longest path in the DAG}
critical path graphABCDEF