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17-1 Project Management
William J. Stevenson
Operations Management
8th edition
17-2 Project Management
CHAPTER
17
Project
Management
McGraw-Hill/Irwin
Operations Management, Eighth Edition, by William J. Stevenson
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
17-3 Project Management
INTRODUCTION
 Network: A network is a graphical representation
of a project, depicting the flow as well as the
sequence of well-defined activities and events.
 Activity is the actual work to be performed.
 An Event marks the beginning or end of an
activity
17-4 Project Management
 The purpose of this chapter is to present these
models with specific examples.
Network Models Developed during 1950s
PERT (Program Evaluation & Review
Technique)
CPM (Critical Path
Method)
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PHILOSOPHICAL FOUNDATIONS OF PERT &
CPM
Planning and Control are two of the most important
functions of management.
 Planning involves the formulation of objectives and
goals that are subsequently translated into specific
plans and projects.
 Control: The function of control is to institute a
mechanism that shows actual performance (in terms
of time, cost, or some other measure of effectiveness)
is deviating from the plan. If such a deviation is
unacceptable to the manager, he will take corrective
action to bring performance in conformity with the
plans.
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EVOLUTION OF PERT AND CPM
 PERT and CPM models are based upon, and have
evolved from GANTT-TYPE bar charts and
milestone charts.
 GANTT CHART is a popular tool for planning
and scheduling simple projects. It shows the start
and finish times of overall project.
17-7 Project Management
GENERAL PURPOSE AND FRAMEWORK OF
PERT & CPM
 PERT & CPM models are useful for the purpose of
planning, analyzing, scheduling and controlling the
progress and completion of large and complex
projects.
 In PERT & CPM the working procedure consists of
five steps:
1. Analyze and break down the project in terms of
specific activities and/or events;
2. Determine the interdependence and sequence of
activities and produce a network;
3. Assign estimates of time, cost or both to all the
activities of the network;
17-8 Project Management
GENERAL PURPOSE AND FRAMEWORK OF
PERT & CPM
4. Identify the longest or critical path through the
network; and
5. Monitor, evaluate and control the progress of the
project by re-planning, rescheduling and
reassignment of resources.
The central task in these models is to identify the
longest path through the network. It is also called the
critical path of the project. If for some reason the
project need to be completed in less time than the
critical path time, additional resources must be devoted
to expedite one or more activities of the critical path.
17-9 Project Management
Paths other than critical path (i.e. non-critical or
SLACK PATHS) offer flexibility in scheduling and
transferring resources, because they take less time to
complete than the critical path.
PERT & CPM models are similar in basic structure,
rationale, and mode of analysis. However, in general,
two distinctions are made between PERT & CPM.
1. The way in which activity times are estimated;
2. The cost estimates for completing various activities
17-10 Project Management
Project Management
 What are the tools?
 Work breakdown structure
 Gantt charts
 GANTT CHART is a popular tool for
planning and scheduling simple projects. It
shows the start and finish times of overall
project. Figure 1
 Milestone Charts
 Network Diagram
17-11 Project Management
Fig. 1 Gantt Chart
MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
Locate new
facilities
Interview staff
Hire and train staff
Select and order
furniture
Remodel and install
phones
Move in/startup
Gantt Chart
17-12 Project Management
Milestone Chart PERT NETWORK diagram
 Milestone Chart (Fig 2) is an improvement on the bar
chart because it identifies significant milestones or
events and shows dependencies within tasks.
 Milestone chart does not show inter-relationships
and inter-dependencies of events among tasks. This
deficiency is eliminated by the PERT NETWORK as
shown in Figure 3.
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MILESTONE CHART
Task 1
Task 2
Task 3
Task 4
Figure 2
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PERT NETWORK
Task 1
Task 2
Task 3
Task 4
Figure 3
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Difference between PERT & CPM
PERT CPM
Activity time estimates are probabilistic
three different time estimates, based on the
concept of probability of completing the
activity are made for each activity.
