GIU_2743_62_16479_2024-03-17T11_45_07.pdf

Project Management – Spring 2024
Dr. Ibrahim Nabil Eldesouky
Faculty of Engineering
German International University (GIU)

Topics
1. Project Management basic concepts
2. Define the Project scope and priorities.
3. Estimate the project time and cost.
4. Develop project schedule.
5. Risk Management.
6. Schedule resources.
7. Project team management.
8. Progress and performance evaluation.
9. Project closing
17 March 2024 Dr. Ibrahim Eldesouky 2

Lecture 6 - The Project Time and Cost

Learning Outcomes
• Calculating the probability that a project will be completed within a
certain time.
• Reducing the project time (crashing).
• Cost evaluation and forecasting.

Probabilistic Time Estimates
• Optimistic time (a)
• Time required under optimal conditions
• Pessimistic time (b)
• Time required under worst conditions
• Most likely time (m)
• Most probable length of time that will be required

CPM with Probabilistic Time Estimates
Step 1: Identify activities.
Step 2: Sequence activities and construct network.
Step 3: Determine the three time estimates for
each activity.
a = optimistic time
m = most likely time
b = pessimistic time
Step 4: Calculate the Expected Time (ET) for each activity.
6
b
4m
a
ET
+
+
=
The calculation is a weighted average of the three-time estimates, a, m, and b
using weights of 1‐4‐1, respectively.

CPM with Probabilistic Time Estimates
Step 5: Calculate the variance (σ2) for each activity.
In this case, the “6” is an assumption that the range of the distribution covers six
standard deviations (6σ) so that 99.7 percent of all cases were greater than a and
less than b; 2
2
6





 

a
b

Activity Optimistic Most Likely Pessimistic Variance
A 2 4 6 0.44
B 3 7 10 1.36
C 2 3 5 0.25
D 4 7 9 0.69
E 12 16 20 1.78
F 2 5 8 1.00
G 2 2 2 0.00
H 2 3 4 0.11
I 2 3 5 0.25
J 2 4 6 0.44
K 2 2 2 0.00

Estimating the Probability of Completion Dates
Step 7: Determine the probability of completing the project
by a certain date.
p
p
ET
D
Z



D = Desired completion date for the project
ETp = Expected completion time for the path
σp = Standard deviation for the path

Project Activity Expected Time
Activity
Optimistic
time
Most likely
time
Pessimistic
time
Expected
time
A 2 4 6 4
B 3 7 10 6.83
C 2 3 5 3.17
D 4 7 9 6.83
E 12 16 20 16
F 2 5 8 5
G 2 2 2 2
H 2 3 4 3
I 2 3 5 3.17
J 2 4 6 4
K 2 2 2 2

Project Activity Variance
Activity Optimistic Most Likely Pessimistic Variance
A 2 4 6 0.44
B 3 7 10 1.36
C 2 3 5 0.25
D 4 7 9 0.69
E 12 16 20 1.78
F 2 5 8 1.00
G 2 2 2 0.00
H 2 3 4 0.11
I 2 3 5 0.25
J 2 4 6 0.44
K 2 2 2 0.00

Build AOA Network & Identify Paths

Variances of Each Path through the Network
Path
Number
Activities on
Path
Path Time
(Weeks)
Path Variance
(weeks)
1 A,B,D,E,G,H,J,k 44.66 4.82
2 A,B,D,E,G,I,J,K 44.83 4.96
3 A,C,F,G,H,J,K 23.17 2.24
4 A,C,F,G,I,J,K 23.34 2.38
ABDEGIJK is the expected critical path & the project has an expected duration
of 44.83 weeks

Example: Calculating the probability of finishing the project
in 48 weeks
• Use the z values in Appendix B to determine probabilities
• e.g. probability for path 1 is
Path
Number
Activities on Path Path Variance
(weeks)
z-value Probability of
Completion
1 A,B,D,E,G,H,J,k 4.82 1.52 0.93
2 A,B,D,E,G,I,J,K 4.96 1.42 0.92
3 A,C,F,G,H,J,K 2.24 16.59 1.00
4 A,C,F,G,I,J,K 2.38 15.98 1.00

Reducing Project Completion Time
• Project completion times may need to be shortened because:
• Penalty.
• Need to put resources on a new project.
• Promised completion dates.
• Reduced project completion time is “crashing”

Reducing Project Completion Time – con’t
• Crashing a project needs to balance
• Shorten a project duration
• Cost to shorten the project duration
• Crashing a project requires you to know
• Crash time of each activity
• Crash cost of each activity
Crash cost/duration = (crash cost-normal cost)/(normal time – crash time)

Reducing the Time of a Project (crashing)
Activity Normal
Time (wk)
Normal
Cost ($)
Crash
Time
(wk)
Crash
Cost ($)
Max. weeks
of reduction
Reduce cost
per week
A 4 8,000 3 11,000 1 3,000
B 6 30,000 5 35,000 1 5,000
C 3 6,000 3 6,000 0 0
D 6 24,000 4 28,000 2 2,000
E 14 60,000 12 72,000 2 6,000
F 5 5,000 4 6,500 1 1500
G 2 6,000 2 6,000 0 0
H 2 4,000 2 4,000 0 0
I 3 4,000 2 5,000 1 1,000
J 4 4,000 2 6,400 2 1,200
K 2 5,000 2 5,000 0 0

