CDT505 Chap.4 Network Scheduling and Critical Paths
Network Scheduling and Critical Paths
Compute dates from dependency logic
An activity-on-node network turns work packages into activities and dependencies. Three-point estimates provide expected durations through the PERT formula. A forward pass establishes earliest dates, using the largest predecessor finish at a merge. A backward pass establishes latest dates, using the smallest successor start at a burst.
Total float is the difference between latest and earliest dates. The longest zero-float route is the critical path that controls the earliest project finish.
Audit logic before trusting arithmetic
Every arrow is a claim that one activity constrains another. Missing links create impossible overlap, while unnecessary links make parallel work falsely serial.
Milestones can carry approval dependencies even when their duration is zero. After calculating float, change one estimate on a near-critical branch and rerun the network; the exercise shows that criticality belongs to the current plan rather than permanently to an activity. Completion probability adds uncertainty, but its interpretation should state the assumed path and any close competing route.
What this chapter covers
- 01
Activity-on-node dependency logic
- 02
Optimistic, most likely and pessimistic estimates
- 03
PERT expected duration
- 04
Forward pass and merge maximums
- 05
Backward pass and burst minimums
- 06
Float, critical paths and completion probability
Worked example · free
Calculate a merged activity network
- 4Run the forward pass.
- 3Run the backward pass.
- 3Identify the path and branch float.
Key terms
- Activity-on-Node
- A network convention in which activities appear as nodes and arrows show precedence.
- Forward Pass
- A left-to-right calculation of earliest activity start and finish dates.
- Backward Pass
- A right-to-left calculation of latest activity start and finish dates.
- Total Float
- The time an activity can move without delaying the project finish.
- Critical Path
- The longest required network route, with zero total float under the current baseline.
Network Scheduling and Critical Paths FAQ
How can I audit a claimed critical path?
Work backward from the finish, selecting the predecessor that determines every merge, and verify each duration against its source estimate. Reperform the forward and backward passes before accepting the zero-float route. Then alter one dependency and recompute, because a logic change can affect the controlling path differently from a simple duration change.
Why does a merge use the largest predecessor finish?
A successor that requires several predecessors cannot start until all of them finish. The last required predecessor therefore controls its earliest start. Adding predecessor finishes would falsely turn parallel work into serial work and overstate the schedule.
What makes an activity critical?
Under the current network and durations, a critical activity has zero total float and sits on a route that controls the earliest project finish. Criticality can change after duration, logic or resource changes, so it should be recalculated.
What must the individual schedule include?
The current brief asks for milestones, at least seven key activities, optimistic, most likely and pessimistic durations, predecessor or successor logic, an expected-duration calculation, a simple logic diagram or table and a clearly identified critical path with an explanation.
Assessment move
Start with activity lists containing seven to nine activities so the network is complex enough to include a burst and a merge but still small enough to audit. Write predecessors before drawing arrows. Check for cycles, disconnected nodes and links that make parallel work falsely serial.
For every activity, calculate the PERT expected duration from optimistic, most likely and pessimistic estimates and keep the unrounded value until the convention in the question requires rounding. Run the forward pass left to right, writing earliest start and finish beside each node. At every merge, box the largest predecessor finish.
Then fix the project finish and run the backward pass, boxing the smallest successor latest start at every burst. Calculate float using both equivalent expressions as an arithmetic check. Trace the zero-float route and explain in words why it controls completion. Repeat the problem after changing one duration on a near-critical branch.
This shows that criticality is a current network property rather than a permanent activity label. Add a due date and, where the source method supplies variances, standardise it against critical-path uncertainty. State the assumption that path identity remains stable and note any close competing path.
For the current individual brief, audit that the plan includes milestones, at least seven activities, three-point estimates and predecessor or successor logic. Finish each practice answer with one management implication: which activity deserves monitoring, where float can absorb movement and what change would require a new baseline. Never present only a highlighted path; show the forward and backward evidence that creates it.
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