PMGT1865 Chap.4 Forward Pass, Backward Pass and the Critical Path
Forward Pass, Backward Pass and the Critical Path
Step five of the schedule process is six moves long: transfer the durations onto the network, run the forward pass, run the backward pass, calculate float on every activity, determine the critical path, and convert the result into a chart. This chapter is the middle four, and they are entirely mechanical.
That is good news and bad news at once, because nothing here requires judgement and every mark lost is therefore lost to a slip. The whole calculation is three lines: early finish is early start plus duration, late start is late finish minus duration, and float is late start minus early start.
Two rules decide which number to pick when a node has several neighbours: take the highest early finish at a merge going forwards, and the lowest late start at a burst coming back. The chapter closes with a diagnostic clinic, because the useful skill is not recomputing a failed pass from scratch but reading the symptom and knowing which single place it points to.
What this chapter covers
- 01
The three lines of arithmetic every schedule question in the unit reduces to
- 02
The vocabulary this chapter is graded on: dependencies, milestones, float, critical activities, critical path
- 03
The forward pass, and the highest early finish rule at a merge
- 04
The backward pass, and the lowest late start rule at a burst
- 05
Why the last node's late finish is seeded with its early finish, and what a different seed would mean
- 06
Float computed two ways, and what a disagreement between them reveals
- 07
Total float against free float, and why one is shared along a chain and the other is not
- 08
The critical path as a connected chain of zero float activities, checked against the project duration
- 09
Six diagnostic symptoms and the single place each one points to
- 10
Why an imposed date earlier than the network gives is a different question, not negative float
Computing a schedule end to end
- +1Forward, start node. A begins at 0 and runs 4 days, so it finishes at 4.
- +1Forward, the burst. B, C and E all start at 4 and finish at 10, 12 and 14.
- +1Forward, first merge. D waits for both B and C, takes the higher early finish of 12, and runs 12 to 17.
- +1Forward, second merge. F waits for D at 17 and E at 14, takes 17, and runs 17 to 20. G then runs 20 to 22, so the project duration is 22 working days.
- +1Backward, finish node. Seed G with a late finish of 22, giving a late start of 20. F therefore has a late finish of 20 and a late start of 17.
- +1Backward, through the merges. D and E both take a late finish of 17, giving late starts of 12 and 7. B and C both take a late finish of 12, giving late starts of 6 and 4.
- +1Backward, the burst. A's successors have late starts of 6, 4 and 7, so A takes the lowest, 4, as its late finish and returns a late start of zero. That zero confirms both passes.
- +1Float and the path. Float is late start minus early start: A 0, B 2, C 0, D 0, E 3, F 0, G 0. The zero float activities form the connected chain A, C, D, F, G, and 4 plus 8 plus 5 plus 3 plus 2 is 22.
Key terms
- Early finish
- The earliest an activity can be completed, computed as its early start plus its duration during the forward pass.
- Late start
- The latest an activity can begin without moving the project finish, computed as its late finish minus its duration during the backward pass.
- Total float
- How far an activity can slip before the project finish moves. It is shared along a chain, so two activities on the same path may each show three days and it is the same three days.
- Free float
- How far an activity can slip before the next activity has to move. It belongs to that activity alone, so spending it disturbs nobody downstream.
- Critical activity
- An activity with no float. Delay it by one day and the project finishes one day later, which is the entire content of the word critical in this unit.
- Parallel critical paths
- Two or more connected chains of zero float activities running from start to finish. Nothing is wrong when this happens; the project simply has two chains to protect rather than one.
Forward Pass, Backward Pass and the Critical Path FAQ
What does it mean if the first node's late start does not come back to zero?
One of two things, and both are local. Either a merge or a burst was resolved with the wrong rule, which is the more common cause, or a duration was used inconsistently between the two passes. Stop and find it before filling in any float, because every number after the error inherits it. Recheck every node with more than one arrow first, then compare the durations cell by cell against the source table.
Can the critical path move?
Yes, and it does so as soon as anything changes. Shortening a critical activity far enough hands the title to a chain that used to have float, which is why a compressed schedule is recomputed from scratch rather than adjusted. It also means the path is a property of the current plan rather than of the project, and reporting it without the date it was computed on is how a stale diagram outlives its usefulness.
Is the longest activity always on the critical path?
No, and the studio example is built to make that visible. The microphone order is the single longest activity at ten days and it is not critical, while the acoustic shell at eight days is. Criticality is about position in the logic, not about length: an activity is critical when nothing downstream can absorb its delay, and a long activity sitting on a short chain can have plenty of room.
What should I do when the sponsor demands an earlier finish than the network gives?
Compute the honest network first and report it, then treat the demand as a separate question. Forcing the backward pass to the imposed date produces negative float, which is not a schedule and cannot be worked to. Say by how much the project must be compressed, then name the candidates, which can only be activities on the critical path, and say what compressing each would cost in resources or in risk.
Assessment move
Speed on this material comes from order, not from hurry, so fix an order and keep it. Copy the durations onto the diagram and check them against the table. Circle every merge and burst. Run the forward pass in one sweep without stopping to think about float. Run the backward pass in one sweep. Confirm the first node returns zero. Only then fill the float column, and only then trace the path.
Interleaving the passes is how a number from one ends up in the other. Practise on tables you have not seen worked, and write every intermediate value on the page, because working done in a calculator cannot be part marked and a single arithmetic slip only costs you the cells downstream of it if the method is visible.
Finally, get into the habit of finishing with a sentence rather than a diagram: which activities must the project manager watch, and which long looking activity has room. That sentence is what the question was actually asking for.
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