Critical Path and Float Analysis in Schedule Management

Critical Path and Float Analysis in Schedule Management

PMBOK v8 Definition

The critical path method (CPM) is a method used to estimate the minimum project duration and determine the amount of scheduling flexibility (float) on the logical network paths within the schedule model. Activities with zero total float form the critical path, which represents the longest path through the schedule network. Float analysis examines total float (time an activity can be delayed without delaying project finish) and free float (time an activity can be delayed without affecting the early start of its successor).

Why It Matters for the Exam

This concept appears in approximately 8-12% of PMI exam questions across the Schedule Management knowledge area. You will encounter it in calculation questions (forward/backward pass, float determination), interpretation questions (critical path identification, float meaning), and scenario-based questions (constraint impacts, acceleration strategies). Mastery of float types and critical path logic is essential for passing.

Key Points to Remember (for the exam)

  • Critical Path Definition: The sequence of activities with zero total float that determines the minimum project duration. Activities on this path cannot be delayed without extending the project finish date.

  • Total Float: The amount of time an activity can be delayed without delaying the project finish date or violating a constraint. Calculated as Late Start – Early Start (or Late Finish – Early Finish).

  • Free Float: The time an activity can be delayed without affecting the early start of its successor. This is always less than or equal to total float.

  • Negative Float: Occurs when constraints force dates earlier than logic and duration allow. Negative float analysis can be used to explore acceleration strategies.

  • Positive Float: May occur if a constraint is placed later than the calculated early finish (from the forward pass). This creates scheduling flexibility.

  • Near-Critical Paths: Some schedule networks may have multiple near-critical paths. Many software tools allow users to define how criticality is measured.

  • Forward/Backward Pass: Forward pass calculates earliest start/finish (ES = Day 1, EF = ES + Duration – 1). Backward pass calculates latest start/finish (LS = LF – Duration + 1).

Typical PMI Exam Example

You are managing a project with activities A (3 days), B (2 days), C (4 days), and D (5 days). Activity A precedes C and D. Activity B precedes D. After completing the forward pass, you find the critical path is A–D with 8 days. Activity B has early start of Day 1 and early finish of Day 2. What is the free float of Activity B? (Answer: 5 days – it can be delayed without affecting the early start of its successor, D).

PMI Exam Traps

  • Trap: Confusing total float with free float Reality: Total float affects project finish; free float only affects successor's early start. Free float is always ≤ total float.

  • Trap: Assuming critical path always has zero float Reality: The critical path usually has zero total float, but positive float may occur if constraints are placed later than calculated early finish.

  • Trap: Forgetting negative float exists Reality: Negative float occurs when constraints force earlier dates than logic allows. This is a real phenomenon tested on the exam.

  • Trap: Using Day 0 instead of Day 1 for calculations Reality: PMBOK v8 uses Day 1 as the starting convention. ES = Day 1, EF = ES + Duration – 1.

Important PMI Connections

Related ConceptRelationship TypeExam Attention Point
Schedule Network AnalysisInput to CPMForward/backward pass calculations are prerequisite to determining critical path
Schedule CompressionOutput from CPMNegative float analysis drives acceleration strategies (crashing, fast-tracking)
Constraints (Date)Input to Float CalculationConstraints can create positive or negative float; must be considered in float analysis
Project Duration EstimationOutput from CPMCritical path determines minimum project duration; any delay on critical path extends project

Quick Review Questions

  1. If an activity has early start of Day 5, late start of Day 8, and duration of 3 days, what is its total float?

  2. An activity with free float of 3 days can be delayed by how many days without affecting what?

  3. What type of float occurs when a constraint forces a date earlier than what logic and duration allow?

  4. In the forward pass calculation, if an activity starts on Day 1 and has duration of 4 days, what is its early finish?

  5. What distinguishes a critical path activity from a near-critical path activity?

PMBOK v8 Reference

Section 5.4 - Critical Path Method (CPM) and Float Analysis