ENG4004 Engineering Project & Operations Management Project

This document presents a comprehensive solution to a project management assignment, addressing key concepts such as network diagrams, critical path analysis, and project crashing. The solution includes a network diagram illustrating project activities and dependencies, followed by the determination of earliest and latest times for each activity to identify the critical path. Float calculations, including total, free, and independent float, are performed for specific activities. A bar chart visualizes the earliest start times and resource requirements per day, which is then redrawn to optimize resource allocation. The assignment also explores project crashing, analyzing the cost and time implications of accelerating project activities. Furthermore, the document calculates the expected time and variance for each activity using PERT estimates and determines the probability of project completion within a specified timeframe. This detailed solution offers valuable insights into project management techniques and their practical application. Desklib provides more solved assignments and resources for students.

Running head: PROJECT MANAGEMENT
Project management
Name of the Student
Name of the University
Author’s Note

1
PROJECT MANAGEMENT
Table of Contents
Question 1:.................................................................................................................................2
1.1 Network diagram..............................................................................................................2
Question 2:.................................................................................................................................3
2.1 Determine earliest and latest times and critical path of the project.................................3
2.2 Total free and independent float associated with activity 3-5..........................................4
2.3 Bar-chart showing earliest start and people required per day..........................................4
2.4 Redrawn chart..................................................................................................................5
1.5 Crashing...........................................................................................................................6
Question 3..................................................................................................................................7
3.1 Expected time and variance for each activity..................................................................7
3.2 Probability calculation.....................................................................................................8
Bibliography...............................................................................................................................9

2
PROJECT MANAGEMENT
Question 1:
1.1 Network diagram
Project activities and their dependency are reflected in the table below:
Activity Activity is dependent on
A -
B -
C -
D C
E C
F D, E
G A, E
H F, G
I F, G
J A, E
The network diagram with the help of project activities and their dependency is
provided below:
Figure 1: Network Diagram

3
PROJECT MANAGEMENT
(Source: Created by Author)
Question 2:
2.1 Determine earliest and latest times and critical path of the project
The earliest start times are reflected in the are indicated by the figure that appears
under each activity.
Figure 2: Earliest start times
(Source: Created by Author)
Latest event times are reflected in the are indicated by the figure that appears under
each activity.
Figure 3: Latest event times

4
PROJECT MANAGEMENT
(Source: Created by Author)
The project paths are listed below:
1st path -1+7= 0+4 =4
2nd path- 1+3+5+7 = (3+6+ 4) =13
3rd path-1+2+4+5+6+7= (4+6+5+4+6) =25
4th path- 1+4+7= (4+6) =10
Minimum project duration is 28
Thus, the critical path of the project is 1+2+4+5+6+7
2.2 Total free and independent float associated with activity 3-5
Float= Latest start time-Earliest start time
18-9=9
2.3 Bar-chart showing earliest start and people required per day
The table that is given below reflects on the people required per day as well as earliest
start date of the project activities.
Activity People required per day Earliest start date
1-2 4 4
1-3 3 3
1-4 6 4
1-7 2 4
2-4 7 10
3-5 3 9
4-5 5 15

5
PROJECT MANAGEMENT
4-6 5 22
4-7 6 16
5-6 2 19
5-7 1 19
6-7 4 28
1-2 1-3 1-4 1-7 2-4 3-5 4-5 4-6 4-7 5-6 5-7 6-7
0
5
10
15
20
25
30
Bar-chart showing earliest start and
people required per day
People required per day Earliest start date
Figure 4: Bar-chart showing earliest start and people required per day
(Source: Created by Author)
2.4 Redrawn chart
The minimum ceiling of people required to complete the project in minimum time is
reflected with the help of the bar graph that is provided below:
1-2 1-3 1-4 1-7 2-4 3-5 4-5 4-6 4-7 5-6 5-7 6-7
0
5
10
15
20
Chart showing people needed per
day
People required per day Float

6
PROJECT MANAGEMENT
Figure 4: Bar-chart showing minimum ceiling of people required
(Source: Created by Author)
1.5 Crashing
Activit
y
People
require
d per
day
Normal Crashed
Duration
(days)
Cost
($)
Duration
(days)
Cost
($)
D
t
Dc Dc/
Dt
1-2 3 3 800 2 900 1 10
0
100
1-3 3 2 1200 2 1200 0 0 0
1-4 6 7 700 5 900 2 20
0
100
2-6 3 5 400 3 560 2 16
0
80
3-4 2 2 350 2 350 0 0 0
3-5 1 3 400 2 450 1 50 50
4-6 3 5 900 2 1260 3 36
0
120
4-7 4 3 300 2 450 1 15
0
150
5-7 3 4 600 2 700 2 10
0
50
6-8 5 6 500 5 680 1 18
0
180
7-8 4 3 1100 3 1100 0 0 0
As per the critical path, the activities that will be crashed is 1-4> 4-6>6-8
The project activities will be completed in minimum time= (18-6)=12 days
The activities will be crashed by duration which is reflected in the table below:

