Operations CASE, SLP and TD
lilkittingurl
powerpoint_slide_2.pptGantt chart
Critical Path Method (CPM)
Program Evaluation and Review Technique (PERT)
Project Management Techniques
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A Simple Gantt Chart
Time
J F M A M J J A S
Design
Prototype
Test
Revise
Production
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Service For A Delta Jet
Figure 3.4
Passengers
Baggage
Fueling
Cargo and mail
Galley servicing
Lavatory servicing
Drinking water
Cabin cleaning
Cargo and mail
Flight services
Operating crew
Baggage
Passengers
Deplaning
Baggage claim
Container offload
Pumping
Engine injection water
Container offload
Main cabin door
Aft cabin door
Aft, center, forward
Loading
First-class section
Economy section
Container/bulk loading
Galley/cabin check
Receive passengers
Aircraft check
Loading
Boarding
0 15 30 45 60
Minutes
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Project Control Reports
Detailed cost breakdowns for each task
Total program labor curves
Cost distribution tables
Functional cost and hour summaries
Raw materials and expenditure forecasts
Variance reports
Time analysis reports
Work status reports
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Network techniques
Developed in 1950’s
CPM by DuPont for chemical plants (1957)
PERT by Booz, Allen & Hamilton with the U.S. Navy, for Polaris missile (1958)
Consider precedence relationships and interdependencies
Each uses a different estimate of activity times
PERT and CPM
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Six Steps PERT & CPM
Define the project and prepare the work breakdown structure
Develop relationships among the activities - decide which activities must precede and which must follow others
Draw the network connecting all of the activities
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Six Steps PERT & CPM
Assign time and/or cost estimates to each activity
Compute the longest time path through the network – this is called the critical path
Use the network to help plan, schedule, monitor, and control the project
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When will the entire project be completed?
What are the critical activities or tasks in the project?
Which are the noncritical activities?
What is the probability the project will be completed by a specific date?
Questions PERT & CPM
Can Answer
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Is the project on schedule, behind schedule, or ahead of schedule?
Is the money spent equal to, less than, or greater than the budget?
Are there enough resources available to finish the project on time?
If the project must be finished in a shorter time, what is the way to accomplish this at least cost?
Questions PERT & CPM
Can Answer
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
Figure 3.5
A comes before B, which comes before C
(a)
A
B
C
B
A
C
A and B must both be completed before C can start
(b)
A
C
C
B
A
B
B and C cannot begin until A is completed
(c)
B
A
C
A
B
C
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
Figure 3.5
A
B
C
D
B
A
C
D
C and D cannot begin until A and B have both been completed
(d)
C
A
B
D
Dummy activity
A
B
C
D
C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA
(e)
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
Figure 3.5
A
C
D
B
A
B
C
D
Dummy activity
B and C cannot begin until A is completed. D cannot begin until both B and C are completed. A dummy activity is again introduced in AOA.
