“Dummy” edges are edges with zero length, usually written with dotted
lines. There are two reasons for drawing them in critical path analysis.
1. “Logic dummies” – To show that activity D depends on both activities A and B, but activity C depends only on activity A.
If you drew the edges for A and B both finishing at the vertex where D starts, then you’d have to draw activity C starting at that same vertex, and your graph would wrongly show activity C depending on both A and B.
Instead you draw separate vertices for the ends of A and B.
You show C as starting at the end of A.
You put in a dummy from the end of A to the end of B.
2. “Numbering dummies” – To have (as Edexcel puts it: best to learn the exact words) every activity uniquely represented in terms of its events.
That means that in this sort of graph you can’t draw two edges both going from the same start vertex to the same end vertex. Avoiding that makes it easier to avoid confusion when scanning forwards and scanning backwards, and is essential if you want to name the edges neatly just by start vertex and end vertex (as you usually do in computerised versions of CPA).
So if A, B, and C all start from the same point, and D depends on all of them, you draw separate vertices for the ends of A and B and C, and then dummies from the end of A and the end of B to the end of C.
(The numbers on the nodes here are just a way of labelling them for computerised versions of CPA, and then labelling the edges “5-to-10”, “5-to-15”, “5-to-20”, instead of all three edges confusingly having the same name “5-to-20”).
The numbers on the nodes are just labels for them, nothing to do with the lengths of the edges. You see them in the Edexcel textbook too, but you do not have to use them at all in calculations for A-level.
Here’s another explanation, from a website.
The second web page makes it clear that the “numbering dummies” are needed primarily for computerised versions of critical path analysis, where you want to be able to describe each activity by the number of its starting node and the number of its ending node. All three different activities in the diagram above would (confusingly) have the same description, “5-to-20”, if we didn’t put in the dummies.
However, Edexcel insists we put them in even if we are doing critical path analysis only with pen and paper.