Master the technique that helps businesses plan complex projects, allocate resources and find the shortest route to completion.
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Foundation
What is a Network Model?
A network model (or network diagram) is a visual planning tool used to manage complex projects. It maps out every activity required, the time each takes, and how they connect. Businesses use network models to determine the shortest possible time to complete a project — this is called Critical Path Analysis (CPA).
A network model requires three pieces of information for each activity: a list of all activities involved, the duration of each activity, and the dependencies (which activities must be finished before others can begin).
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Component
Nodes
A node is a circle on the network diagram. It represents a point in time — not an activity itself. Each node is divided into three sections: the node number (left), the Earliest Start Time (top right), and the Latest Finish Time (bottom right).
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Component
Activities
An activity is a task that must be completed as part of the project. On the diagram, activities are shown as arrows connecting two nodes. Each arrow is labelled with the activity's letter and its duration (how long it takes).
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Key Concept
Earliest Start Time (EST)
The Earliest Start Time is the earliest point at which an activity can begin, assuming all preceding activities were completed as quickly as possible. ESTs are calculated by working forward through the network from left to right.
Where multiple activities lead into a node, the EST is the highest value of all incoming paths.
EST = highest (preceding EST + duration) of all incoming activities
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Key Concept
Latest Finish Time (LFT)
The Latest Finish Time is the latest point at which an activity must be completed in order not to delay the entire project. LFTs are calculated by working backwards through the network from right to left.
Where multiple activities leave a node, the LFT is the lowest value of all outgoing paths subtracted from the next node's LFT.
LFT = lowest (following node LFT − duration) of all outgoing activities
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Key Concept
Float (Slack) Time
Float time (also called slack) is the amount of spare time available within an activity without delaying the project. Activities on the critical path always have zero float.
Float is valuable because it allows managers to reallocate resources from non-critical activities to critical ones, improving overall efficiency.
Float = LFT − Duration − EST
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Key Concept
The Critical Path
The critical path is the longest sequence of dependent activities through the network. It determines the minimum time in which the project can be completed. Any delay to an activity on the critical path delays the entire project.
Critical path activities have zero float — meaning EST and LFT at their end node are equal. They are typically highlighted on the diagram.
A project manager must prioritise critical path activities and monitor them closely, as there is no room for delay.
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Key Concept
Dependencies & Sequencing
Dependencies describe which activities must be completed before another can begin. An activity that depends on another is said to have a prerequisite.
Sequencing is the process of ordering activities logically. Some activities can run concurrently (at the same time), while others must follow in strict sequence. Good sequencing reduces overall project duration.
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Key Concept
Bottlenecks
A bottleneck occurs when a single activity significantly restricts the flow or speed of the entire project. Bottlenecks are typically found on or near the critical path. If an activity on the critical path takes longer than planned, it creates a bottleneck that extends the project's total duration.
Identifying bottlenecks allows managers to allocate extra resources to that activity to prevent overall delay.
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Application
Contingency Planning
Contingency planning involves preparing backup plans in case an activity overruns or fails. CPA supports contingency planning by making float time visible — showing exactly where spare time exists and where it does not.
For activities with zero float, managers must have contingency resources ready. Float time in non-critical activities can act as a buffer, absorbing minor delays without impacting the overall timeline.
CPA links directly to risk management — it transforms vague project uncertainty into specific, manageable time data.
Quick Task: Dependencies & Sequencing
A firm is planning a new product launch. Below are the activities involved. For each one, identify whether it can start immediately or must wait for another activity to be completed first. Select the correct prerequisite from the dropdown.
Step 1
Calculating the Earliest Start Time (EST)
1
Work forwards — left to right
Start at node 1. Its EST is always 0 — the project hasn't begun yet. Then move to each successive node and add the duration of the activity connecting them.
Where two or more activities lead into the same node, calculate all possible totals and take the highest value. This is because every preceding activity must be complete before the next can begin.
Why EST first? Because you must know the earliest any activity can start before you can work out how late it can finish. The EST tells you the floor — you can't begin sooner than this.
Exemplar — calculating ESTs (forward pass)
Activity table for the exemplar above:
Activity
Duration (weeks)
Depends on
EST at end node
A
4
—
4
B
6
—
6
C
3
A
7
D
5
B
11
E
4
C, D
15 (max of 7+4=11 vs 11+4=15)
Step 2
Calculating the Latest Finish Time (LFT)
2
Work backwards — right to left
Begin at the final node. Its LFT equals its EST — the project must finish by this point. Then work backwards, subtracting each activity's duration from the LFT of the following node.
Where two or more activities leave a node, calculate all possible values and take the lowest. This ensures no outgoing activity is forced to start too late.
Why LFT second? You can only work out the latest an activity can finish once you know when the project must end. LFT tells you the ceiling — you can't finish later than this without delaying the whole project.
Same exemplar — now with LFTs added (backward pass)
Step 3
Identifying the Critical Path
3
Zero float = critical activity
Once all ESTs and LFTs are filled in, calculate the float for each activity: Float = LFT − Duration − EST
Any activity with float = 0 sits on the critical path. Trace these activities from start to finish node — this route is the critical path and represents the minimum project duration. Activities with positive float are non-critical and have spare time that can be used to reallocate resources or absorb minor delays.
Critical path highlighted in green
Scenario Analysis
Bottlenecks & Changes to Activities
Scenario
Using the same network, the operations director learns that Activity D (installing equipment) has been delayed by a supplier. It will now take 8 weeks instead of 5. How does this affect the project?
Before change
Critical Path: B → D → E
Duration: 6 + 5 + 4 = 15 weeks D has zero float. Any delay to D delays the project.
After D increases to 8 weeks
Critical Path: B → D → E (extended)
Duration: 6 + 8 + 4 = 18 weeks The project is delayed by 3 weeks. The critical path remains the same but D is now a more significant bottleneck.
Impact on float
Float for Activity C changes
C's float was: LFT(11) − 3 − EST(4) = 4 weeks After change: LFT(14) − 3 − EST(4) = 7 weeks float C now has even more spare time.
Management response
Contingency Options
The manager could: move resources from Activity C (which now has 7 weeks float) to D, negotiate a faster supplier, or look at whether part of D can be started earlier or run concurrently with another task.
Updated network — Activity D extended to 8 weeks (project now 18 weeks)
Interactive Practice
Randomised Scenarios
Activity
Description
Duration (weeks)
Prerequisite(s)
Your task
Step 1 — Enter EST and LFT for each node
Your task
Step 2 — Calculate Float for each activity
Activity
LFT (end node)
Duration
EST (start node)
Your float answer
Your task
Step 3 — Identify the Critical Path
Write the critical path as a sequence of node numbers (e.g. 1 → 2 → 4 → 5)