Project Management

This document provides answers to questions related to project management, including calculating expected duration, crashing the project, and analyzing costs. It also includes a comparison of normal and crash costs. The document is based on the case study of a project and provides detailed explanations and calculations.

Running Head: PROJECT MANAGEMENT
Project Management
Name of the Student
Name of the University

1PROJECT MANAGEMENT
Answer to Question 1
Based on the three durations specified, the expected duration for the project can be
calculated using the formula TE = (O + P + 4M) / 6, where TE is expected duration, O is
optimistic duration, P is pessimistic duration and M is most likely duration. The calculated
expected duration is shown in the following table (all durations are in weeks).
Optimistic
Duration
Most Likely
Duration
Pessimistic
Duration
Expected
Duration
2 3 4 3
4 7 10 7
5 6 9 6.3
6 7 16 8.3
7 9 10 8.8
4 5 6 5
3 6 10 6.2
2 4 7 4.2
2 2 2 2
3 4 14 5.5
2 3 4 3
Now, considering the direct costs for the project and the most expected duration scenario,
the detailed budget is calculated as follows.
Task Name Cost
Internet Forecasting Project $205,000.00

2PROJECT MANAGEMENT
Requirements $10,000.00
Market Assessment $20,000.00
Design $15,000.00
Development $45,000.00
Testing $10,000.00
Revising $15,000.00
Documentation $20,000.00
Quality Assurance $10,000.00
Pricing $5,000.00
Production $40,000.00
Distribution $15,000.00
Again, it has been mentioned that there is an indirect cost of $200 per week of the
project. Hence, the total indirect cost for the project = $(200*39.9) = $7980.
Hence, the total cost for the project = Direct Cost + Indirect Cost = $(205,000 + 7980) =
$212,980.
Now, in order to determine the critical path of the project, first, the paths of the project
are determined as shown in the following AON Diagram.

3PROJECT MANAGEMENT
Figure 1: AON Diagram of the Project
(Source: Created by Author)
Now, the starting point of the project is A and the ending point is K. Now, the various
paths from A to K, determined from the diagram above are specified as follows.
i. A  B  F  J  K
ii. A  B  I  J  K
iii. A  C  H  J  K
iv. A  C  D  E  F  J  K
v. A  C  D  E  H  J  K
vi. A  C  D  G  J  K
Hence, there are six possible paths from the starting to the ending point of the project.
Now, in order to determine the highest duration path (critical path), it is required to determine the
durations of each path of the project. These durations are shown in the following table.
No. Path Duration (weeks)

4PROJECT MANAGEMENT
1 A  B  F  J  K 3 + 7 + 5 + 5.5 + 3 = 23.5
2 A  B  I  J  K 3 + 7 + 2 + 5.5 + 3 = 20.5
3 A  C  H  J  K 3 + 6.3 + 4.2 + 5.5 + 3 = 22
4 A  C  D  E  F  J  K 3 + 6.3 + 8.3 + 8.8 + 5 + 5.5 + 3 = 39.9
5 A  C  D  E  H  J  K 3 + 6.3 + 8.3 + 8.8 + 4.2 + 5.5 + 3 = 39.1
6 A  C  D  G  J  K 3 + 6.3 + 8.3 + 6.2 + 5.5 + 3 = 32.3
From this table, it is seen that Path 4 i.e. [A  C  D  E  F  J  K] is the critical
path of the project since it has the longest duration of all paths (39.9 weeks). Now, the critical
path is highlighted in the AON diagram.
Figure 2: AON Diagram with Critical Path (Critical Path Marked Red)
(Source: Created by Author)
Answer to Question 2
Minimum expected time required for the project corresponds with the longest path of the
path. As analyzed in the previous question, there are six paths in the project from start to the end

5PROJECT MANAGEMENT
point and the longest duration is for Path 4 (A  C  D  E  F  J  K) and corresponds to
39.9 weeks in total. Thus, the minimum expected duration for the project is 39.9 weeks.
Answer to Question 3
Crashing the project refers to reducing the overall duration of the project while the cost of
the project increases. When crashing the total duration of the project, it must be done only on the
critical path as crashing on a non-critical path will not have any effect on the overall duration of
the project and the extra costs will turn out to be unnecessary expenditure. It is also generally
accepted convention to crash the activities that require lowest additional costs to avoid too much
budget overshoot.
Now, for this particular question, the project has to be crashed to 35 weeks with
minimum possible additional cost. Again, it is unnecessary to crash the non-critical tasks as it
will not have any effect on the overall duration of the project. Hence, crashing is to be done in
one or more of the activities A, C, D, E, F, J and K.
It is required to crash the project by (39.9 – 35) = 4.9 weeks. The normal and crash
durations for the project (as per the expected duration calculated earlier and the crash duration
given in the case study) is shown in the following table.
Activit
y
Normal Crashed
Duration (days) Cost ($)
Duration
(days)
Cost
($)
Reduction in
Duration
Extra
cost
A 3 10000 3 10000 0 0
B 7 20000 6 25000 N/A N/A

