NETWORK ANALYSIS CPM PERT CRASH

1. The table below provides cost and tie estimates of seven activities of a project.

Activity Time estimates Direct cost estimates

Normal Crash Normal Crash
1-2 2 1 10 15
1-3 8 5 15 21
2-4 4 3 20 24
3-4 1 1 7 7
3-5 2 1 8 15
4-6 5 3 10 16
5-6 6 2 12 36

I. Draw the project network corresponding to normal time.

II. Determine the critical path and the normal duration and normal cost of the project.
III. Crash the activities so that the project completion time reduces to 9 weeks with
minimum additional cost.

2. The following time-cost table (time in weeks, cost in Rupees) applies to a project. Use it to
arrive at the network associated with completing the project in minimum time at minimum
cost.

Activity Normal Crash

Time Cost Time Cost
1-2 2 800 1 1400
1-3 5 1000 2 2000
1-4 5 1000 3 1800
2-4 1 500 1 500
2-5 5 1500 3 2100
3-4 4 2000 3 3000
3-5 6 1200 4 1600
4-5 3 900 2 1600

3. The time and cost estimates of different activities of a project and their precedence
relationships are given below.

Activity Preceding Time (IN WEEKS) Cost (Rs)

Normal Crash Normal Crash
A - 6 4 10000 14000
B - 4 3 5000 8000
C A 3 2 4000 5000
D B 8 3 1000 6000
E B 14 6 9000 13000
F C,D 8 4 7000 8000
Overhead costs amount to Rs. 1000 per week

I. Draw the project network and show the critical path.

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 II. Crash the network to the minimum possible duration. What will be the critical
activities after such crashing?

4. A list of activities along with their precedence requirements, normal time and cost and crash
time and cost are given in the table below.

Activity Preceding Normal Crash

Time Time
Cost (Rs) Cost (Rs)
(Days) (Days)
A - 4 300 2 450
B A 9 600 5 960
C A 6 620 4 780
D B 4 320 3 395
E B,D 6 1440 3 1980
F C,D 4 350 2 470
G E,F 3 270 2 335
I. Draw the project network
II. What are the normal and crash costs and duration of the project? How many days
will be saved and what will be the project cost if all the activities are crashed to the
maximum possible extent? It is expected that earlier completion of the project will
result in additional profit of Rs 50 per day. The indirect cost is Rs 80 per day.
III. Analyze the project cost is Rs 80 per day.

5. The activity data for a project is given below:

Activity A B C D E F G H I
1-2 1-3 1-4 2-5 2-6 3-6 4-7 5-7 6-7
Least Time 5 18 26 16 15 6 7 7 3
Greatest time 10 22 40 20 25 12 12 9 5
Most likely time 8 20 33 18 20 9 10 8 4
Determine the following:
I. Expected task times and variances.
II. The Earliest and latest expected times to reach each node.
III. The critical path, and
IV. He probability of node occurring at the proposed completion date If the original
contract time of completing the project is 41.5 weeks.
V. Analyze the project cost is Rs 80 per day.

6. A project is composed of the following 7 activities:

1-2, 1-3, 1-4, 2-5, 3-5, 4-6, 5-6

A B C D E F G
Activity 1-2 1-3 1-4 2-5 3-5 4-6 5-6
to 12 3 12 1 2 4 5
tm 15 4 22 1 5 5 6
tp 17 7 28 1 14 8 10

I. Draw he network.
II. Identify all the paths through it.
III. Identify critical path through it.

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 IV. Find the expected project length.

7. Consider the following table:

Activity Preceding Time in weeks

to tm tp
A - 2 3 10
B - 2 3 4
C A 1 2 3
D A 4 6 14
E B 4 5 12
F C 3 4 5
G D ,E 1 1 7

I. Draw he network.
II. Find the critical path and variance of each event.
III. What is the probability that the project ill be completed in 16 weeks?
IV. Find the project duration at 95% probability.

8. In the PERT network shown in Fig. 14.46, the activity time estimates (in weeks) are given
along he arrows. If the scheduled completion time of the project is 23 weeks, calculate he
latest possible occurrence times on the basis of the scheduled date and final event. Calculate
the slack for each event and identify the critical path. What is the probability that the project
will be completed on the scheduled date?

9. An architect has been awarded a contract to prepare a plan for an urban renewal project.
The job consists of the following activities and their estimates times:

Activity Preceding Time in weeks

A - 2
B - 1
C A 3
D A,B 2
E C,D 1
F B,D 3
G E,F 1

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 I. draw an arow diagram for this project.
II. Indicate the critical path. Find all floats.

10. A project has the following characteristics:

Activity Preceding Time in weeks

A - 5
B A 2
C A 6
D B 12
E D 10
F D 9
G D 5
H B 9
I C,E 1
J G 2
K F , I, J 3
L K 9
M H, G 7
N M 8

I. Draw network for this project.

II. Find the various paths, the critical path and the project completion time.
III. Prepare an activity schedule showing the ES, EF, LS, LF and Float for each activity.
IV. Will the critical path change if activity G takes 10 weeks instead of weeks? If so what
will be the new critical path?

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