IB Business Management HLTopic 6 — The Business Management ToolkitPapers 1, 2 & 3HL only~12 min read
Using Critical Path Analysis
Critical path analysis finds the shortest time a project can possibly take, and then tells you exactly which tasks would wreck that time if they slipped. Everything else has some slack. Knowing the difference is what lets a manager move staff around without missing the deadline.
📘 What you need to know
A network diagram shows every activity, how long it takes, and what it depends on.
Nodes are circles split in three: activity number on the left, earliest start time (EST) top right, latest finish time (LFT) bottom right.
Activities are the lines between nodes, with a letter above and a duration below.
Forward pass: work left to right adding durations to get each EST. Where two arrows meet, take the larger.
Backward pass: work right to left subtracting durations to get each LFT. Where two arrows meet, take the smaller.
The critical path runs through every node where EST = LFT. Those activities have zero float.
The network diagram
Node 3 is the only one where the two numbers differ (3 and 4). That one week of difference is the float on activity B.
The forward pass: earliest start times
Start at node 1 with zero, then add each duration as you move right. When two activities feed into the same node, take the larger number, because the node cannot be reached until the slower one has finished.
WORKED EXAMPLE
Calculate the earliest start time at every node in the diagram above. [3 marks]
Nodes 1 to 3Node 1 = 0Node 2 = 0 + 4 (A) = 4Node 3 = 0 + 3 (B) = 3Node 4: two routes arrive, take the largervia C: 4 + 5 = 9 via D: 3 + 5 = 8 so 9Nodes 5 and 6Node 5 = 9 + 2 (E) = 11Node 6 = 11 + 3 (F) = 14The project takes 14 weeksforward pass = add, and take the bigger number where paths merge
The backward pass: latest finish times
Start at the last node, copying its EST into the LFT box, then subtract each duration as you move left. When two activities lead back into the same node, take the smaller number, because that is the tighter deadline.
WORKED EXAMPLE
Calculate the latest finish time at every node, and identify the critical path. [4 marks]
Work backwards from node 6Node 6 = 14Node 5 = 14 − 3 (F) = 11Node 4 = 11 − 2 (E) = 9Node 2 = 9 − 5 (C) = 4Node 3 = 9 − 5 (D) = 4Node 1: two routes back, take the smallervia A: 4 − 4 = 0 via B: 4 − 3 = 1 so 0Find where EST equals LFTNodes 1, 2, 4, 5 and 6 all match. Node 3 does not (3 against 4).Critical path = A, C, E, Fbackward pass = subtract, and take the smaller number where paths merge
Float: the spare time
Total float for an activity
LFT at the end node − duration − EST at the start node
WORKED EXAMPLE
Calculate the total float for activity B. [3 marks]
Step 1: gather the three numbersB ends at node 3, so LFT = 4. Duration = 3. B starts at node 1, so EST = 0.Step 2: substitute4 − 3 − 0 = 1Step 3: say what it meansB can start or overrun by one week without delaying the project at all.Total float on B = 1 weekevery activity on the critical path has a float of exactly zero — a useful check
Float is not wasted time. It is where a manager finds spare staff. If activity B has a week of slack, those workers can be moved onto C for a week, and C is the task that actually controls the deadline.
Quick self-check. The LFT at node 1 must always be 0. If it is not, you have made an arithmetic error somewhere in the backward pass. Check that before you write anything else down.
Why businesses use it
Benefit
Limitation
Gives the shortest possible completion time
Durations are estimates, and estimates slip
Identifies exactly which activities cannot be delayed
Large projects become huge diagrams needing software
Allows just-in-time ordering of materials, freeing up cash
Does not guarantee success; it only schedules the plan
Shows where spare resources sit, so staff can be moved
Staff may need training before they can be moved onto another task
Lets managers see the knock-on effect of a delay immediately
Says nothing about cost or quality, only time
💡 Exam tips
Forward pass first, always. You cannot start the backward pass until the final EST exists.
Remember the rule: larger going forward, smaller going backward.
The critical path is the chain of activities where EST = LFT at every node.
State the project duration in the correct unit — weeks, days, whatever the table used.
When explaining a delay, follow the chain and say whether the end date moves.
For evaluation, note that critical path analysis handles time only. Pair it with contribution or cash flow for the money side.
⚠ Common mix-ups
Taking the smaller number on the forward pass. It is the larger one.
Putting EST and LFT in the wrong halves. EST top right, LFT bottom right.
Adding all durations together to get project length. Parallel activities do not add up.
Thinking float means the task is unimportant. It still has to be done.
Forgetting the LFT at node 1 must be zero.
Assuming any delay delays the project. Only a delay bigger than the float does.
Up next: Using Simple Linear Regression — the last tool in the box, and the one that turns two columns of data into a forecast.
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