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BUS-CONS57-02 · Lesson 3 · 14 clock hours · theory

Network Logic and the Critical Path Method

Objective. Students will construct a Precedence Diagramming Method (PDM) network, calculate early/late start and finish times using forward and backward passes, and identify the critical path.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a credentialed professional in the field or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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What Is the Critical Path Method?

The Critical Path Method (CPM) is a scheduling technique that identifies the longest chain of dependent activities in a project — the sequence that determines the earliest the project can finish. Any delay on that chain, called the critical path, delays the entire project by the same amount. CPM was developed in the late 1950s and remains the foundation of professional project scheduling today.

As a construction manager or estimator, you will use CPM every time you build a project schedule, negotiate a completion date, or analyze a delay claim. NCCER Project Management and the CMAA CMIT exam both test CPM directly.

Precedence Diagramming Method (PDM)

Modern CPM uses the Precedence Diagramming Method (PDM), where each activity is represented by a box called a node. Arrows connecting the nodes show the logical relationships between activities. PDM supports four relationship types:

When building a PDM network for a residential addition, you might use FS for most trades (framing before sheathing), SS for concurrent tasks (site grading starting with excavation), and FF for tasks that must wrap up together (inspections finishing with punch-list work).

Each node box holds six values arranged in a standard format:

```

| ES | Activity Name | EF |

|-----|-----------------|----|

| LS | Duration | LF |

|-----|-----------------|----|

| TF | |

```

Forward Pass — Calculating Early Dates

The forward pass moves left to right through the network to find the Early Start (ES) and Early Finish (EF) for every activity.

Rules:

Work through every activity in sequence until you reach the last node. The EF of the last activity is the project duration.

Backward Pass — Calculating Late Dates

The backward pass moves right to left to find the Late Finish (LF) and Late Start (LS) for every activity — the latest each can occur without delaying the project.

Rules:

Calculating Total Float

Total Float (TF) is the amount of time an activity can be delayed without delaying the project finish.

TF = LS − ES (equivalently, LF − EF)

Activities with TF = 0 are on the critical path. Any slip in duration on a zero-float activity pushes the project end date back by the same number of days.

Identifying the Critical Path

Trace every continuous chain of zero-float activities from the project start node to the project finish node. That chain is the critical path. On a PDM network diagram, highlight it in red so it is immediately visible to owners, superintendents, and subcontractors.

A project can have more than one critical path. Near-critical paths (float of one or two days) deserve close monitoring as well, because a small delay can make them critical.

Why This Matters on the Job

If a critical activity slips two days — say, a concrete pour is rained out — the project finish moves two days later unless you take corrective action. Options include crashing (adding resources to shorten a critical activity) or fast-tracking (overlapping activities that were originally sequenced). Both cost money and carry risk, which is why protecting the critical path is a daily management responsibility.

Safety Note

Scheduling sessions take place in the office or classroom, but the activities you are scheduling involve real field hazards. When you visit the site to verify sequencing or confirm progress, follow all site safety requirements: wear the PPE designated for that site (hard hat, safety glasses, high-visibility vest, and steel-toed boots at minimum), sign in, and comply with the site's emergency action plan. Never step into an active work zone to verify a predecessor without alerting the superintendent. Lockout/tagout procedures govern any equipment isolation needed to allow inspectors or surveyors into confined or energized areas — scheduling personnel must understand those requirements even if they do not perform them.

Key terms10

Critical PathThe longest sequence of dependent activities through a project network; it determines the minimum project duration and has zero total float.
Precedence Diagramming Method (PDM)A network scheduling technique in which activities are represented as nodes (boxes) and arrows show the logical dependencies between them.
Early Start (ES)The earliest time an activity can begin, based on when all predecessor activities can finish; calculated during the forward pass.
Early Finish (EF)The earliest time an activity can be completed; EF = ES + Duration.
Late Start (LS)The latest time an activity can begin without delaying the project; LS = LF − Duration, calculated during the backward pass.
Late Finish (LF)The latest time an activity can be completed without delaying the project; calculated during the backward pass.
Total Float (TF)The amount of time an activity can be delayed beyond its early start without delaying the overall project finish; TF = LS − ES.
Forward PassThe left-to-right calculation through a CPM network that establishes the Early Start and Early Finish for each activity.
Backward PassThe right-to-left calculation through a CPM network that establishes the Late Finish and Late Start for each activity.
Finish-to-Start (FS)The most common PDM relationship type; the successor activity cannot start until the predecessor activity is finished.

