Home / Critical Path Analysis / Activity networks
3.8a · Critical Path Analysis · Sub-skill
Turn a list of activities and their dependencies into an activity network — and follow algorithms step by step.
See it first
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Build it up, step by step
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An algorithm is a finite list of clear, unambiguous steps that always produces an answer. To follow one, do the steps in order and write down the result of each step. For example: put seven scores in order, delete the highest and lowest, add up the rest, divide by how many are left. This algorithm gives a trimmed mean, which is less affected by one extreme score.
A project is broken into activities. Each has a duration and a list of immediate predecessors — the activities that must be finished before it can start. A precedence table records all of this. An activity with a dash (–) has no predecessors, so it can start straight away.
The network algorithm: (1) draw a column of boxes for the activities with no predecessors; (2) to the right, draw boxes for activities whose predecessors are all drawn; (3) repeat until every activity is drawn; (4) draw an arrow from each immediate predecessor to the activity that follows it. Each box shows the activity and its duration, with room for an early time and a late time.
To read a network back into a table, look at the arrows into each box: those boxes are its immediate predecessors. A box with several arrows in must wait for all of them. Activities that are not linked by a chain of arrows can happen at the same time.
Draw an activity network for: A (3 days, –), B (5 days, –), C (4 days, after A), D (3 days, after B), E (3 days, after C and D).
Column 1: A and B (no predecessors). Column 2: C (needs A) and D (needs B). Column 3: E (needs both C and D). Arrows: A→C, B→D, C→E, D→E.
A and B can run in parallel, as can C and D. E cannot start until both C and D are finished.
Test yourself
A kitchen is being refitted. A: Remove old units (1 day, –); B: Fit electrics (2 days, after A); C: Fit plumbing (2 days, after A); D: Fit new units (3 days, after B and C); E: Lay floor (2 days, after D); F: Decorate (2 days, after D).
(a) Draw an activity network for the project.
(b) Write down one activity that can be done at the same time as C. [5 marks]
(a) Box A on the left; boxes B and C to its right, each with an arrow from A; box D with arrows from both B and C; boxes E and F to the right of D, each with an arrow from D. Each box shows the letter and duration. (4 marks: all 6 boxes, correct order, arrows from every immediate predecessor, no extra arrows)
(b) B (B and C both follow A only, so they can run at the same time). (1 mark)
Practice
Five short questions. Work through them, then reveal the mark scheme to check.