Critical Path Q’s
Question 4 (HEFF 11)
There are 10 activities, A – J, that need to be completed to set up the infrastructure for the
music festival.
These activities; together with their earliest start time (EST), latest start time (LST), duration (in
days) and immediate predecessor(s) are shown in the table below. The EST for activity G has
been omitted and the LST for activity H has been omitted.
Activity Duration EST LST
Immediate
(days) (days) (days) Predecessor(s)
A
3
0
5
B
4
0
3
C
4
0
0
D
6
3
8
A
E
3
4
4
C
F
5
4
8
C
G
7
7
B, E
H
6
7
B, E
I
6
9
13
F
J
5
14
14
D, G
a.
Find the earliest start time (EST) for activity G.
1 mark
b.
Find the latest start time (LST) for activity H.
1 mark
c.
What is the float time for activity F?
1 mark
d.
Which activities are critical to setting up the infrastructure in the shortest possible time?
1 mark
e.
What is the shortest time possible in which the infrastructure can be set up?
1 mark
f.
Activity B has a major hold up and will now have a duration of 8 days. What is the
shortest time possible now, in days, for the infrastructure to be set up?
1 mark
Question 2 (6 marks) (HEFF 14)
The tropical island sometimes faces the threat of a cyclone.
The resort manager has a list of tasks that must be undertaken around the resort when there
is a cyclone alert.
These tasks, A – M, together with their duration in hours and the predecessor(s) for each task,
are shown below.
Task
Duration
Predecessor(s)
(hours)
A
4
-
B
6
-
C
7
-
D
5
-
E
4
A
F
3
A
G
4
B, F
H
5
D
I
6
D
J
5
E
K
7
B, F
L
5
C, G, H
M
4
I
The network diagram below shows the information in the table. Task K has been left off the
E,4
diagram.
F,3
A,4
G,4
B,6
start
J,5
finish
L,5
C,7
H,5
D,5
M,4
I,6
a.
By inserting task K, complete the network diagram above.
1 mark
b.
Find the earliest start time for task L.
1 mark
c.
What is the minimum time required to complete all the tasks?
1 mark
d.
Which task has the greatest slack (or float) time?
1 mark
On one occasion, after a cyclone warning has been given, the resort manager gains access to
extra resources and is able to crash task G by 1 hour.
e.
Write down the tasks that are now critical to all the preparations being completed in
the minimum possible time.
2 marks
Question 3 (7 marks) (HEFF 15)
A new coolroom is to be built at the homestead. The fourteen activities required to achieve this together with their
completion times in days are shown on the network below.
E,6
L,4
K,4
C,3
F,5
start
A,4
M,5
G,6
D,4
finish
H,6
B,5
I,8
N,6
J,4
a.
What is the earliest starting time for activity K?
1 mark
b.
What is the latest starting time for activity H?
1 mark
c.
Which activity has the greatest float time?
1 mark
d.
What is the minimum number of days in which the new coolroom can be built?
1 mark
e.
One of the activities has a threatened delay of 7 days, which will not affect the minimum completion time of the
project.
Which activities could be this one with the threatened delay?
1 mark
Just before construction begins there is an actual delay of 2 days with activity E.
f.
Which activities lie on the critical path after this actual delay to activity E?
1 mark
After the 2 day delay to activity E occurred, the station owners were given the option of crashing activity K by up to 3
days at a cost of $250 per day.
g.
What is the least cost of crashing activity K so that the largest reduction in the minimum completion time of the
project can be achieved?
1 mark
Question 3 (HEFF 13)
On competition days at the golf course, there are fifteen additional activities that ground staff have to complete over
and above their usual work.
These fifteen additional activities together with their completion time in minutes are shown on the directed network
below. A dummy activity is also shown which starts at the end of activity G.
I,15
D,15
A,30
N,25
E,10
F,20
J,20
L,10
B,20
start
finish
O,20
K,30
G,25
dummy
C,35
M,35
H,30
d.
Write down the immediate predecessor(s) of activity M.
1 mark
e.
What is the earliest start time for activity J?
1 mark
f.
What is the latest start time for activity A?
1 mark
g.
Write down the activities, in order, that form the critical path.
1 mark
h.
If activity G is delayed by 15 minutes, what will be the shortest time, in minutes that all fifteen activities can be
completed in?
1 mark