Project Management Part 2

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Project ManagementPart 2
Lecture 8
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PERT - The probabilistic Approach to Project
Scheduling

• Three time estimate approach
• a an optimistic time to perform the activity
• m the most likely time to perform the activity
• b a pessimistic time to perform the activity

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Assumptions for Distributionof Activity Times in
PERT

• For each activity in PERT/CPM Network
• 1. The probability density function for the
  activitys completion time is a unimodal Beta
  distribution
• 2. Average (Mean) Completion Time
• m (a 4m b) / 6
• 3. Standard Deviation of Completion Time
• s (b - a) / 6

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Symmetric Unimodal Beta Distribution
m m
a
b
Unimodal Beta Distribution Skewed Left
Unimodal Beta Distribution Skewed Right
b
a
m
m
b
a
m
m
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Example (Mean and Standard Deviation ofActivity
Times for a Project)
D m 50 s 12
A m 10 s 1
C m 25 s 4
Finish
B m 20 s 2
E m 24 s 5
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Determining the Distribution of the Overall
Project Completion Time

• 1. For each activity j, calculate
• mj (a 4m b) / 6
• sj (b - a) / 6
• 2. Determine the critical path using the mjs as
  fixed times.
• 3. The overall project completion time has a
  normal distribution with
• Mean m S mj
• Variance s 2 S sj 2
• Standard deviation s Ö s 2

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Klone Computers Inc. Example
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• Management at Klone is interesting in the
  following
• The probability that the project will be
  completed within 194 days
• A reasonable interval estimate of the number of
  days to complete the project
• The probability that the project will be
  completed within 180 days
• The probability that the project will take longer
  than 210 days
• An upper limit for the number of days within
  which it can be virtually sure the project will
  be completed

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Solution

• The mean, variance and standard deviation for
  activity A can be found by
• mA (76 4(86) 120) / 6 90
• sA (120 - 76) / 6 7.33
• sA2 (7.33)2 53.73

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(No Transcript)
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Example Network
E 21
B 15
C 5
A 90
F 25
G 14
D 20
H 28
FINISH
J 45
I 30
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The Critical Path A-F-G-D-J

• Expected completion time of the project
• m mA mF mG mD mJ
• m 90 25 14 20 45 194
• Project variance
• s2 sA2 sF2 sG2 sD2 sJ2
• s2 53.78 5.44 4.00 9.00 13.44
  85.66
• Standard deviation for the project
• s Ö s 2 9.26

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• X completion time of the project
• Z standard normal random variable
• Z (X m ) / s

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• 1. The probability that the project will be
  completed within 194 days
• P(X?194) P(Z ? 0) 0.5000

X Z
194 0
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2. A reasonable interval estimate of the number
of days to complete the project 95 Interval m ?
z0.25 s z0.25 1.96 194 ? 1.96 (9.255) 194 ?
18.14 days 175 213 days
X Z
194 0
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• 3. The probability that the project will be
  completed within 180 days
• P(X?180)
• x 180
• Z (180 - 194) / 9.255 - 1.51
• P(X ? 180) P(Z ? -1.51) 0.5000 0.4345
• 0.0655 (6.55)

0.4345
0.5
X Z
194 0
180 -1.51
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• 4. The probability that the project will take
  longer than 210 days
• P(Xgt210)
• x 210
• z (210 - 194) / 9.255 1.73
• P(X gt 210) P(Z gt 1.73) 0.5000 0.4582
• 0.0418 (4.18)

0.4582
0.5
X Z
194 0
210 1.73
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• 5. An upper limit for the number of days within
  which it can be virtually sure the project will
  be completed
• P(Z ? z) 0.9900
• P(0 ? Z ? z) 0.4900
• Z (x m ) / s
• x m zs
• x 194 2.33 (9.255) 215.56 days 216 days

0.4900
0.5
X Z
194 0
x 2.33
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The Critical Path Method

• NT Normal completion time
• NC Normal cost
• CT Crash completion time
• CC Crash cost

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CPM Linearity Assumption

• If any amount between CC is spent to complete an
  activity, the percentage decrease in the
  activitys completion time from its normal time
  to its crash time equals the percentage increase
  in cost from its normal cost to its crash cost.

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Time
Job Cost 2600 Job Time 18 days 25 of the
extra cost gives 25 of the maximum time reduction
Normal NC 2000 NT 20 days
20
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Crashing NC 4400 NT 12 days
12
8
4
Cost x 1,000
10
15
20
25
30
35
40
45
5
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• T NT - CT the maximum possible time reduction
  (crashing) of an activity
• C CC - NC the maximum additional (crash)
  costs required to achieve the maximum time
  reduction
• M C / T the marginal cost of reducing an
  activitys completion time by one unit

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Tom Larkins Political Campaign
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The Project Network
A
H
C
G
F
D
E
I
B
FINISH
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Campaign Crash Schedule
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Campaign Status Report End of Week 20
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Budget, Completion Time, and Costs for Campaign
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Budget, Completion Time, and Costs for Campaign