Worked examples4

1. A simple three-activity network: Activity A (duration 4 days) → Activity B (duration 6 days) → Activity C (duration 3 days). All relationships are Finish-to-Start. Calculate ES and EF for every activity using a Day-0 convention.
  1. Activity A has no predecessor, so ES(A) = 0.
  2. EF(A) = ES(A) + Duration = 0 + 4 = 4.
  3. Activity B can start when A finishes: ES(B) = EF(A) = 4.
  4. EF(B) = ES(B) + Duration = 4 + 6 = 10.
  5. Activity C can start when B finishes: ES(C) = EF(B) = 10.
  6. EF(C) = ES(C) + Duration = 10 + 3 = 13. Project duration = 13 days.
Answer: ES/EF values — A: 0/4 | B: 4/10 | C: 10/13. Project duration = 13 days.
2. Using the same three-activity network (project duration = 13 days), perform the backward pass to find LS and LF for every activity.
  1. Set LF(C) equal to the project duration: LF(C) = 13.
  2. LS(C) = LF(C) − Duration = 13 − 3 = 10.
  3. Activity B must finish before C can start: LF(B) = LS(C) = 10.
  4. LS(B) = LF(B) − Duration = 10 − 6 = 4.
  5. Activity A must finish before B can start: LF(A) = LS(B) = 4.
  6. LS(A) = LF(A) − Duration = 4 − 4 = 0.
Answer: LS/LF values — A: 0/4 | B: 4/10 | C: 10/13.
3. Calculate Total Float for each activity in the three-activity network and identify the critical path.
  1. TF = LS − ES for each activity.
  2. TF(A) = LS(A) − ES(A) = 0 − 0 = 0.
  3. TF(B) = LS(B) − ES(B) = 4 − 4 = 0.
  4. TF(C) = LS(C) − ES(C) = 10 − 10 = 0.
  5. All three activities have TF = 0, so all three are on the critical path.
  6. The critical path is A → B → C with a total duration of 13 days.
Answer: TF for all activities = 0. Critical path: A → B → C (13 days).
4. A four-activity network has two parallel paths: Path 1 — Activity A (3 days) → Activity C (5 days); Path 2 — Activity B (4 days) → Activity D (2 days). Both paths merge at a single finish. All relationships are FS, ES of A and B both = 0. Identify the critical path and the total float on Path 2.
  1. Forward pass Path 1: ES(A)=0, EF(A)=3; ES(C)=3, EF(C)=8.
  2. Forward pass Path 2: ES(B)=0, EF(B)=4; ES(D)=4, EF(D)=6.
  3. The finish node takes the largest EF: project duration = max(8, 6) = 8 days.
  4. Backward pass Path 1: LF(C)=8, LS(C)=3; LF(A)=3, LS(A)=0.
  5. Backward pass Path 2: LF(D)=8, LS(D)=6; LF(B)=6, LS(B)=2.
  6. TF Path 1: TF(A)=0−0=0, TF(C)=3−3=0 → critical path.
  7. TF Path 2: TF(B)=2−0=2, TF(D)=6−4=2 → not critical.
Answer: Critical path: A → C (8 days). Path 2 (B → D) has 2 days of total float.
In class: Instructor demonstrates a forward and backward pass on a 10-activity network on the whiteboard; students replicate the calculation independently on a printed blank network template. · Students build a PDM network for a 15-activity residential addition project using index cards on a tabletop, assigning Finish-to-Start, Start-to-Start, and Finish-to-Finish relationships where logically appropriate. · Students calculate Total Float for every activity and highlight the critical path in red; they write one paragraph explaining why that path is critical and what would happen if any critical activity slipped two days.
Materials: Blank PDM network templates, index cards, colored markers, calculator, NCCER Project Management module section on CPM, instructor-prepared 15-activity activity list
Check: Completed network with all node values (ES, EF, LS, LF, TF) checked by instructor against answer key; all critical path activities correctly identified. Pass: no math errors on critical path nodes and at least 85% of all node values correct.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Project Management — Project Scheduling
1. In a Precedence Diagramming Method network, what does a Finish-to-Start relationship mean?
NCCER Project Management — Project Scheduling
2. During a forward pass, what rule applies when an activity has two predecessors whose Early Finish values are 8 and 12?
CMAA CMIT — Schedule Analysis
3. Activity G has an Early Start of 5, a Late Start of 9, and a duration of 4 days. What is Activity G's Total Float?
NCCER Project Management — Project Scheduling
4. Which of the following correctly describes the critical path in a CPM network?
NCCER Project Management — Project Scheduling
5. During the backward pass, what rule applies when an activity has two successors whose Late Start values are 14 and 10?
CMAA CMIT — Schedule Analysis
6. A critical activity on a residential addition schedule is delayed by two days due to a concrete delivery shortage. Assuming no corrective action is taken, what happens to the project completion date?
OSHA 30 — Construction Site Safety
7. A project manager visits the job site to verify that framing is complete before scheduling the rough-in inspection. What is the minimum PPE she should wear upon entering the active construction site?
NCCER Project Management — Project Scheduling
8. Activity H has ES = 6, EF = 11, LS = 9, LF = 14. Which statement about Activity H is correct?
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