Activity charts and network diagrams

Reading an activity chart (precedence table), immediate predecessors, drawing an activity-on-arc network, and using a dummy activity when two activities share some but not all of their predecessors.

A project is a set of activities (jobs) that take time. Some can happen at the same time; others have to wait. Before you can work out how long the project takes, you need a picture that shows exactly which jobs wait for which. That picture is a project network.

Activity charts

An activity chart (also called a precedence table) lists each activity, its duration, and its immediate predecessors: the activities that must be finished just before it can start. "Immediate" matters. If filming needs rehearsals, and rehearsals need casting, then casting is a predecessor of filming, but not an immediate one. The chart only lists the last link in the chain.

Activity	Task (school video)	Days	Immediate predecessors
A	Write the script	$3$	–
B	Cast the actors	$2$	A
C	Book locations	$1$	A
D	Rehearse	$2$	B
E	Film	$4$	C, D

Drawing the network

In HSC networks, each activity is an arc (an arrow) labelled with its letter and duration. Each node (circle) is an event: the moment the activities coming into it are all finished, so the activities leaving it can start. There is one start node and one finish node.

Example 1●

Draw the network for the school video chart above.

Draw node 1, then arc A ($3$) to node 2.

A has no predecessor, so it leaves the start node.

Arc B ($2$) from node 2 to node 3. Arc C ($1$) from node 2 to node 4.

B and C both need only A, so both leave node 2, the moment A finishes.

Arc D ($2$) from node 3 to node 4.

D needs B, so it leaves node 3.

Arc E ($4$) from node 4 to node 5, the finish.

E needs C and D. Both arrive at node 4, so node 4 means 'C and D are done'.

Each activity appears once, and every arrow starts where all of its predecessors have finished.

Check every row of the chart against the drawing.

You can also go the other way. To read the immediate predecessors of an activity from a network, look at the node its arrow leaves from, and list every activity whose arrow ends at that node (following any dummy back to where it started).

Dummy activities

Sometimes the chart is impossible to draw with real activities alone. A dummy activity fixes that. It is drawn as a dashed arrow, takes zero time and does no work. It only carries the message "this activity has finished" from one node to another.

You need a dummy when two activities share some, but not all, of their immediate predecessors. Try it below: S needs P and Q, but R needs only P.

InteractiveFrom activity chart to network

Try this

Step through the build one activity at a time. At step 5, before you read the explanation, decide where S should start. Why can't it start at node 2? Why can't it start at node 3 without the dummy?

Cover the network and redraw it yourself from the table, then step through to check.

Example 2●●

A café is opening in Newtown. Draw the network.

Activity	Task	Days	Immediate predecessors
K	Sign the lease	$2$	–
L	Hire staff	$5$	–
M	Fit out the kitchen	$6$	K
N	Train staff on site	$3$	K, L

K ($2$) from node 1 to node 2. L ($5$) from node 1 to node 3.

K and L have no predecessors, so both leave the start node.

M ($6$) from node 2 to node 4.

M needs K only, so it leaves node 2.

Draw a dummy (dashed, $0$) from node 2 to node 3. Now node 3 means "K and L are both done".

M and N share K, but N also needs L. N can't leave node 2 (L may not be done) and can't leave node 3 (K may not be done).

N ($3$) from node 3 to node 4, the finish.

Both M and N end the project.

Your turn

A network has these arcs: A from node 1 to 2, B from node 1 to 3, C from node 2 to 3, D from node 3 to 4, E from node 2 to 4. Write the immediate predecessors of C, D and E.

Show the answer

C leaves node 2, where only A arrives: C needs A. D leaves node 3, where B and C arrive: D needs B and C. E leaves node 2: E needs A.

Flashcards

Immediate predecessor

An activity that must finish just before another can start

Activity-on-arc network

Activities are arrows labelled with duration; nodes are the moments activities finish and start

When is a dummy needed?

When two activities share some, but not all, of their immediate predecessors. It is dashed and takes $0$ time.

Practice

In the project networks used in this course, each activity is shown as:
Painting needs plastering, and plastering needs wiring. Which is true?
A dummy activity is needed when:
How many days does a dummy activity take?
An activity chart has A (no predecessors), B (no predecessors), C (after A) and D (after B). How many arcs leave the start node?
A network has arcs A from node 1 to 2, B from node 1 to 3, C from node 2 to 3, D from node 3 to 4 and E from node 2 to 4. The immediate predecessors of D are:
For the same network, the immediate predecessor of E is:
Exam style: An activity chart has J (–), K (–), L (after J) and M (after J and K). Where should the dummy go?
Exam style: A network has A from node 1 to 2, B from node 1 to 3, a dummy from node 2 to 3, C from node 2 to 4 and D from node 3 to 4. Which activities must be finished before D can start?