Welcome to Critical Path Analysis!

Ever wondered how massive projects like building a skyscraper or launching a new smartphone stay on track? They use Critical Path Analysis (CPA). In this chapter, we are going to learn how to break down a big project into smaller tasks, figure out which ones are the most important, and calculate exactly how long the whole thing will take. Don't worry if it looks like a lot of boxes and arrows at first—once you learn the "Forward Pass" and "Backward Pass" rhythm, it’s just like solving a puzzle!

1. Building the Network: Activity-on-Node (AoN)

Before we can calculate times, we need a map. In the AQA syllabus, we use the Activity-on-Node method. This means each task (activity) is represented by a box (a node), and the arrows (arcs) show the order in which they must happen.

Key Terms to Know

  • Activity: A specific task that takes time (e.g., "Paint the walls").
  • Precedence: Which tasks must be finished before another can start. We often use a Precedence Table to list these rules.
  • Duration: How long an activity takes.
Example: You can't put your socks on after your shoes. Putting on socks is a precedent for putting on shoes!

How to Draw the Box (Node)

In AQA exams, a standard node box is usually divided like this:

[ Activity Label | Duration ]
[ Earliest Start Time | Latest Finish Time ]

(Note: Always check the specific diagram provided in your exam paper, as layouts can sometimes vary slightly, but these four pieces of information are the core!)

Quick Review: The Rules of the Network
  • Every network should have a single "Start" node and a single "Finish" node.
  • Arrows always point from left to right.
  • No "loops" allowed! You can't have a task that depends on itself.
Key Takeaway: The network is a logical map. If Activity B depends on Activity A, there must be an arrow from A to B.

2. Scheduling: The Forward and Backward Pass

Now for the math! We need to find the Earliest Start Time (EST) and the Latest Finish Time (LFT) for every task.

The Forward Pass (Finding the EST)

We start at the beginning and work toward the end. We are looking for the earliest possible time a task can begin.

  1. The very first activity starts at time 0.
  2. EST + Duration = Earliest Finish Time (EFT).
  3. If a task has two or more arrows pointing to it, you must pick the LARGEST value.

Analogy: Imagine you are waiting for two friends to arrive before you can start a game. Friend A arrives at 2:00, and Friend B arrives at 2:30. You can't start until 2:30. In the forward pass, the "latest" arrival determines the "earliest" start.

The Backward Pass (Finding the LFT)

We start at the "Finish" node and work backward to find the latest a task can finish without delaying the whole project.

  1. The LFT of the final task is equal to its EFT (the project duration).
  2. LFT - Duration = Latest Start Time (LST).
  3. If an activity has two or more arrows coming out of it (going backward), you must pick the SMALLEST value.
Common Mistake to Avoid

Students often get confused and pick the smallest number on the forward pass and the largest on the backward pass. Remember: Forward = MAX, Backward = MIN.

Key Takeaway: The Forward Pass tells you how long the project takes. The Backward Pass tells you the deadlines for each task.

3. Critical Activities, Critical Paths, and Float

Not all tasks are created equal. Some have "wiggle room," and some don't.

What is a Critical Activity?

An activity is Critical if any delay in that task delays the entire project. For these tasks, the Earliest Start Time and the Latest Start Time are exactly the same.

The Critical Path

The Critical Path is a continuous path of critical activities from Start to Finish. It represents the longest path through the network.

Float: The "Wiggle Room"

The Total Float is the amount of time an activity can be delayed without delaying the whole project.

Formula: \( \text{Total Float} = \text{LFT} - \text{Duration} - \text{EST} \)

(Or more simply: LST - EST)

Did you know?

Critical activities always have a Total Float of zero. If you calculate a negative float, you've probably made a mistake in your backward pass!

Key Takeaway: Identifying the critical path helps managers know exactly which tasks need the most supervision to avoid delays.

4. Visualising the Project: Gantt Diagrams

A Gantt Diagram (also called a Cascade Diagram) is a horizontal bar chart that shows the schedule. It's much easier for a non-mathematician to read than a network diagram!

How to Draw a Gantt Diagram

  • The x-axis represents time.
  • The y-axis lists the activities.
  • A solid bar shows the duration of the activity starting at its EST.
  • A dotted line (or shaded area) shows the Float after the activity.
  • Critical activities will have no dotted lines—their bars are "locked" in place.

Resource Histograms

Sometimes tasks require workers (resources). A Resource Histogram is a bar chart showing how many workers are needed at any given time, assuming every task starts as early as possible (at its EST).

Key Takeaway: Gantt charts show when things happen; Histograms show what resources are needed.

5. Refining the Model: Resource Levelling

In the real world, you might only have 3 workers, but your Histogram shows you need 5 on Tuesday. This is where Resource Levelling comes in.

Heuristic Procedures

A "heuristic" is just a fancy word for a "rule of thumb" or a logical strategy. To level resources, we use the Float:

  1. Identify times where worker demand exceeds the limit.
  2. Look for non-critical activities happening at that time.
  3. Delay those activities (shift them into their float) until workers become available.
What if we can't level it?

If you delay a task beyond its float, it becomes a new critical path, and the entire project duration will increase. In exams, you might be asked to "refine the model" by explaining how a change in duration or workers affects the finish date (Section DE4).

Memory Trick: Think of Float like "lazy time." If you have 2 days of float, you can be "lazy" for 2 days before you actually have to start, without getting in trouble with your boss (the Project Manager)!

Key Takeaway: Use float to smooth out the workload. If you run out of float and still don't have enough workers, the project will take longer.

Quick Review Summary

1. Draw the Network: Use the precedence table to connect boxes.
2. Forward Pass: Find ESTs (use the Max value at junctions).
3. Backward Pass: Find LFTs (use the Min value at junctions).
4. Find the Critical Path: Look for the path where Float = 0.
5. Calculate Float: \( \text{LFT} - \text{Duration} - \text{EST} \).
6. Gantt/Histogram: Draw the schedule and check for resource overloads.