7
PROJECT MANAGEMENT
Activ
ity
Peopl
e
requir
ed per
day
Normal Duration
(days)
Crash Duration
(days)
Crashed by
duration
1-4 6 7 5 2
4-6 3 5 2 3
6-8 5 6 5 1
The table that is given below reflects the additional cost that is generally required will
be $740
Activi
ty
People
requir
ed per
day
Normal Crashed
Duration
(days)
Cost
($)
Duration
(days)
Cost
($)
D
t
Dc Dc/
Dt
Extra
cost
1-2 3 3 800 2 900 1 10
0
100
1-3 3 2 1200 2 1200 0 0 0
1-4 6 7 700 5 900 2 20
0
100 200
2-6 3 5 400 3 560 2 16
0
80
3-4 2 2 350 2 350 0 0 0
3-5 1 3 400 2 450 1 50 50
4-6 3 5 900 2 1260 3 36
0
120 360
4-7 4 3 300 2 450 1 15
0
150
5-7 3 4 600 2 700 2 10
0
50
6-8 5 6 500 5 680 1 18
0
180 180
7-8 4 3 1100 3 1100 0 0 0
Additional cost 740
Question 3
3.1 Expected time and variance for each activity
The expected time and variance for each of the activities are provided in the table
below:
Activit
y
Optimisti
c
Most
likely
Pessimisti
c
PERT
estimate
varianc
e
Standard
deviation

8
PROJECT MANAGEMENT
A 5 11 11 10 2 1
B 10 10 10 10 0 0
C 2 5 8 5 2 1
D 1 7 13 7 4 2
E 4 4 10 5 2 1
F 4 7 10 7 2 1
G 2 2 2 2 0 0
H 0 6 6 5 2 1
I 2 8 14 8 4 2
J 1 4 7 4 2 1
3.2 Probability calculation
The critical path of the project is A-D-J
=10+7+4
=21 days
The probability of undertaking the project operational= 1/3

9
PROJECT MANAGEMENT
Bibliography
Badewi, A., 2016. The impact of project management (PM) and benefits management (BM)
practices on project success: Towards developing a project benefits governance
framework. International Journal of Project Management, 34(4), pp.761-778.
Conforto, E.C., Salum, F., Amaral, D.C., da Silva, S.L. and de Almeida, L.F.M., 2014. Can
agile project management be adopted by industries other than software
development?. Project Management Journal, 45(3), pp.21-34.
de Carvalho, M.M., Patah, L.A. and de Souza Bido, D., 2015. Project management and its
effects on project success: Cross-country and cross-industry comparisons. International
Journal of Project Management, 33(7), pp.1509-1522.
Hornstein, H.A., 2015. The integration of project management and organizational change
management is now a necessity. International Journal of Project Management, 33(2),
pp.291-298.
Joslin, R. and Müller, R., 2015. Relationships between a project management methodology
and project success in different project governance contexts. International Journal of Project
Management, 33(6), pp.1377-1392.
Kaiser, M.G., El Arbi, F. and Ahlemann, F., 2015. Successful project portfolio management
beyond project selection techniques: Understanding the role of structural
alignment. International Journal of Project Management, 33(1), pp.126-139.
Marcelino-Sádaba, S., Pérez-Ezcurdia, A., Lazcano, A.M.E. and Villanueva, P., 2014. Project
risk management methodology for small firms. International journal of project
management, 32(2), pp.327-340.

10
PROJECT MANAGEMENT
Sánchez, M.A., 2015. Integrating sustainability issues into project management. Journal of
Cleaner Production, 96, pp.319-330.
Todorović, M.L., Petrović, D.Č., Mihić, M.M., Obradović, V.L. and Bushuyev, S.D., 2015.
Project success analysis framework: A knowledge-based approach in project
management. International Journal of Project Management, 33(4), pp.772-783.
Too, E.G. and Weaver, P., 2014. The management of project management: A conceptual
framework for project governance. International Journal of Project Management, 32(8),
pp.1382-1394.