Activity times are deterministic. A single
time estimate is made for each activity.
Activity costs are not explicitly provided. CPM model gives explicit estimates of
activity costs. Two sets of estimates are
provided. One set gives normal time and
normal cost required to complete each
activity under normal condition.
Second set gives crash time and crash cost
required to complete each activity under
condition to reduce project completion time
by expending more money.
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PERT
 PERT was developed in 1958 by the special
projects office of US Navy. The development was
a result of the research conducted for the purpose
of coordinating and expediting the work of several
thousand contractors involved in the POLARIS
MISSILE PROGRAM. It is claimed that, with the
aid of PERT, the completion of the Polaris Missile
Program was expedited by almost two years.
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PERT & CPM
 PERT WAS EVOLVED THROUGH THE JOINT
EFFORTS OF Lockheed Aircraft, Booz, Allen &
Hamilton in the effort to speed up the Polaris Missile
Project.
 CPM was developed by J.E. Kelly of the Remington
Rand Corporation and M.R. Walker of DuPont in
1957 in connection with building and maintenance
projects in chemical plants. As its name implies it
identifies the critical (largest) path through the
network and use it to exercise control on the progress
of the project.
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PERT AND CPM
By using PERT OR CPM, managers are able to
obtain:
1. A graphical display of project activities;
2. An estimate of how long the project will take;
3. An indication of which activities are the most
critical to timely project completion;
4. An indication of how long any activity can be
delayed without lengthening the project
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PERT
 As PERT is a probalistic model; and factor of
uncertainties involved in the time required to complete
work activities.
 PERT’s originator decided three different time
estimates:
(a) Most Optimistic Time (this is short test time, assuming
most favorable conditions)
(m) Most likely time (most realistic time required to
complete an activity);
(b) Most pessimistic time (this is the longest time,
assuming most unfavorable conditions)
Three times can be represented by Beta Distribution and can
be skewed to the right as shown in Figure 4.
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Figure 4, Beta Distribution
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Figure 17.2: Activity Time Distribution
for the Activity B of the R.C. Coleman
Project
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Probabilistic Estimates, Another notations
Activity
start
Optimistic
time
Most likely
time (mode)
Pessimistic
time
to tp
tm te
Figure 17.8
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Discussion of the Beta Distribution for Activity
Completion time and Probabilistic Time Estimates
 a – most optimistic time estimate. Assume that a
= 10 weeks, then the probability of completing the
activity within “10 or less” weeks is 1/100.
 m – most likely time. Assume m = 16 weeks
means that most of the time this activity will take
16 weeks to complete.
 b – most pessimistic time estimate. Assume b =
40 weeks; then the probability that the activity will
take more than 40 weeks is 1/100.
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The Network Diagram
 Network (precedence) diagram
 Activity-on-arrow (AOA)
 Activity-on-node (AON)
 Activities
 Events
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NETWORK CONVENTIONS
17-26 Project Management
Network Conventions
a
b
c a
b
c
a
b
c
d
a
b
c
Dummy
activity
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The Network Diagram (cont’d)
 Path
 Sequence of activities that leads from the starting
node to the finishing node
 Critical path
 The longest path; determines expected project
duration
 Critical activities
 Activities on the critical path
 Slack
 Allowable slippage for path; the difference the
length of path and the length of critical path
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Expected Time for Completing the Activity, te
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Variance
2 = (tp – to)2
36
2 = variance
to = optimistic time
tp = pessimistic time
17-30 Project Management
Table 17.1: Activities for the Coleman
Automated-Warehouse Project
Activities Immediate Predecessors
A Determine equipment needs –
B Obtain vendor proposals –
C Select vendor A, B
D Order system C
E Design new warehouse layout C
F Layout warehouse E
G Design computer interface C
H Interface computer D, F, G
I Install system D, F
J Train system operators H
K Test system I, J
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Figure 17.1: PERT/CPM Network for the R.C.
