Project Management: Critical Path Analysis and Speeding Activities

This project management assignment solution analyzes a project's critical path, calculating the shortest possible time for completion. The solution identifies the critical path, which is A-G, and determines the project's variance and standard deviation. It calculates the probability of completing the project in 24 days using the z-score. Furthermore, the assignment explores the impact of speeding up activities B and E, examining the resulting changes in path durations and associated costs. The analysis concludes that speeding up activities B or E does not affect the critical path, so focusing on speeding up activities A or G is more effective.

(a) From the project management flow/network diagram, there are four possible paths:
1. A-G: 12+15 = 27 days
2. A-C-D: 12+8+6 = 26 days
3. A-E-F: 12+5+3 = 20 days
4. B-E-F: 18+5+3 = 26 days
From the above path, A-G is the critical path and the minimum duration to complete the task,
keeping all the factors constant, is 27 days. In project management, a critical path is the sequence
of project network activities which results in the longest overall duration. Critical path determines
the shortest time possible to complete the project.
We need to calculate the probability of completing the project in 24 days instead of the
estimated 27 days. We therefore make use of the standard deviation and the z-score tables to
achieve this. From the give activity time table and variances, the project variance is:
Variance: 16+18+4+2.25+1.8+1+8 = 51.05
Standard deviation: √ 50.05=7.1449
z= x−u
sd , where x = 24, u = 27 and sd = 7.1449
Hence,z= 24−27
7.1449 =−0. 41988(Used -0.42 in z-score)
From z-score table for z = -0.42, P = 1-0.3372 = 0.6628
Hence, the probability of completing the project is 24 days is 0.6628
(b) Speeding activity B to be done in 12 days affects the path B-E-F so that the duration for this
path is: 12+5+3 = 20 days. This comes at an extra cost of $4,000.
Speeding up activity E to be done in 3 days affects the following paths, at $2,000 extra cost:
1. A-E-F: 12+3+3 = 18 days
2. B-E-F: 18+3+3 = 24 days

Speeding up both activity B and E, path B-E-F becomes:
12+3+3 = 18 days, at $6,000
Observation:
It is observed that despite imposing an extra cost on the project, speeding up any or both of the
given paths (B and E) does not in any way affect the project’s critical path. Hence, it would have a
positive impact on the project completion time. It is therefore not necessary to speed up these
activities. Instead, it is advisable to work on the possibility of speeding up activity A or G since
either of them will have positive effect on the critical path(s).