Critical Path Method (CPM): Master Network Analysis

📋 Course Contents

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1 Module 1: Introduction to CPM

1.1 What is the Critical Path Method?

CPM (Critical Path Method) is a network-based scheduling technique that identifies the longest path through a project network, determining the minimum project duration.

1.2 History

• 1957: Developed by DuPont and Remington Rand
• Purpose: Reduce turnaround time in chemical plant maintenance
• Result: Reduced shutdown time by 25%

1.3 Why CPM Matters

Benefit	How CPM Helps
Project Duration	Calculates minimum possible completion time
Critical Activities	Identifies which activities must not be delayed
Resource Focus	Prioritize resources on critical tasks
Schedule Flexibility	Shows which activities have float (slack)
Delay Analysis	Basis for forensic schedule analysis

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2 Module 2: Network Diagrams

2.1 Types of Network Diagrams

Type	Full Name	Activities On
PDM	Precedence Diagramming Method	Nodes (boxes) ✅ Most common
ADM	Arrow Diagramming Method	Arrows

2.2 Relationship Types (PDM)

Relationship	Meaning	Example
FS (Finish-to-Start)	B starts after A finishes	Foundation → Framing
SS (Start-to-Start)	B starts when A starts	Excavation → Shoring
FF (Finish-to-Finish)	B finishes when A finishes	Testing → Commissioning
SF (Start-to-Finish)	B finishes when A starts	Rarely used

2.3 Lag and Lead

• Lag (+): Waiting time between activities (e.g., concrete curing)
• Lead (-): Overlap between activities (fast-tracking)

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3 Module 3: Forward Pass (ES & EF)

3.1 Forward Pass Purpose

Calculate the earliest possible start and finish dates for each activity.

3.2 Formulas

3.3 Forward Pass Rules

1. Start from project beginning
2. First activity ES = 0 (or project start date)
3. Work left-to-right through network
4. When multiple predecessors, take the maximum EF

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4 Module 4: Backward Pass (LS & LF)

4.1 Backward Pass Purpose

Calculate the latest allowable start and finish dates without delaying the project.

4.2 Formulas

4.3 Backward Pass Rules

1. Start from project end
2. Last activity LF = Project completion date (usually = EF)
3. Work right-to-left through network
4. When multiple successors, take the minimum LS

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5 Module 5: Float Analysis

5.1 Types of Float

Float Type	Formula	Meaning
Total Float (TF)	LF - EF (or LS - ES)	Max delay without delaying PROJECT
Free Float (FF)	ES(successor) - EF(current)	Max delay without delaying SUCCESSOR

5.2 Critical Path Identification

5.3 Float Relationships

• Free Float ≤ Total Float (always)
• Critical activities: TF = 0
• Near-critical: TF ≤ 5 days (monitor closely)
• Using float removes it from successors

5.4 Float Ownership

Who "owns" the float is a contractual issue:

• Contractor: Can use for flexibility
• Owner: May claim for changes
• Shared: First-come, first-served

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6 Module 6: CPM vs PERT

6.1 Comparison

Aspect	CPM	PERT
Duration	Single (deterministic)	Three estimates (probabilistic)
Focus	Time-cost trade-off	Time uncertainty
Best For	Construction (repetitive, known durations)	R&D (uncertain durations)
Calculation	Direct	Statistical (mean, variance)

6.2 PERT Duration Estimates

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7 Module 7: Schedule Compression

7.1 Crashing

Adding resources to shorten critical activities.

• Increases cost
• Only effective on critical path
• Diminishing returns (law of diminishing returns)

7.2 Fast-Tracking

Overlapping activities that were planned sequentially.

• Increases risk
• May require rework
• Change FS to SS with lag

7.3 Compression Decision

Method	Cost Impact	Risk Impact
Crashing	Higher (more resources)	Lower
Fast-Tracking	Lower	Higher (rework possible)

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8 Module 8: Worked Example

8.1 Network Data

Activity	Duration	Predecessors
A	3 days	-
B	5 days	A
C	4 days	A
D	6 days	B
E	3 days	C
F	4 days	D, E

8.2 Forward Pass

Activity	ES	Duration	EF
A	0	3	3
B	3	5	8
C	3	4	7
D	8	6	14
E	7	3	10
F	14	4	18

Project Duration = 18 days

8.3 Backward Pass

Activity	LF	Duration	LS
F	18	4	14
D	14	6	8
E	14	3	11
B	8	5	3
C	11	4	7
A	3	3	0

8.4 Float Calculation

Activity	TF (LF-EF)	Status
A	0	CRITICAL
B	0	CRITICAL
C	4	Non-critical
D	0	CRITICAL
E	4	Non-critical
F	0	CRITICAL

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🎯 Final Quiz

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