Crashing Example: Suppose the Cables By Us project manager
wants to reduce the new product project from 41 to 36 weeks.
• Crashing Costs are considered to be linear
• Look to crash activities on the critical path
• Crash the least expensive activities on the critical path first
(based on cost per week)
• Crash activity I from 3 weeks to 2 weeks $1000
• Crash activity J from 4 weeks to 2 weeks $2400
• Crash activity D from 6 weeks to 4 weeks $4000
• Recommend Crash Cost $7400

Crashed Network A-O-N Diagram

Estimate Activity Costs
Elements
• Labor
• Materials
• Equipment
• Facilities
• Subcontractors and consultants
• Travel
• Reserve
Good Practices
• Have the person responsible
estimate costs.
• Use historical data to inform the
current project manager.
• Be reasonable and realistic.
• Estimate near-term activities more
accurately.
• Elaborate on other costs as
additional information is known.

Consumer Market Study Project
Estimated Costs

Total Budgeted Cost
• Establish a Total Budgeted
Cost TBC for each work
package
• Determine the process
• Top-down
• Bottom-up
• If sum of initial estimates
exceeds sponsor budget,
then reduce costs and
recalculate

Packaging Machine Project
Aggregate Total Budgeted Cost

Develop Cumulative Budgeted Cost
• Determine budgeted cost by period
• Graph the cumulative budgeted cost
curve

Determine Actual Cost
• Actual Cost
• Collect data regularly for funds actually spent
• Charge to work package numbers
• Compare Actual Cost To Budgeted Cost
• Calculate cumulative actual cost
• Compare to cumulative budgeted cost

Determine Actual Cost
• End of Week 8
• Planned cost = $64,000
• Actual cost = $68,000
• Compare Cumulative Actual
Cost CAC with Cumulative
Budgeted Cost CBC

Determine the Earned Value of Work Performed
Example Project
• Paint 10 similar rooms
• Total budgeted cost of $2,000
• Budget is $200 per room
At Day 5
• $1,000 has been spent
• 3 rooms have been painted
• Earned value =
0.30 X $2,000 = $600
• Have spent $400 more than the
Earned Value

Determine the Earned Value of Work Performed
EV = % of work completed x TBC

Analyze Cost Performance
• Four cost-related measures
• TBC – Total Budgeted Cost
• CBC – Cumulative Budgeted Cost
• CAC – Cumulative Actual Cost
• CEV – Cumulative Earned Value
• To analyze project cost performance
• Plot CBC, CAC, and CEV curves on the same graph
• Reveal any trends toward improving or deteriorating cost performance

Analyze Cost Performance
CBC CAC CEV

Cost Performance Index
• Measure of the cost efficiency with which the project is being
performed
• Cost performance index =
Cumulative earned value/Cumulative actual cost
CPI = CEV/CAC

Cost Performance Index
End of Week 8
• $64,000 was budgeted
• $68,000 was actually expended
• $54,000 was the earned value of
work actually performed
• CEV = $54,000
• CAC = $68,000
Determine CPI
• CPI = CEV/CAC
= $54,000/$68,000
= 0.79
For every $1.00 actually
expended, only $0.79 of earned
value was received.

Cost Variance
• Indicator of cost performance
• Difference between the cumulative earned value of the work
performed and the cumulative actual cost
• Cost variance =
Cumulative earned value – Cumulative actual cost
CV = CEV – CAC

Cost Variance
End of Week 8
• CEV = $54,000
• CAC = $68,000
Determine CV
• CV = CEV – CAC
= $54,000 – $68,000
= –$14,000
The value of the work
performed through week 8 is
$14,000 less than the amount
actually expended.

Estimate Cost at Completion
• Forecast what the total costs will be at the completion of the project
or work package
• 3 different methods
• FCAC = TBC / CPI
• FCAC = CAC + (TBC – CEV)
• FCAC = CAC + Re-estimate of remaining work
• Another method
• To Complete performance index
• TCPI = (TBC – CEV)/(TBC – CAC)

To complete performance index
• TCPI indicates the target cost performance index (CPI) that is needed
to complete the project at the target budget.
• To-complete-performance index is the result of dividing the
remaining budget according to the plan by the actually available
budget.
• TCPI = 1: the project can continue with the current budget
consumption rate
• TCPI < 1: based on the current cost variance, the project will be
completed at total cost lower than the budget.
• TCPI > 1: if the project continues working with the present cost
variance, it will complete at a budget overrun.

Estimate Cost at Completion
End of Week 8
• CEV = $54,000
• CAC = $68,000
• CPI = 0.79
• TBC = $100,000
Determine FCAC
• FCAC = TBC / CPI
= $100,000/0.79 = $126,582
• FCAC = CAC + (TBC – CEV)
= $68,000 + ($100,000 – $54,000)
= $68,000 + $46,000
= $114,000
• TCPI = (TBC – CEV)/(TBC – CAC)
= ($100,000 − $54,000)/($100,000 − $68,000)
= $46,000/$32,000
= 1.44

Manage Cash Flow
• Ensure that cash comes in faster than it goes out
• Negotiate payment terms
• Provide a down payment
• Make equal monthly payments
• Provide frequent payments
• Avoid only one payment at end of project
• Control outflow of cash

Any questions?

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