Topics to cover in 2nd part

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Topics to cover in 2nd part
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Chapter 8 - Project ManagementChapter Topics

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Project Management

• Questions
• Why do we need to study Project Management?
• How does a project management technique work?

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Objective

• The main purpose is to govern the operations of a
  project such that all activities involved are
  well administrated and that we can also control
  its completion time

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Project management technique

• Steps to solve a project management
• problem
• to represent a project problem graphically
• to determine its completion time
• to carry out sensitivity analysis, if any

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1. Represent a project problem graphically
Event Processing Time Precedent constraints
A B C 20 30 10 -- A B

• Steps
• Gather all information and organize them in a
  table format that consists of event, processing
  time, and precedent constraints as follows
• Draw a semantic network to represent them
• Special case!

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Semantic network to represent them

• Here, we use three symbols
• node to represent stage
• line/branch to represent event
• arrow to represent precedent
• constraint
• Example

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Example
Path Event Proc Time Pred Const
1-2 2-3 3-4 A B C 20 30 10 -- A B
C
A
B
1
2
3
4
30
10
20
Rule1 All nodes must starts from one Node and
ends with one node
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Special case!

• When two or events taken places in the same time
  interval
• (known an concurrent events)
• Consider the following example!
• How to draw it?

Event Processing Time Precedent constraints
A B C 3 5 7 -- A A
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Case 1
A
B
2
3
1
5
3
C
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Wrong!
Rule2 no node can have two outcomes and end
with the same note
Solution
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Solutions for Rule 2
A dummy activity shows a precedence
relationship Reflects no processing time

• Three ways to draw it

3
B
Dummy 10
A
1
2
5
C
Solution 1
4
Dummy 2 0
What one is better?
A
B
1
2
4
Solution 2
C
3
Dummy 0
3
Dummy 0
B
A
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1
2
4
Solution 3
C
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2. Determine its completion time

• Consider the project network as shown in next
  slide
• Question Is it an easy way to find out the
• solution?
• Answer YES, it knows as
• Critical Path Method (CPM)

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The Project Network All Possible Paths for
Obtaining a Solution
Figure 8.3 Expanded network for building a house
showing concurrent activities.


Table 8.1 Possible Paths to complete the
House-Building Network
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Then the completion time for paths A, B, C and D
can be computed as
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The Project Network
Completion time for path A 1?2 ? 3 ? 4
? 6 ? 7, 3 2 0 3 1 9 months (Critical
Path)

path B 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7, 3 2 0
1 1 1 8 months

path C 1 ? 2 ? 4 ? 6 ? 7, 3 1 3 1
8 months path D 1 ? 2 ? 4 ? 5 ? 6 ? 7,
3 1 1 1 1 7 months The critical path is
the longest path through the network the minimum
time the network can be completed.
This is the Solution!
Figure 8.5 Alternative paths in the network
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Critical Path Method (CPM)

• General concepts
• For each branch of the project network, we
  firstly determine four values of ES, EF, LS and
  LF
• For each branch, we compute their slack time,
• Slack time (LS-ES) or (LF-EF)
• The critical path is located at branch that has
• slack time 0
• (Do you know the reason why?)
• How it works?

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How CPM works?

• Steps
• Prepare the project network
• Construct a table as follows
• Compute ES and EF
• Compute LS and LF
• Compute LS-ES or LF-EF

Branch ES EF LS LF

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ESij max (EFi) EFij ESi tij with
EF10
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Critical path when LS-ES0
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Compute ES and EF

• Note
• When computing these values, the pattern is like
  moving zic-zac format by firstly computer ES12
  and then adding it to EF12 and move to next
  branch by copying the max values of the branch
  1-2 to say, 2-3
• We compute them from top to bottom!
• Their relationship
• Example 1

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The starting point of ES and EF

• Consider
• Then
• EF1 0
• ES12 max (EF1) EF12 ES12 t12
• 0 0 t12

t12
1
2
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Branches ESij max(EFi) EFijESijtij
1-2 2-3 2-4 3-4 4-5 4-6 5-6 6-7 ES12 max(EF1) ES23max(EF2) ES24max(EF2) ES34max(EF3) ES45max(EF4) ES46max(EF4) ES56max(EF5) ES67max(EF6) EF12ES12t12 EF23ES23t23 EF24 EF34 EF45 EF46 EF56 EF67
The overall computation is shown in next slide
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Complete solution
- ES is the earliest time an activity can
start. ESij Maximum (EFi) - EF is the earliest
start time plus the activity time. EFij ESij
tij
add all ti for note 2
Add all t to note 4 and take the longest time Max
(node 3t34, node2t24) max (50,
31) max(5,4)5
Max(node4t46,node5t56 max(53,51)8
(noteyou can compute these values and show in
the network diagram as well)
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The Project Network Activity Scheduling-
Earliest Times
- ES is the earliest time an activity can
start. ESij Maximum (EFi) - EF is the earliest
start time plus the activity time. EFij ESij
tij
Figure 8.6 Earliest activity start and finish
times
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Compute LS and LF

• Note We compute these values from the bottom to
  top, with assigning
• LSij LFi -tij LFij min LSj
• with
• the end of LFij EFij
• Example computing Figure 8.3