Coleman Project
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Table 17.2: Optimistic, Most Probable, and Pessimistic
Activity Time Estimates in Weeks for the R.C. Coleman
Project
Activity Optimistic a Most Probable m Pessimistic b
A 2 3 4
B 3 4 11
C 1 2 3
D 4 5 12
E 3 5 7
F 2 3 4
G 2 3 10
H 2 3 4
I 2 3 10
J 1 2 3
K 1 2 3
17-33 Project Management
Table 17.3: Expected Times and Variances for the
R.C. Coleman Activities
Activity Expected Time t (in Weeks) Variance 2
A 3 .11
B 5 1.78
C 2 .11
D 6 1.78
E 5 .44
F 3 .11
G 4 1.78
H 3 .11
I 4 1.78
J 2 .11
K 2 .11
17-34 Project Management
Table 17.4: Activity Schedule in Weeks for the R.C. Coleman
Project
Activity
Earliest
Start
Earliest
Finish
Latest
Start
Latest
Finish
Slack
(LS-ES)
Critical
Path
A 0 3 2 5 2
B 0 5 0 5 0 
C 5 7 5 7 0 
D 7 13 9 15 2
E 7 12 7 12 0 
F 12 15 12 15 0 
G 7 11 11 15 4
H 15 18 15 18 0 
I 15 19 16 20 1
J 18 20 18 20 0 
K 20 22 20 22 0 
17-35 Project Management
 
3
A [0, 3]
Activity
Earliest Start
Time Earliest Finish
Time
Expected Activity
Time
35
17-36 Project Management
Figure 17.8: R.C. Coleman Project with Latest
Start and Latest Finish Times in Parentheses
17-37 Project Management
Project Network – Activity on Arrow
1
2
3
4
5 6
Locate
facilities
Order
furniture
Furniture
setup
Interview
Hire and
train
Remodel
Move
in
Figure 17.4
AOA
17-38 Project Management
Project Network – Activity on Node
1
2
3
5
6
Locate
facilities
Order
furniture
Furniture
setup
Interview
Remodel
Move
in
4
Hire and
train
7
S
Figure 17.4
AON
17-39 Project Management
Time Estimates
 Deterministic
 Time estimates that are fairly certain
 Probabilistic
 Estimates of times that allow for variation
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Example 1
1
2
3
4
5 6
8 weeks
6 weeks
3 weeks
4 weeks
9 weeks
11 weeks
1 week
Move
in
Deterministic
time estimates
Figure 17.5
17-41 Project Management
Example 1 Solution
Path Length
(weeks)
Slack
1-2-3-4-5-6
1-2-5-6
1-3-5-6
18
20
14
2
0
6
Critical Path
17-42 Project Management
 Network activities
 ES: early start
 EF: early finish
 LS: late start
 LF: late finish
 Used to determine
 Expected project duration
 Slack time
 Critical path
Computing Algorithm
17-43 Project Management
Example 5
3-4-5
d
3-5-7
e
5-7-9
f
2-4-6
b
4-6-8
h
Optimistic
time
Most likely
time
Pessimistic
time
17-44 Project Management
Path Probabilities
Z =
Specified time – Path mean
Path standard deviation
Z indicates how many standard deviations of the path distribution
the specified time is beyond the expected path duration.
