Network Analysis and Critical Path

Network analysis (also called Critical Path Analysis or CPA) is a project management technique that enables businesses to plan, schedule, and manage complex projects. It identifies the sequence of activities that determines the minimum project duration and highlights where delays will affect completion.

---

Key Terminology

Before constructing or interpreting a network diagram, you need to understand these terms:

Term	Definition
Activity	A task or job that consumes time and resources (represented by an arrow in activity-on-arrow diagrams)
Node	A circle representing the start or end of an activity. Contains the event number, Earliest Start Time (EST), and Latest Finish Time (LFT)
Duration	The time required to complete an activity
Predecessor	An activity that must be completed before another can begin
Earliest Start Time (EST)	The earliest point at which an activity can begin (calculated by a forward pass)
Latest Finish Time (LFT)	The latest point at which an activity can finish without delaying the project (calculated by a backward pass)
Critical path	The longest sequence of dependent activities through the network — it determines the minimum project duration
Float (total float)	The amount of time an activity can be delayed without delaying the overall project
Dummy activity	A dotted arrow with zero duration, used to show logical dependencies without consuming time

---

Node Structure

Each node in an activity-on-arrow diagram is divided into three sections:

     ┌──────────┐
     │  Event   │
     │  Number  │
     ├────┬─────┤
     │EST │ LFT │
     └────┴─────┘

• Event number — a unique identifier (top)
• EST — Earliest Start Time (bottom left)
• LFT — Latest Finish Time (bottom right)

---

Constructing a Network Diagram

Step 1: List All Activities

Identify every activity, its duration, and its predecessors.

Worked Example: Launching a New Product

Activity	Description	Duration (weeks)	Predecessor
A	Market research	4	—
B	Product design	6	A
C	Supplier sourcing	3	A
D	Prototype development	5	B
E	Packaging design	3	C
F	Testing	4	D
G	Marketing campaign	6	C
H	Production setup	3	E, F
I	Launch	2	G, H

Step 2: Draw the Network (Forward Pass — Calculate ESTs)

Start at node 1 (time 0) and work forwards. At each node, the EST is the highest value from all incoming paths.

Node 1: EST = 0
  A(4) → Node 2: EST = 0 + 4 = 4
    B(6) → Node 3: EST = 4 + 6 = 10
    C(3) → Node 4: EST = 4 + 3 = 7
      D(5) → Node 5: EST = 10 + 5 = 15
      E(3) → Node 6 (needs E and F):
        From E: 7 + 3 = 10
        From F: 15 + 4 = 19
        EST at Node 6 = 19 (take the highest)
      G(6) → Node 7 (needs G and H):
        From G: 7 + 6 = 13
        From H: 19 + 3 = 22
        EST at Node 7 = 22 (take the highest)
      F(4) → feeds into Node 6 (see above)
      H(3) → feeds into Node 7 (see above)
  I(2) → Node 8: EST = 22 + 2 = 24

Minimum project duration: 24 weeks

Step 3: Backward Pass — Calculate LFTs

Start at the final node and work backwards. At each node, the LFT is the lowest value from all outgoing paths.