CVEN9702 Chap.2 Project Networks and Critical Paths
Project Networks and Critical Paths
Project networks translate activity dependency into time. A forward pass calculates earliest times and takes the latest predecessor finish at a merge. A backward pass calculates latest times and takes the earliest successor late start at a burst. The longest complete path sets minimum duration. Float explains how much movement is available and whether that movement affects successors or project completion.
What this chapter covers
- 01
Represent physical and approval dependencies explicitly
- 02
Calculate earliest starts and finishes with a forward pass
- 03
Calculate latest starts and finishes with a backward pass
- 04
Identify every zero-float critical path
- 05
Distinguish total, free and interfering float
- 06
Recalculate criticality after logic or duration changes
Worked example · free
Find the controlling branch at a merge
- +1Forward pass gives A zero to three, B three to eight and C three to seven.
- +1D waits for the later predecessor, runs eight to ten and sets project duration at ten days.
- +1Backward pass sets D late start eight, B late start three and C late start four.
- +1A-B-D totals ten days and is critical; A-C-D totals nine.
- +1C total float is four minus three, or one day, matching the path-length difference.
Key terms
- Precedence relationship
- The logical rule connecting activities because one depends on the progress or completion of another.
- Forward pass
- The calculation of earliest activity times from project start toward project finish.
- Backward pass
- The calculation of latest allowable times from project finish back toward project start.
- Critical activity
- An activity on a longest controlling path whose delay can delay project completion.
- Interfering float
- The portion of total float that can be used only by moving a successor later while protecting project finish.
Project Networks and Critical Paths FAQ
Why does a merge use the maximum predecessor finish?
A successor that needs several predecessors cannot start until all are complete. The latest predecessor therefore controls its earliest start. Taking an average or the earliest finish would allow work to begin before one required input is ready.
Is every important activity critical?
No. Criticality is a time property produced by network logic and durations. A commercially important activity may have float, while a modest inspection may be critical because it controls all following work. State both importance and criticality when they differ.
What is the difference between total and free float?
Total float protects project completion. Free float is the movement available without delaying a successor. Using total float beyond free float can keep the project finish unchanged while transferring pressure to downstream activities.
How should an overlapping relationship be checked?
State its physical reason, type, lag and calendar, then change both durations to test behaviour. Replace unexplained long lags with visible work that needs ownership.
Exam move
Draw networks before calculating. For each activity, write the predecessor reason so missing and artificial links are easier to detect. Run the forward pass from left to right, taking the maximum predecessor finish at every merge. Run the backward pass from right to left, taking the minimum successor late start at every burst. Calculate total float two ways from start and finish values and make sure the answers agree.
Then calculate free float and explain the difference in words. Build a quick path-length check beside the formal passes; for a small network, the controlling path total should equal the project duration. Practise cases with two critical paths, because later compression and resource questions depend on identifying every controlling branch.
When an answer produces negative float, ask whether the target finish is externally imposed or whether the pass contains an error. Add relationship types only after the finish-to-start network is reliable. For each start-to-start, finish-to-finish or lagged link, write the physical reason and test whether it accidentally duplicates another constraint.
Translate the relationship into a sentence before calculating: for example, the follower may start two days after the predecessor starts, but neither statement says when either activity finishes. Construct one network with a merge, a burst and two near-critical paths; then change one duration by a day and observe which floats and controlling paths move.
This sensitivity drill prepares you for compression and delay questions where criticality is not fixed. Audit event numbering or activity labels so every predecessor and successor can be traced. If using a table, reconcile its early and late dates with a hand-drawn path list. Finally, explain float ownership cautiously.
Total float is a property of the network and its constraints, not a private stock that one trade may consume without consequence. State which successor moves, whether completion changes and which assumption creates the flexibility. A complete answer therefore combines a valid dependency model, transparent max-and-min calculations, an independent path check and a management interpretation of the resulting movement.