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Branches LSij LFij-tij LFijmin(LSj)
1-2 2-3 2-4 3-4 4-5 4-6 5-6 6-7 LS12 Li12-t12 LS23 LF23-t23 LS24 LF24-t24 LS34 LF34-t34 LS45 LF45-t45 LS46 LF46-i46 LS56 LF56-t56 LS67 LF67-t67 LF12min(LS2) LF23min(LS3) LF24min(LS4) LF34min(LS4) LF45min(LS5) LF46min(LS6) LF56min(LS6) LF67min(LS7)
The overall computational is shown in next slide
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- LS is the latest time an activity can start
without delaying critical path time. LSij LFij
- tij - LF is the latest finish time
LFij Minimum (LSj)
Min(node3-t23,node4-t24) Min(5-2,5-1)Min(3,4)3
Min(node 6-t46,node5-t45) Min(8-3,7-1) Min(5,6)
5
Min(node 7-t67) Min(9-1)8
Same as EF67 from the previous slide
Start with the end node first
Again, you can place these values onto the
branches
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The Project Network Activity Scheduling - Latest
Times
- LS is the latest time an activity can start
without delaying critical path time. LSij LFij
- tij - LF is the latest finish time
LFij Minimum (LSj)
Figure 8.7 Latest activity start and finish times
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Compute LS-ES or LF-EF

• Two ways you can achieve it
• by compiling slack, Sij
• by showing branches

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The Project Network Calculating Activity Slack
Time
- Slack, Sij, computed as follows Sij LSij
- ESij or Sij LFij - EFij

Table 8.2 Activity
Slack   Figure 8.9 Activity
Slack

What does it mean?
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The Project Network Activity Slack

• Slack is the amount of time an activity can be
  delayed without delaying the project.
• Slack time exists for those activities not on
  the critical path for which the earliest and
  latest start times are not equal.
• Shared slack is slack available for a sequence
  of activities.

Figure 8.8 Earliest activity start and finish
times
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Sensitivity Analysis

• Today, we only consider one case
• Probabilistic Activity Times
• Refer to activity time estimates usually can not
  be made with certainty
• PERT is known as the solution method

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PERT

• In PERT, three different time estimations are
  applied
• most likely time (m),
• the optimistic time (a) , and
• the pessimistic time (b).
• How do we make use of these three values?

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Probabilistic Activity Times

• We used these values to estimate the mean and
  variance of a beta distribution
• mean (expected time)
• variance
• How to use these values to solve a project
  network problem?

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PERT

• We simply apply t values in CPM and determine the
  values of
• ES
• EF
• LS
• LF
• S
• and branches with slack 0 still consider as
  critical paths
• Example.

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Procedures for PERT

• Step 1 based on the values of a, b and m,
  determine the t and v values for each path
• Step 2 determine the critical path by using t
  values in the CPM
• Step 3 compute its corresponding means and
  standard deviations according.
• Example
• Result implication
• Applications

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PERT Example

• Step 1 computer t and v values
• Step 2 determine the CPM
• Step 3 determine v value

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Step 1 computer t and v values

Figure 8.11 Network with mean activity times and
variances
Table 8.3 Activity Time Estimates for Figure
8.10
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Step 2 determine the CPM
Figure 8.12 Earliest and latest activity times
Table 8.4 Activity Earliest and Latest Times and
Slack
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Step 3 determine v value

• The expected project time is the sum of the
  expected times of the critical path activities.
• The project variance is the sum of the variances
  of the critical path activities.
• The expected project time is assumed to be
  normally distributed (based on central limit
  theorum).
• In example, expected project time (tp) and
  variance (vp) interpreted as the mean (?) and
  variance (?2) of a normal distribution
• ? 25 weeks
• ?2 6.9 weeks

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Probability Analysis of the Project Network
- Using normal distribution, probabilities are
determined by computing number of standard
deviations (Z) a value is from the mean. - Value
is used to find corresponding probability in
Table A.1, App. A.
Figure 8.13 Normal distribution of network
duration
Critical value
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• Consider when
• x 30
• x 22
• Tutorial Assignment

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Probability Analysis of the Project
NetworkExample 1

• ?2 6.9 ? 2.63
• Z (x-?)/ ? (30 -25)/2.63 1.90
• Z value of 1.90 corresponds to probability of
  .4713 in Appendix A of p715. Probability of
  completing project in 30 weeks or less (.5000
  .4713) .9713,
• or 97.13 (Why so high a probability
  rate?)

Figure 8.14 Probability the network will be
completed in 30 weeks or less
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Probability Analysis of the Project
NetworkExample 2
Z (22 - 25)/2.63 -1.14 Z value of 1.14
(ignore negative) corresponds to probability of
.3729 in Table A.1, appendix A. Probability that
customer will be retained is .1271 ( 0.5-
0.3729) , or 12.71 (Again, why so low
probability rate?)
Figure 8.15 Probability the network will be
completed in 22 weeks or less
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Tutorial Assignment

• Try to use QM to solve CPM/PERT problems (see
  slide 19)
• Exercises (Chapter 8)
• Old 8, 10, 17
• New 4, 6, 11

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Probability Analysis of the Project
NetworkCPM/PERT Analysis with QM for Windows
Exhibit 8.1
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The Project Network Activity Slack

• Slack is the amount of time an activity can be
  delayed without delaying the project.
• Slack time exists for those activities not on
  the critical path for which the earliest and
  latest start times are not equal.
• Shared slack is slack available for a sequence
  of activities.

Figure 8.8 Earliest activity start and finish
times
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The Project Network Calculating Activity Slack
Time
- Slack, Sij, computed as follows Sij LSij
- ESij or Sij LFij - EFij

Table 8.2 Activity
Slack   Figure 8.9 Activity
Slack