(f)
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AON Example
Milwaukee Paper Manufacturing's
Activities and Predecessors
Table 3.1
| Activity | Description | Immediate Predecessors |
| A | Build internal components | — |
| B | Modify roof and floor | — |
| C | Construct collection stack | A |
| D | Pour concrete and install frame | A, B |
| E | Build high-temperature burner | C |
| F | Install pollution control system | C |
| G | Install air pollution device | D, E |
| H | Inspect and test | F, G |
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AON Network for Milwaukee Paper
Figure 3.6
A
Start
B
Start Activity
Activity A
(Build Internal Components)
Activity B
(Modify Roof and Floor)
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AON Network for Milwaukee Paper
Figure 3.7
C
D
A
Start
B
Activity A Precedes Activity C
Activities A and B Precede Activity D
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AON Network for Milwaukee Paper
Figure 3.8
G
E
F
H
C
A
Start
D
B
Arrows Show Precedence Relationships
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AOA Network for Milwaukee Paper
Figure 3.9
H
(Inspect/ Test)
7
Dummy Activity
6
F
(Install Controls)
E
(Build Burner)
G
(Install Pollution Device)
5
D
(Pour Concrete/ Install Frame)
4
C
(Construct Stack)
1
3
2
B
(Modify Roof/Floor)
A
(Build Internal Components)
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Determining the Project Schedule
Perform a Critical Path Analysis
- The critical path is the longest path through the network
- The critical path is the shortest time in which the project can be completed
- Any delay in critical path activities delays the project
- Critical path activities have no slack time
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Determining the Project Schedule
Perform a Critical Path Analysis
Table 3.2
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25
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Determining the Project Schedule
Perform a Critical Path Analysis
Table 3.2
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack 2
D Pour concrete and install frame 4
E Build high-temperature burner 4
F Install pollution control system 3
G Install air pollution device 5
H Inspect and test 2
Total Time (weeks) 25
Earliest start (ES) = earliest time at which an activity can start, assuming all predecessors have been completed
Earliest finish (EF) = earliest time at which an activity can be finished
Latest start (LS) = latest time at which an activity can start so as to not delay the completion time of the entire project
Latest finish (LF) = latest time by which an activity has to be finished so as to not delay the completion time of the entire project
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Determining the Project Schedule
Perform a Critical Path Analysis
Figure 3.10
Activity Name or Symbol
A
Earliest Start
ES
Earliest Finish
EF
Latest Start
LS
Latest Finish
LF
Activity Duration
2
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Forward Pass
Begin at starting event and work forward
Earliest Start Time Rule:
If an activity has only one immediate predecessor, its ES equals the EF of the predecessor
If an activity has multiple immediate predecessors, its ES is the maximum of all the EF values of its predecessors
ES = Max (EF of all immediate predecessors)
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Forward Pass
Begin at starting event and work forward
Earliest Finish Time Rule:
The earliest finish time (EF) of an activity is the sum of its earliest start time (ES) and its activity time
EF = ES + Activity time
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ES/EF Network for Milwaukee Paper
Start
0
0
ES
0
EF = ES + Activity time
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ES/EF Network for Milwaukee Paper
Start
0
0
0
A
2
2
EF of A =
ES of A + 2
0
ES
of A
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ES/EF Network for Milwaukee Paper
B
3
Start
0
0
0
A
2
2
0
3
EF of B =
ES of B + 3
0
ES
of B
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ES/EF Network for Milwaukee Paper
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
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ES/EF Network for Milwaukee Paper
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
D
4
= Max (2, 3)
3
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ES/EF Network for Milwaukee Paper
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
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ES/EF Network for Milwaukee Paper
Figure 3.11
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
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Backward Pass
Begin with the last event and work backwards
Latest Finish Time Rule:
If an activity is an immediate predecessor for just a single activity, its LF equals the LS of the activity that immediately follows it
If an activity is an immediate predecessor to more than one activity, its LF is the minimum of all LS values of all activities that immediately follow it
LF = Min (LS of all immediate following activities)
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Backward Pass
Begin with the last event and work backwards