6PROJECT MANAGEMENT
C 6.3 15000 5 30000 1.3 15000
D 8.3 45000 6 65000 2.3 20000
E 8.8 10000 8 20000 0.8 10000
F 5 15000 4 18000 1 3000
G 6.2 20000 4 30000 N/A N/A
H 4.2 10000 3 15000 N/A N/A
I 2 5000 2 5000 N/A N/A
J 5.5 40000 5 50000 0.5 10000
K 3 15000 2 25000 1 10000
In the table, the crash duration and costs for non-critical paths are ignored as they are
unnecessary. For the critical path (ACDEFJK), the crashed durations and crash costs are shown
in the table. The calculation from the table shows that crashing can be done up to 6.9 weeks,
whereas for this particular case, 4.9 weeks crash is required. There are two activities that can be
crashed for 1 week each (F and K). So, if these activities are not crashed, the rest of the critical
activities can be crashed up to the required 4.9 weeks. Now, the crashing is performed as
follows.
Step 1: Activity A – As per the given data, activity A cannot be crashed and hence, it
remains unchanged.
Step 2: Activity C – Activity C is crashed by 1.3 weeks and hence, the total duration is
reduced to (39.9 – 1.3) = 38.6 weeks and additional cost is $15,000.
Step 3: Activity D – Activity D is crashed by 2.3 weeks reducing the total duration to
(38.6 – 2.3) = 36.3 weeks and additional cost is $20,000.
Step 4: Activity E – Activity E is crashed by 0.8 weeks reducing the total duration to
(36.3 – 0.8) = 35.5 weeks and additional cost is $10,000.
Step 5: Activity J – The remaining (35.5 – 30) = 0.5 weeks crashing is done on Activity J
incurring an additional cost of $10,000.

7PROJECT MANAGEMENT
Thus, the total project duration is crashed to 35 weeks incurring additional cost of
$(15,000 + 20,000 + 10,000 + 10,000) = $55,000.
Justification for Selecting the Crash Activities – While the project is crashed to the
required a total of 35 weeks, it is important know why only four activities have been chosen to
crash instead of all the tasks. The main reason is that all the activities that have been chosen to
crash lie within the critical path of the project (as specified in the first question itself). The non-
critical activities could have also been crashed but that would have no additional impact on the
duration of the project and the extra crash costs would have been unnecessary and not required.
Hence, only the four activities have been crashed until the total expected duration of the project
has been reduced to 35 weeks.
Answer to Question 4
Considering the case presented, the expected duration of task B is increased from 7 to 9.
In the following table, the duration of B is increased from 7 to 9 and it is checked whether it
impacts the critical path or not (B does not lie on the critical path as per initial conditions).
No. Path Duration (weeks)
1 A  B  F  J  K 3 + 9 + 5 + 5.5 + 3 = 25.5
2 A  B  I  J  K 3 + 9 + 2 + 5.5 + 3 = 22.5
It is seen that even after increasing the duration of B, neither of the paths through B
exceeds the critical duration of the project. Thus, B remains a non-critical path and does not

8PROJECT MANAGEMENT
impact of the overall duration of the project. Hence, it can be concluded that the increase in
duration of B does not have direct impact on the crashing solution presented in Question 3.
However, if the increase in duration for activity B results in reduced cost for the activity, the
reduction in the cost can help in reduction of the total crash cost of the project.
Answer to Question 5
The cost function for the normal duration of the project is shown in the following graphs.
A B C D E F G H I J K
$-
$5,000.00
$10,000.00
$15,000.00
$20,000.00
$25,000.00
$30,000.00
$35,000.00
$40,000.00
$45,000.00
$50,000.00
Direct Cost
Indirect Cost
Cumulative Cost
Figure 1: Cost Function Graph for Normal Duration
(Source: Created by Author)
The cost function for the crash duration of the project is shown in the following graph.

9PROJECT MANAGEMENT
A B C D E F G H I J K
$-
$10,000.00
$20,000.00
$30,000.00
$40,000.00
$50,000.00
$60,000.00
$70,000.00
Direct Cost
Indirect Cost
Cumulative Cost
Figure 2: Cost Function Graph for Crashed Duration
(Source: Created by Author)
Finally, the comparison between the normal and crash costs is shown in the following
cost graph.
A B C D E F G H I J K
0
10000
20000
30000
40000
50000
60000
70000
Normal Cost (Direct +
Indirect)
Crash Cost (Direct +
Indirect)
Figure 3: Comparison of Normal and Crash Costs

10PROJECT MANAGEMENT
(Source: Created by Author)

11PROJECT MANAGEMENT
Bibliography
Kerzner, H., & Kerzner, H. R. (2017). Project management: a systems approach to planning,
scheduling, and controlling. John Wiley & Sons.
Koulinas, G., Kotsikas, L., & Anagnostopoulos, K. (2014). A particle swarm optimization based
hyper-heuristic algorithm for the classic resource constrained project scheduling
problem. Information Sciences, 277, 680-693.
Lamas, P., & Demeulemeester, E. (2016). A purely proactive scheduling procedure for the
resource-constrained project scheduling problem with stochastic activity
durations. Journal of Scheduling, 19(4), 409-428.
Mubarak, S. A. (2015). Construction project scheduling and control. John Wiley & Sons.
Naber, A., & Kolisch, R. (2014). MIP models for resource-constrained project scheduling with
flexible resource profiles. European Journal of Operational Research, 239(2), 335-348.
Tavana, M., Abtahi, A. R., & Khalili-Damghani, K. (2014). A new multi-objective multi-mode
model for solving preemptive time–cost–quality trade-off project scheduling
problems. Expert Systems with Applications, 41(4), 1830-1846.
Van Peteghem, V., & Vanhoucke, M. (2014). An experimental investigation of metaheuristics
for the multi-mode resource-constrained project scheduling problem on new dataset
instances. European Journal of Operational Research, 235(1), 62-72.

12PROJECT MANAGEMENT
Wang, W. C., Weng, S. W., Wang, S. H., & Chen, C. Y. (2014). Integrating building information
models with construction process simulations for project scheduling support. Automation
in construction, 37, 68-80.