Finding the critical path

With early and late dates for every activity, you can see how much room each one has.

Total float

Total float = LS − ES = LF − EF

It is the number of days an activity can slip without moving the project finish. For the product launch:

ID	Activity	ES	LS	Total float
A	Define requirements	0	0	0
B	Design the product	3	3	0
C	Plan the marketing	3	4	1
D	Build the product	7	7	0
E	Produce the campaign	5	6	1
F	Set up the web shop	5	13	8
G	Launch rehearsal	12	12	0
H	Go live	16	16	0

The critical path

The activities with zero float form a chain from start to finish: A → B → D → G → H. That is the critical path. It is also the longest path through the network: 3 + 4 + 5 + 4 + 2 = 18 days, which is exactly the project duration. Any delay on it delays the project, day for day.

The next path, A → C → E → G → H, takes 17 days. Its activities have 1 day of float, so it is near-critical: one bad day and it becomes critical too. F’s path is only 10 days long, so F has 8 days to spare.

Scheduling tools usually mark an activity critical when its total float is zero or less; that is P6’s default. P6 can also show the longest path instead, which stays reliable when calendars and constraints make float numbers hard to compare.

Shortening the project

Two lessons follow from the table.

1. Only the critical path sets the finish. Shortening F by 5 days changes nothing; shortening D by 1 day brings the finish in by a day.
2. The critical path can move. Shorten the A-B-D-G-H path by more than 1 day and A-C-E-G-H, at 17 days, takes over. To finish 2 days earlier you have to shorten both paths.

There are two ways to shorten a path:

• Crashing: add people or equipment so an activity takes less time. It usually costs money, and not every activity can be crashed.
• Fast-tracking: overlap activities that were in sequence, for example by turning an FS into an SS with a lag. It costs nothing up front but adds risk, because the second activity starts on incomplete information.

Your turn

In the lab, the target is Go live by Day 16. You may shorten only B, D and E. Watch the float column after each change: the moment one path has been cut enough, the other one turns red.