Crashing Worksheet 7
Complete ALL Question in your book.
Question 1:
The activities and completion times for a project are shown in the network diagram
below.
A,6
E,4
E’,0
E,4
E’,0
FINISH
START
B,5
C,2
F,6
I,2
G,2
The completion time of some of the remaining activities in the project can be
reduced at a cost.
The following table shows the reduced times (least possible time to complete an
activity after maximum reduction of time).
The cost of this reduction, per hour, is also shown.
Activity
A
B
C
E
F
G
Usual completion
time (hours)
6
5
2
4
6
2
Reduced time
(hours)
3
4
2
2
4
2
Cost of reduction
per hour ($)
50
100
20
50
-
a. Determine the shortest completion time for the project, the critical path
and any float times for activities.
b. i. Find the activities that should be reduced in time to minimise the
completion time for the project.
ii. Find the maximum time in hours that can be saved by this reduction.
iii. Find the minimum cost to achieve this time saving.
TMI / DBE
1
Question 2:
The table below gives the activities involved in landscaping a garden. It is possible
to crash this project.
The reduction time and cost are also provided.
Activity
Description
Duration
(days)
Predecessor
A
B
C
D
E
Design garden
7
2
1
2
4
5
4
2
1
Clear ground area
Peg out design
Carry out heavy digging
Install watering system
and drainage
Buy and collect plants
F
G
H
J
Pave pathways
Plant trees and shrubs
Plant lawn
Cost per
day ($)
A, B
C
D
Possible
Reductions
(days)
2
1
1
1
A
E
F, G
H
1
1
1
-
400
500
400
-
400
300
500
500
a. Construct a network diagram for the project.
b. Find the:
i.
Minimum completion time for the project;
ii.
Critical path; and
iii.
Any slack times (no crashing yet).
c. Calculate the:
i.
Minimum completion time using as many of the reductions as
necessary; and
ii.
Find the cost for this crash.
d. If the project completion time needs to be reduced by only three days:
TMI / DBE
i.
Which activities should be reduced so that the cost is a minimum?
ii.
What would be the minimum cost?
2
Question 3:
A community centre is to be built on a new housing estate.
Nine activities have been identified for this building project.
The directed network below shows the activities and their completion times in
weeks.
D, 1
A, 4
Start
G, 3
B, 4
E, 4
C, 3
H, 2
J, 6
Finish
F, 4
a. Determine the minimum time, in weeks, to complete this project.
b. Determine the slack time, in weeks, for Activity D.
The builders of the community centre are able to speed up the project.
Some of the activities can be reduced in time at an additional cost.
The activities that can be reduced in time are A, C, E, F and G.
c. Which of these activities, if reduced in time individually, would not result in
an earlier completion of the project?
The owner of the estate is prepared to pay the additional cost to achieve early
completion.
The cost of reducing the time of each activity is $5000 per week.
The maximum reduction in time for each one of the five activities, A, C. E, F, G, is
2 weeks.
d. Determine the minimum time, in weeks, for the project to be completed now
that certain activities can be reduced in time.
e. Determine the minimum additional cost of completing the project in this
reduced time.
TMI / DBE
3
Question 3:
A community centre is to be built on a new housing estate.
Nine activities have been identified for this building project.
The directed network below shows the activities and their completion times in
weeks.
D, 1
A, 4
Start
G, 3
B, 4
E, 4
C, 3
H, 2
J, 6
Finish
F, 4
a. Determine the minimum time, in weeks, to complete this project.
b. Determine the slack time, in weeks, for Activity D.
The builders of the community centre are able to speed up the project.
Some of the activities can be reduced in time at an additional cost.
The activities that can be reduced in time are A, C, E, F and G.
c. Which of these activities, if reduced in time individually, would not result in
an earlier completion of the project?
The owner of the estate is prepared to pay the additional cost to achieve early
completion.
The cost of reducing the time of each activity is $5000 per week.
The maximum reduction in time for each one of the five activities, A, C. E, F, G, is
2 weeks.
d. Determine the minimum time, in weeks, for the project to be completed now
that certain activities can be reduced in time.
e. Determine the minimum additional cost of completing the project in this
reduced time.
TMI / DBE
4