AQA A-level Business | Unit 3.2.2 Critical Path Analysis

Don't Be Critical

A project is just a set of activities that have to happen in the right order. A network diagram lays them out so you can see how long the whole thing takes, where there is spare time, and which activities cannot slip without delaying everything else.

Welcome to the firm

This is No Slack Solutions, a consultancy that untangles project plans for a living. Three clients are waiting, each with a tighter plan than the last. Your task is to read each network, find what cannot slip, and steer the client away from a missed deadline.

Colin Critical
Senior Partner, No Slack Solutions
"Find the path that cannot slip. Everything else is just noise."
Flo Time
Partner, No Slack Solutions
"Every activity has spare time, right up until it does not. I count every day of it."

👋 Your role

You are the new intern at No Slack Solutions. Colin and Flo will hand you three live client briefs, one at a time, and let you make the calls. Get it right and the clients hit their dates. Get it wrong and someone pays for it.

📁 Today's clients

Client 1
The Copper Kettle
A new cafe racing towards its launch night. A gentle start: learn to read the plan.
Easy
Client 2
Oakfield Furniture
A hotel order with a fixed delivery date and two production lines running at once.
Medium
Client 3
Halton Logistics
A whole warehouse moving site during a shutdown, with a delay already biting.
Hard
About 5 to 10 minutes.

How to read a network 🧭

Colin

"Same rules on every client. Before you touch a single brief, learn to read the diagram. It is quicker than it looks."

  • Circles are events (moments in time). Each one shows its number, its EST (the earliest the project can reach this point) and its LFT (the latest you can leave it without delaying the finish).
  • Arrows are the activities. The number on an arrow is how many days that activity takes.
  • The critical path is the chain of activities with no spare time. If any activity on it slips by even one day, the whole project finishes later.
  • Float is the spare time an activity has. An activity with float can run over a little and the project still finishes on time, because other activities are taking longer anyway.
Float = (LFT at the activity's finishing circle) minus (the activity's length) minus (EST at the activity's starting circle)

In plain terms: float is slack. Activities on the critical path have a float of zero. The bigger an activity's float, the more it can drift before anyone needs to worry.

Flo

"Every client's plan works the same way: activities in the arrows, events in the circles, and one chain that sets the finish date. Find that chain and you find where the pressure really is."

Client 1 of 3 · The Copper Kettle

Client 1: The Copper Kettle ☕

Sam, the owner

"I have walked away from a steady salary and put my savings into the lease. The landlord charges rent from day one whether the doors are open or not. I have booked the launch night for day 25: eighty guests, a local food writer, and a band. If we open late, I lose the launch buzz, I am refunding tickets, and I am paying rent on an empty room. I cannot afford that."

Colin

"Before we manage anything, read the plan. Tap the activities you think cannot slip, the ones with no spare time. That chain is the critical path. Take your best guess, then lock it in."

EST (earliest) LFT (latest) Critical path
Total project time
25 days
Launch booked for
Day 25

Tap to mark the activities you think have no spare time:

Client 2 of 3 · Oakfield Furniture

Client 2: Oakfield Furniture 🪑

Priya, the owner

"A boutique hotel ordered sixty handmade chairs. Delivery is locked to day 28, with a penalty in the contract if I am late, and if I lose this order the hotel drops us for good. I have four makers. Lose this contract and two of them are out of work. Right now the fabric side is slow: preparing the upholstery (activity E) is running about four days over. Does that move my delivery?"

Flo

"This one is mine. Spare time. The fabric prep is over by four days. Either the plan soaks it up, or it pushes the whole delivery. Read the diagram, work out the float on activity E, and call it. Then we watch the model."

EST (earliest) LFT (latest)

Tip: float on E = (LFT at E's finishing circle) minus (E's length) minus (EST at E's starting circle).

Client 3 of 3 · Halton Logistics

Client 3: Halton Logistics 📦

What is at risk

Halton is moving its whole operation to a new site during a four week shutdown. Everything must be live by day 31. They have hit a snag: fitting the new racking (activity B) has run into structural problems and now needs 13 days instead of 9. That pushes go-live to day 35. Miss the window and they cannot fulfil the Christmas contracts: hundreds of orders, and the client has warned they will walk.

Devin, the site manager

"I have budget for one extra crew, no more. Put them on one activity and they will take about four days off it (an activity cannot drop below one day). Where do I send them so we are live by day 31? Get this wrong and I am explaining to the board why we lost the contract."

Colin

"One question, intern: is the activity on the critical path? Spend that crew anywhere else and you have spent it on nothing."

Flo

"I have marked the spare time on each card. Read it before you commit the crew."

EST LFT Critical path
Go-live right now
Day 35
Window closes
Day 31

Send the extra crew to one activity. Each card shows how much spare time that activity has right now:

End of the day 📋

How the internship went
0 / 15
 
Colin

 

Flo

 

Some weeks later

 

 

 

What you learned today 💡

  • Float is slack. An activity with float can run over a little and the finish date does not move, because slower activities elsewhere are setting the pace.
  • Only critical activities have zero float. They form the critical path. Delay any of them and the whole project finishes later.
  • A delay larger than the float changes the picture. Once an activity uses up all its spare time, it can become critical itself, and the critical path can switch to a new route.
  • Speed costs nothing where there is float. Putting an extra crew on an activity with spare time does not bring the finish forward at all. Effort only counts on the critical path.

🧠 Colin and Flo's playbook

When a project slips, a good manager does not panic about every late activity. They ask three things, in order:

  • Is this activity on the critical path? If it has float, a small slip costs you nothing, so do not spend money fixing it.
  • How big is the slip compared with the float? A delay inside the float is absorbed. A delay beyond it pushes the finish date out and may hand the critical path to a different chain of activities.
  • Where will extra time or money actually help? Always on the critical path, because that is the only chain that controls the finish date. That is how you decide where attention and resources should go.

This is the heart of network analysis: not every delay matters equally, and the diagram tells you which ones do.