Summary — the whole chapter in one scroll
- Activity networks turn a list of jobs (a precedence table) into a directed graph: nodes = events ("stepping stones"), arrows = activities with a duration.
- Dummy activities (dotted, zero-duration, no letter) exist purely to fix the logic of the diagram — either giving an activity a unique start/end pair, or showing a "split" in what depends on what.
- Forward pass through the network gives earliest event times — the fastest a project can reach each stepping stone. The final one is the minimum project duration.
- Backward pass gives latest event times — the latest you can leave each stepping stone without delaying the whole project.
- Total float = wiggle room an activity has. Zero float = critical activity. The chain of critical activities from start to finish = critical path.
- Gantt (cascade) charts turn all this into a visual timeline — critical activities stacked back-to-back on one row, non-critical ones shown with a dotted "float" tail.
- Resource histograms stack up how many workers are needed on each day, built from a Gantt chart.
- Resource levelling = shifting non-critical activities within their float to smooth out (minimise) the number of workers needed on the busiest days.
- Scheduling = the reverse problem — given the workers, how do you assign them to activities (one worker, one job at a time) to hit either the minimum project time, or fit inside a worker limit?
1. Activity Networks & Precedence Tables
What is an activity network?
Imagine you're building a house. You can't put up the walls before the foundations are laid, but you
can fit the windows and doors at the same time as each other. An activity network
is a graph that captures exactly this kind of "what must happen before what" logic for an entire project.
It has two parts:
- Arcs (the arrows) represent the activities — the actual jobs. Each arc is labelled with a capital letter (A, B, C...) and its duration in brackets, e.g.
D (6) means "activity D takes 6 days".
- Nodes (the circles) represent events — think of them as "stepping stones". You cannot move past a stepping stone until every activity leading into it has finished.
Because activities can only flow one way (you can't un-lay foundations), this is technically a
directed graph — every arc has an arrowhead showing the direction of progress, generally left to right.
The very first event (before anything has happened) is the source node, labelled 0 or S.
The very last event (once everything is done) is the sink node — the highest-numbered node, or labelled T.
START 2
(0)──A(4)──►(1)──B(5)──►(2)──D(6)──►(4)──F(6)──►(5) END
│ ▲
└────C(3)──►(3)──E(4)───┘
both
What is a precedence table?