Latest Start Time Rule:
The latest start time (LS) of an activity is the difference of its latest finish time (LF) and its activity time
LS = LF – Activity time
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LS/LF Times for
Milwaukee Paper
Figure 3.12
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = EF
of Project
15
13
LS = LF – Activity time
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LS/LF Times for
Milwaukee Paper
Figure 3.12
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = Min(LS of following activity)
10
13
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LS/LF Times for
Milwaukee Paper
Figure 3.12
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
LF = Min(4, 10)
4
2
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LS/LF Times for
Milwaukee Paper
Figure 3.12
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
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Computing Slack Time
After computing the ES, EF, LS, and LF times for all activities, compute the slack or free time for each activity
Slack is the length of time an activity can be delayed without delaying the entire project
Slack = LS – ES or Slack = LF – EF
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Computing Slack Time
Table 3.3
Earliest Earliest Latest Latest On
Start Finish Start Finish Slack Critical
Activity ES EF LS LF LS – ES Path
A 0 2 0 2 0 Yes
B 0 3 1 4 1 No
C 2 4 2 4 0 Yes
D 3 7 4 8 1 No
E 4 8 4 8 0 Yes
F 4 7 10 13 6 No
G 8 13 8 13 0 Yes
H 13 15 13 15 0 Yes
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Critical Path for
Milwaukee Paper
Figure 3.13
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
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ES – EF Gantt Chart
for Milwaukee Paper
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install frame
E Build high-temperature burner
F Install pollution control system
G Install air pollution device
H Inspect and test
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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LS – LF Gantt Chart
for Milwaukee Paper
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install frame
E Build high-temperature burner
F Install pollution control system
G Install air pollution device
H Inspect and test
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
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CPM assumes we know a fixed time estimate for each activity and there is no variability in activity times
PERT uses a probability distribution for activity times to allow for variability
Variability in Activity Times
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Three time estimates are required
Optimistic time (a) – if everything goes according to plan
Most–likely time (m) – most realistic estimate
Pessimistic time (b) – assuming very
unfavorable conditions
Variability in Activity Times
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Estimate follows beta distribution
Variability in Activity Times
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b – a)/6]2
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Estimate follows beta distribution
Variability in Activity Times
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b − a)/6]2
Probability of 1 in 100 of
< a occurring
Probability of 1 in 100 of > b occurring
Probability
Optimistic Time (a)
Most Likely Time (m)
Pessimistic Time (b)
Activity Time
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Computing Variance
Table 3.4
Most Expected
Optimistic Likely Pessimistic Time Variance
Activity a m b t = (a + 4m + b)/6 [(b – a)/6]2
A 1 2 3 2 .11
B 2 3 4 3 .11
C 1 2 3 2 .11
D 2 4 6 4 .44
E 1 4 7 4 1.00
F 1 2 9 3 1.78
G 3 4 11 5 1.78
H 1 2 3 2 .11
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Probability of Project Completion
Project variance is computed by summing the variances of critical activities
s2 = Project variance
= (variances of activities
on critical path)
p
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Probability of Project Completion
Project variance is computed by summing the variances of critical activities
Project variance
s2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
Project standard deviation
sp = Project variance
= 3.11 = 1.76 weeks
p
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Probability of Project Completion
PERT makes two more assumptions:
- Total project completion times follow a normal probability distribution
- Activity times are statistically independent
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Probability of Project Completion
Standard deviation = 1.76 weeks
Figure 3.15
15 Weeks
(Expected Completion Time)
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Probability of Project Completion
What is the probability this project can be completed on or before the 16 week deadline?
Where Z is the number of standard deviations the due date lies from the mean
Z = – /sp
= (16 wks – 15 wks)/1.76
= 0.57
due expected date
date of completion
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Probability of Project Completion
What is the probability this project can be completed on or before the 16 week deadline?
