Dummy Activities (Edexcel IAL Maths)

Dummies

Spec point — 4.1

What is a dummy activity?

• A dummy activity is an activity that has a weight of zero

  • Dummies are not assigned names (letters)
  • Dummies are represented by dotted lines

• Dummies are only used to show precedences in more complicated activity networks

When and where are dummies used in an activity network?

• Two situations can lead to the need for a dummy activity

• The first situation is to ensure each activity (arc) has a unique pair of start and end nodes

  • E.g. In the activity network below, activity D has immediate predecessors B and C

    • B and C cannot both start at event (node) 1 and end at event (node) 2 (this would not be a unique pair)
    • a dummy activity is used so that B has start/end pair (1, 3) and C has start/end pair (1, 2)

• Note that the dummy could also go from event 2 to event 3 with activity D commencing from event 3

• The second situation that requires a dummy is when there is a split of immediate predecessors

  • E.g. In the activity network below, activity D has immediate predecessors B and C

    • Activity E only has B as an immediate predecessor
    • A dummy activity is used to show that D depends on both B and C

Exam Hint

• Exam questions will not always require you to draw the whole activity network

  • A diagram of part of the network may be given

• Exam questions are often specific about the number of dummies you should use

  • If you think you need more, go back to see if you can make improvements
  • It is generally expected that an activity network is as concise/efficient as possible with the minimum use of dummies

Worked Example The activities involved in a project are listed in the precedence table below.

Activity	Immediately preceding activities	Duration (days)
A	-	5
B	-	4
C	A	7
D	B	3
E	A, D	7
F	B	6
G	C	6
H	C	4
I	G, H	5
J	E, F	4

The project is also represented on the partially completed activity network below.

Using exactly two dummy activities, complete the activity network by adding activities D, E, G, H, I and J.

Answer:

Activity D is dependent on activity B so draw an arc from event/node 2 for D

Looking ahead, activity E is dependent on both A and D, whereas activity C is dependent on just A This is the second situation ('split predecessors') for the use of a dummy activity

Also from looking ahead activity J depends on both E and F - so the arcs for E and F will need to meet

Activities G and H are both dependent on C, and activity I is dependent on both G and H This could lead to G and H having the same start/end node pair This is the first situation ('unique start/end node pair') for the use of a dummy activity

No activities depend on I so its arc can be drawn to the end of the project (sink node)

The activity network can now be completed with activity J and the sink node