Project Management Assignment: Critical Path and Probabilities

This project management assignment solution addresses various aspects of project planning and execution. It begins with an Activity-on-Arrow (AoA) diagram to visualize project activities and dependencies. The solution then calculates Early Start (ES), Late Start (LS), Early Finish (EF), and Late Finish (LF) times. It explores the impact of changing task durations on the critical path and overall project timeline, analyzing scenarios where task durations are altered. Finally, the solution delves into probability analysis, calculating the likelihood of project completion within specific timeframes and determining the time within which management can be 97% sure of project completion, using PERT analysis. The assignment includes references to relevant project management literature.

Running head: PROJECT MANAGEMENT
Project Management
Name of Student
Name of University

PROJECT MANAGEMENT
Table of Contents
Answer to question a....................................................................................................................................................................................................3
Activity-on-Arrow (AoA) Diagram..........................................................................................................................................................................4
Answer to question b....................................................................................................................................................................................................6
ES, LS, EF LF, F Table............................................................................................................................................................................................6
Answer to question c....................................................................................................................................................................................................7
i. Task E - reduced to 2 weeks..................................................................................................................................................................................7
ii. Task F - increased to 6 weeks...............................................................................................................................................................................8
iii. Task A - increased to 10 weeks...........................................................................................................................................................................9
Answer to question d..................................................................................................................................................................................................10
i. The probability that project is completed within 30 weeks.................................................................................................................................10
ii. The probability that project is completed within 23 weeks................................................................................................................................11
iii. The time within which the management 97 per cent sure completion will occur.............................................................................................11
References..................................................................................................................................................................................................................12

PROJECT MANAGEMENT
Answer to question a
Activity Description Dependencies Optimistic
Time
(weeks) (to)
Most
Likely
Time
(weeks)
(tm)
Pessimistic
Time
(weeks) (tp)
Mean (te)
[te = (to + 4tm + tp) / 6]
Variance (σ2)
[σ2 = {( tp - to ) / 6}2]
A Equipment
Installation
6 8 10 8 0.44
B System
Development
3 6 9 6 1.00
C Position Recruiting 1 3 5 3 0.44
D Equipment Testing
and Modification
A 2 4 12 5 2.78
E Manual Testing B 2 3 4 3 0.11
F Job Training C 3 4 5 4 0.11
G Orientation C 2 2 2 2 0.00
H System Training A, E, F 3 7 11 7 1.77
I System Testing A, E, F 2 4 6 4 0.44
J Final Debugging D 1 4 7 4 1.00
K System Changeover G, H, I 1 10 13 9 4.00

PROJECT MANAGEMENT
Activity-on-Arrow (AoA) Diagram

PROJECT MANAGEMENT
Critical Path initially
Total duration of the project is 25 weeks
Critical Path = 1→3→2→7→8
Critical Path duration = 25 weeks

PROJECT MANAGEMENT
Answer to question b
ES, LS, EF LF, F Table
Activity ES EF LS LF F
A 0 8 1 9 1
B 0 6 0 6 0
C 0 3 2 5 2
D 8 13 16 21 8
E 6 9 6 9 0
F 3 7 5 9 2
G 3 5 7 9 4
H 9 16 9 16 0
I 9 13 12 16 3
J 13 17 21 25 8
K 16 25 16 25 0

PROJECT MANAGEMENT
Answer to question c
i. Task E - reduced to 2 weeks
Total duration of the project is 24 weeks
Critical Path = 1→2→7→8
Critical Path = 1→3→2→7→8
Critical Path duration = 24 weeks

PROJECT MANAGEMENT
ii. Task F - increased to 6 weeks
Total duration of the project is 25 weeks
Critical Path = 1→3→2→7→8
Critical Path = 1→4→2→7→8
Critical Path duration = 25 weeks

PROJECT MANAGEMENT
iii. Task A - increased to 10 weeks
Total duration of the project is 26 weeks
Critical Path = 1→2→7→8
Critical Path duration = 26 weeks

PROJECT MANAGEMENT
Answer to question d
Critical Path Activity
Activity Description Optimistic
Time
(weeks) (to)
Most Likely
Time (weeks)
(tm)
Pessimistic
Time (weeks) (tp)
Mean (te)
[te = (to + 4tm + tp) / 6]
Variance (σ2)
[σ2 = {( tp - to ) / 6}2]
B System
Development
3 6 9 6 1.00
E Manual Testing 2 3 4 3 0.11
H System Training 3 7 11 7 1.77
K System Changeover 1 10 13 9 4.00
Total Mean (μ) = 25 Total Variance (σ2) =
6.88
σ = √6.88 = 2.62
i. The probability that project is completed within 30 weeks
=
= 0.9713
The probability that project is completed within 30 weeks is 0.9713

PROJECT MANAGEMENT
ii. The probability that project is completed within 23 weeks
=
= 0.2236
The probability that project is completed within 30 weeks is 0.2236
iii. The time within which the management 97 per cent sure completion will occur
z = 0.8340
x = 0.8340 x 2.62 + 25 = 27.19
97 per cent sure completion will occur in 27.19 weeks

PROJECT MANAGEMENT
References
Kerzner, H. and Kerzner, H.R., 2017. Project management: a systems approach to planning, scheduling, and controlling. John Wiley & Sons.
Pinto, J.K., 2015. Project management: achieving competitive advantage. Prentice Hall.