Where Z is the number of standard deviations the due date lies from the mean
Z = − /sp
= (16 wks − 15 wks)/1.76
= 0.57
due expected date
date of completion
.00 .01 .07 .08
.1 .50000 .50399 .52790 .53188
.2 .53983 .54380 .56749 .57142
.5 .69146 .69497 .71566 .71904
.6 .72575 .72907 .74857 .75175
From Appendix I
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Probability of Project Completion
Figure 3.16
Time
Probability
(T ≤ 16 weeks)
is 71.57%
0.57 Standard deviations
15 16
Weeks Weeks
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Determining Project Completion Time
Figure 3.17
Probability of 0.01
Z
From Appendix I
Probability of 0.99
2.33 Standard deviations
0
2.33
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Variability of Completion Time for Noncritical Paths
Variability of times for activities on noncritical paths must be considered when finding the probability of finishing in a specified time
Variation in noncritical activity may cause change in critical path
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What Project Management Has Provided So Far
The project’s expected completion time is 15 weeks
There is a 71.57% chance the equipment will be in place by the 16 week deadline
Five activities (A, C, E, G, and H) are on the critical path
Three activities (B, D, F) have slack time and are not on the critical path
A detailed schedule is available
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Trade-Offs And Project Crashing
The project is behind schedule
The completion time has been moved forward
It is not uncommon to face the following situations:
Shortening the duration of the project is called project crashing
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Factors to Consider When Crashing A Project
The amount by which an activity is crashed is, in fact, permissible
Taken together, the shortened activity durations will enable us to finish the project by the due date
The total cost of crashing is as small as possible
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Steps in Project Crashing
- Using current activity times, find the critical path and identify the critical activities
(Crash cost – Normal cost)
(Normal time – Crash time)
Crash cost
per period
=
- Compute the crash cost per time period. If crash costs are linear over time:
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Steps in Project Crashing
If there is only one critical path, then select the activity on this critical path that (a) can still be crashed, and (b) has the smallest crash cost per period. If there is more than one critical path, then select one activity from each critical path such that (a) each selected activity can still be crashed, and (b) the total crash cost of all selected activities is the smallest. Note that a single activity may be common to more than one critical path.
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Steps in Project Crashing
Update all activity times. If the desired due date has been reached, stop. If not, return to Step 2.
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Crashing The Project
Table 3.5
Time (Wks) Cost ($) Crash Cost Critical
Activity Normal Crash Normal Crash Per Wk ($) Path?
A 2 1 22,000 22,750 750 Yes
B 3 1 30,000 34,000 2,000 No
C 2 1 26,000 27,000 1,000 Yes
D 4 2 48,000 49,000 1,000 No
E 4 2 56,000 58,000 1,000 Yes
F 3 2 30,000 30,500 500 No
G 5 2 80,000 84,500 1,500 Yes
H 2 1 16,000 19,000 3,000 Yes
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Crash and Normal Times and Costs for Activity B
Figure 3.18
| | |
1 2 3 Time (Weeks)
$34,000 —
$33,000 —
$32,000 —
$31,000 —
$30,000 —
—
Activity Cost
Crash
Normal
Crash Cost
Normal Cost
Crash Time
Normal Time
Crash Cost/Wk =
Crash Cost – Normal Cost
Normal Time – Crash Time
=
$34,000 – $30,000
3 – 1
= = $2,000/Wk
$4,000
2 Wks
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Critical Path And Slack Times For Milwaukee Paper
Figure 3.19
E
4
F
3
G
5
H
2
4
8
13
15
4
8
13
7
13
15
10
13
8
13
4
8
D
4
3
7
C
2
2
4
B
3
0
3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
Slack = 1
Slack = 1
Slack = 0
Slack = 6
Slack = 0
Slack = 0
Slack = 0
Slack = 0
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Advantages of PERT/CPM
Especially useful when scheduling and controlling large projects
Straightforward concept and not mathematically complex
Graphical networks help to perceive relationships among project activities
Critical path and slack time analyses help pinpoint activities that need to be closely watched
*
Advantages of PERT/CPM
Project documentation and graphics point out who is responsible for various activities
Applicable to a wide variety of projects
Useful in monitoring not only schedules but costs as well
*
Project activities have to be clearly defined, independent, and stable in their relationships
Precedence relationships must be specified and networked together
Time estimates tend to be subjective and are subject to fudging by managers
There is an inherent danger of too much emphasis being placed on the longest, or critical, path
Limitations of PERT/CPM
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Using Microsoft Project
Program 3.1
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Using Microsoft Project
Program 3.2
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Using Microsoft Project
Program 3.3
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Using Microsoft Project
Program 3.4
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Using Microsoft Project
Program 3.5
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Using Microsoft Project
Program 3.6
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Using Microsoft Project
Program 3.7
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