Critical path and float

The critical path is “the sequence of activities that must be completed on schedule in order for the project to be completed on schedule” [1]. Float (or slack) is how far any other task can slip before it, too, moves a date that matters.

1. What it is

The method comes from DuPont and Remington Rand UNIVAC, developed in 1957 and published in 1959. Its rule: “A delay in a critical job will cause a comparable delay in the project completion time” [2]. Brooks put it in a manager’s terms: the network “shows who is on the critical path, where any slip moves the end date” [3].

2. How the two passes work

The forward pass walks the activity network from the start: each task begins as soon as its last predecessor finishes, giving its earliest start and the project’s shortest length. The backward pass walks back from that finish: each task must end before its first successor has to start, giving its latest finish. Float is the window between the two, minus the duration. Tools do the arithmetic; the manager reads the result.

3. Example: the last nine weeks of Quill

Quill is a fictional word processor, nine weeks from going live at a publishing house. Three streams of work merge into one acceptance run (durations in weeks).

Quill's activity network: A, B and G form the nine-week critical path with zero float; C–D carry one week of float and E–F four

The passes give each task its float, in weeks:

Task Total Free What it means for the manager
A, B, G 0 0 Critical: a week lost here is a week lost on go-live
C. Set up EU data centre 1 0 One spare week, shared with D
D. Cloud sync 1 1 The week is D’s only if C finishes on time
E. Citation styles 4 0 Dana may slip four weeks, but every week she takes is F’s
F. Accessibility review 4 4 The reviewer’s four weeks are his alone

The critical path is A–B–G, nine weeks. For example, the vendor’s PDF engine arriving a week late moves go-live by a week; setting up the data centre a week late moves nothing, but leaves cloud sync no margin.

4. Total float and free float

Kelley and Walker defined four kinds of float [2]; managers use two [1]:

  • Free float is “the range of dates in which an activity can finish without causing a delay in the early schedule of any activities that are its immediate successors.”
  • Total float is “the range of dates in which an activity can finish without delaying the project completion date.”

Total float belongs to the path: “Slack is not additive along a path; it must be shared by all activities on the path” [4]; the first task to spend it takes it from the ones after. So free float is the one for task-level decisions: a developer can spend it without disturbing anyone. Quill’s E and F show the same four weeks of total float, yet only F’s are its own. Before telling someone they have float, say which kind.

Quill's tasks E and F on a week axis, each with four weeks of total float: E's free float is zero, because every week E takes comes out of F's, while F's four weeks are its own

5. Near-critical paths

A path nearly as long as the critical one deserves the same attention: “It is very likely that this near-critical path may actually drive the project completion date even though the total path length is less than that of the critical path” [1]. Quill’s C–D path is one week short, and PERT and merge bias shows why that week is thinner than it looks. The critical path also moves when a task changes, so recheck it after every change.

6. When to use it, and where it misleads

Use it to decide where money and attention go. On DuPont’s first test, a $10 million plant with 393 jobs, “only a very few jobs were critical - about 10% - and only these needed expediting”: two months came off the schedule at no extra cost, and two more for a 1% rise in direct cost [2].

The limits are built in. The passes assume known durations and that anyone can start any task the moment it is free. The computed date is therefore a lower bound: PERT shows why uncertainty pushes it later, and resource planning why people do.

How solid is this?

  • Where it comes from. The inventors’ own report, whose DuPont figures are self-reported with no independent comparison; a practitioner textbook; a defence-acquisition primer.
  • What is contested. Slack definitions drift; one textbook joins free and total float with “or” [5]. The Quill network is constructed for teaching.

Acknowledgments

This page adapts material from lectures by Eduardo Miranda [6] on software project management.

References

  1. R. K. Wysocki and R. McGary,
    Effective Project Management: Traditional, Adaptive, Extreme, 3rd ed. Wiley Publishing, 2003.
  2. J. E. Kelley Jr. and M. R. Walker,
    “Critical-Path Planning and Scheduling,” in Papers Presented at the December 1–3, 1959, Eastern Joint IRE-AIEE-ACM Computer Conference, ACM, 1959, pp. 160–173. doi: 10.1145/1460299.1460318.
  3. F. P. Brooks,
    The mythical man-month (anniversary ed.). Addison-Wesley Longman Publishing Co., Inc., 1995.
  4. W. W. Bahnmaier, Ed.,
    Scheduling Guide for Program Managers. Defense Systems Management College Press, 2001.
  5. C. L. Hoover, M. Rosso-Llopart, and G. Taran,
    Evaluating Project Decisions: Case Studies in Software Engineering. Addison-Wesley Professional, 2010. [Online]. Available: https://www.oreilly.com/library/view/evaluating-project-decisions/9780321685629/
  6. E. Miranda,
    “Managing Software Development.” 2014.

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