A Better Definition of Longest Path

We provide the only intuitive view of CPM schedules, while improving upon the definitions of both critical path and longest path. Our software uniquely targets both completion milestones and start activities and ensures the complete longest path of every activity is returned for ranking. This allows us to associate every dynamic impact to each discrete cause. We encourage you to analyze your schedule updates with our secure, no-obligation demo.

Industry definitions for critical path and longest path can cause confusion because they can be used interchangeably. Furthermore, the definition for critical path includes notable assumptions that make it ambiguous in practice. AACEi’s Recommended Practice 49R-06 defines the critical path of a schedule, similar to PMI’s PMBOK Guide, as “the longest logical path through the CPM network and consists of those activities that determine the shortest time for project completion” [1]. Both describe the critical path as the longest path that “determines the shortest possible project duration” [2], where a delay to an activity of the path will delay project completion.

These definitions assume there is only one critical path of a CPM network that spans the full duration, but schedules can have multiple critical paths as a result of any combination of four conditions:

  1. concurrent paths with the same duration;
  2. constrained milestones or activities;
  3. multiple calendars; and/or
  4. critical paths of individual schedules that are combined into an integrated master schedule, producing either a new critical path or sets of critical paths.

These real life exceptions to the critical path definition make the concept of the longest path necessary. Longest path shares the same definition as critical path with the additional condition that a schedule’s longest path must start at the first activity of a schedule and complete at the last activity. The longest path may be different from the critical path when the critical path includes interim constraints and does not drive project completion. Because of this, the longest path can show more float than the “least float critical path” [3] of the same schedule. Like critical paths, a schedule can have multiple concurrent longest paths with the same duration and float.

When the least float critical path is constrained ahead of project completion, the longest path becomes the path that determines the project’s duration. Though uncommon, this doesn’t necessarily mean a delay to an activity of the longest path will delay project completion. For example, a longest path can include different calendars and constraints that create relationship free float between major project phases. Despite this exception, the longest path of a schedule is always the continuous chain between the first and last activity with the least relationship free float.

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AFS returns both critical and longest paths, but ranks longest above critical because of their unique forensic value in emphasizing start targets at the data date. Because more than just the first and last activity of a schedule are evaluated, we define longest path as the continuous chain between a specific set of activities having the lowest relationship free float. An activity set includes a start target that is either at the data date or constrained after the data date, specific evaluation activity, and finish target such as a contractual milestone.  

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The longest path of an evaluation activity may not be its most critical path because the start and finish targets may exist beyond constraints that delineate path segments with higher total float. In these cases, AFS will return the critical path of the evaluation activity as a separate path where the interim constraints are defined as the start and/or finish targets. This allows analysts to compare critical paths alongside longest paths to better understand the effects of constraints.

In the AACEi paper, S.07: When is the Critical Path Not the Most Critical Path?, Mr. Woolf presents the following discussion: “Because we believe that the definition for the term, path, should make reference to the path’s point of terminus, as well as its point of origin, we are faced with this difficult question: Where does a path begin and end? If we cannot define a path’s starting or ending points, how can we begin to define the term, critical-path?” [3].

AFS compliments Mr. Woolf’s discussion by targeting both points of “origin” and “terminus”. This approach removes ambiguity by constructing both longest and critical paths with individual context and accurate, exhaustive ranking. AFS retains context of the data date and contractual milestones, fully exhibiting the practical difference between longest and critical paths.

REFERENCES

[1] Carson, C.W., & Winter, R.M. (2010) AACE International Recommended Practice No. 49R-06: Identifying the Critical Path.

[2] Project Management Institute. (2013) A Guide to the Project Management Body of Knowledge, PMBOK Guide, 5 ed., 155.

[3] Woolf, M. (2008) When is the Critical Path Not the Most Critical Path? AACE International Transactions, PS.07.