Path Start Finish and Constraints: Critical Path Method for Exam

Path Start Finish and Constraints: Critical Path Method for Exam

PMBOK v8 Definition

The critical path is the longest path through a project network diagram, determining the shortest possible project duration. Early Start (ES) is the earliest possible time an activity can begin, calculated using forward pass. Early Finish (EF) is ES plus duration minus one. Late Start (LS) is the latest time an activity can begin without delaying project completion, calculated using backward pass. Late Finish (LF) is LS plus duration minus one. Total Float is the amount of time an activity can be delayed without affecting project completion date (LS – ES or LF – EF). The critical path has zero total float.

Why It Matters for the Exam

Path Start Finish calculations appear in approximately 15-20% of PMI exam questions, typically in schedule management scenarios. Questions test your ability to identify the critical path, calculate float, and understand how delays impact project completion. You will face both calculation questions and conceptual questions about schedule compression and network logic.

Key Points to Remember (for the exam)

  • Critical Path Definition: The longest path through the network with zero total float. Any delay on this path delays the entire project.

  • Forward Pass Calculation: Start at Day 1. ES of first activity = 1. EF = ES + Duration – 1. For successor activities, ES = predecessor EF + 1 (for FS relationships). The project completion date equals the highest EF among all activities.

  • Backward Pass Calculation: Start from project completion date. LF of last activity = project completion date. LS = LF – Duration + 1. For predecessor activities, LF = successor LS – 1 (for FS relationships).

  • Total Float Formula: Total Float = LS – ES = LF – EF. Critical path activities have Total Float = 0.

  • Dependency Types (4 Types):

    • Finish-to-Start (FS): Predecessor must finish before successor starts (most common)
    • Start-to-Start (SS): Predecessor must start before successor can start
    • Finish-to-Finish (FF): Predecessor must finish before successor can finish
    • Start-to-Finish (SF): Predecessor cannot finish until successor has started (rare)

  • Path Duration Calculation: Sum durations of all activities on a path. The path with the highest total duration is the critical path.

  • Multiple Critical Paths: A project can have multiple critical paths. Each has zero total float and requires equal management attention.

Typical PMI Exam Example

A project has three paths: A-B-D (25 days), A-C-D (30 days), and E-F-G (22 days). Path A-C-D is the critical path. Activity B has 5 days of total float (LS=11, ES=6). If activity C is delayed by 3 days, the critical path shifts to 33 days, and the project completion date extends from Day 30 to Day 33. The project manager must apply schedule compression techniques.

PMI Exam Traps

  • Trap: Confusing Early Start with Late Start

    • Reality: ES is the earliest possible start; LS is the latest possible start without delaying the project. They differ by Total Float.

  • Trap: Assuming all paths with zero float are critical

    • Reality: Only the longest path (maximum duration) with zero float is the critical path. Shorter paths may have positive float.

  • Trap: Starting forward pass calculation from Day 0

    • Reality: PMBOK v8 uses the convention of starting on Day 1. ES of first activity = 1, not 0.

  • Trap: Confusing Total Float with Free Float

    • Reality: Total Float affects project completion; Free Float affects only the next activity. PMI exam focuses on Total Float for critical path.

Important PMI Connections

Related ConceptRelationship TypeExam Attention Point
Schedule Network AnalysisTool/TechniqueCritical path is output of network analysis using forward/backward pass
Resource LevelingApplied to scheduleCan change critical path by extending duration when resources are overallocated
Schedule CompressionApplied after critical path identifiedCrashing and fast tracking are applied to critical path activities only
Leads and LagsModifies dependency relationshipsLead overlaps activities (negative lag); Lag adds waiting time (positive lag)

Quick Review Questions

  1. A project has activities A (5 days), B (10 days), C (8 days), D (6 days). A-B-D = 21 days, A-C-D = 19 days. What is the critical path and total project duration?

  2. Activity X has ES=5, Duration=4, LS=7. What is Total Float? Is Activity X on the critical path?

  3. A successor activity cannot start until its predecessor has finished. What dependency type is this?

  4. During backward pass, if the last activity has LF=30 and Duration=5, what is its LS?

  5. A project has two paths with identical duration. How many critical paths exist, and what is their Total Float?

PMBOK v8 Reference

Section 5 – Tools and Techniques (Figure 5-4, Figure 5-13, Schedule Development Steps)