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17
Weeks
Weeks
Weeks
Weeks
10.0
16.0
13.5
1.00
1.00
a-b-c
d-e-f
g-h-i
Example 6
17-46 Project Management
Time-cost Trade-offs: Crashing
 Crash – shortening activity duration
 Procedure for crashing
 Crash the project one period at a time
 Only an activity on the critical path
 Crash the least expensive activity
 Multiple critical paths: find the sum of
crashing the least expensive activity on each
critical path
17-47 Project Management
Time-Cost Trade-Offs: Crashing
Total
cost
Shorten
Shorten
Cumulative
cost of
crashing
Expected indirect costs
Optimum
CRASH
Figure 17.11
17-48 Project Management
4
d
2
f
Example 7
17-49 Project Management
Advantages of PERT
 Forces managers to organize
 Provides graphic display of activities
 Identifies
 Critical activities
 Slack activities
1
2
3
4
5 6
17-50 Project Management
Limitations of PERT
 Important activities may be omitted
 Precedence relationships may not be correct
 Estimates may include
a fudge factor
 May focus solely
on critical path 1
2
3
4
5 6
142 weeks
17-51 Project Management
 Computer aided design (CAD)
 Groupware (Lotus Notes)
 Project management software
 CA Super Project
 Harvard Total Manager
 MS Project
 Sure Track Project Manager
 Time Line
Technology for Managing Projects
17-52 Project Management
 Imposes a methodology
 Provides logical planning structure
 Enhances team communication
 Flag constraint violations
 Automatic report formats
 Multiple levels of reports
 Enables what-if scenarios
 Generates various chart types
Advantages of PM Software
17-53 Project Management
 Risk: occurrence of events that have
undesirable consequences
 Delays
 Increased costs
 Inability to meet specifications
 Project termination
Project Risk Management
17-54 Project Management
 Identify potential risks
 Analyze and assess risks
 Work to minimize occurrence of risk
 Establish contingency plans
Risk Management
17-55 Project Management
EARLIEST START AND EARLIEST
FINISH
 Consider the network in Fig (T), using the starting
time of 0, compute an earliest start and earliest
finish time for each activity in the network.
Letting
ES = Earliest Start Time for a particular activity;
EF = Earliest Finish Time for a particular activity;
te = Expected activity time for the activity.
17-56 Project Management
 The following expression can be used to find the
earliest finish time for a given activity:
EF = ES + te
 e.g.; for activity A, ES=0, & te =3; the earliest
finish time for activity is EF=0+3=3.
 We write the earliest start and earliest finish times
directly on the network in brackets next to the
letter of the activity. Using activity A as an
example, we have:
17-57 Project Management
EARLIEST START TIME RULE
 The earliest start time for an activity leaving a
particular node is equal to the largest value of the
earliest finish times for all activities entering the
node.
 Applying this rule to the portion of the network
involving node 1,2,3 and 4, we obtain the
following (on tran:
 Note that after activity C, earliest start time is 5,
which is equal to the largest earliest finish times of
dummy and activity B.
57
17-58 Project Management
EARLIEST START TIME RULE
 Proceeding in a FORWARD PASS through the
network, we can establish first an earliest start and
then an earliest finish time for each activity. (see
fig. 3)
 Note that finish time for activity K, the last
activity, is 22 week. Thus the earliest completion
time for the entire project is 22 weeks.
58
17-59 Project Management
EARLIEST START TIME RULE
 We now continue the algorith for finding the
critical path by making a BACKWARD PASS
calculation.
 Starting at the completion point (node 10) and using
a latest finish time of 22 for activity K, we trace
back through the network computing a latest start
and latest finish time for each activity.
LS = Latest starting time for a particular activity;
LF = Latest finishing time for a particular activity
59
17-60 Project Management
EARLIEST START TIME RULE
 The following expression can be used to find the
latest start time for a given activity:
LS = LF-t
 Given and note that LF = EF for last activity
 Therefore LS = 22-2 = 20 Weeks
60
17-61 Project Management
LATEST FINISH TIME RULE
 The latest finish time for an activity entering a
particular node is equal to the smallest value of the
latest starting times for all activities leaving the
node.
 The calculation for LS and LF are given (in
transparency)
 After finding start and finish activity times as
summarized in the bottom figure of (transparency),
we can find the amount of slack or free time
associated with each of the activities.
61
17-62 Project Management
LATEST FINISH TIME RULE
 Slack is defined as the length of time and activity can
be delayed w/o affecting the completion date for the
project.
 The amount of slack for each activity is computed as
follows:
Slack = LS-ES = LF-EF (A1)
e.g. slack associated with activity A is LS-ES=2-0=2
weeks. This means that activity A can be delayed upto 2
weeks (start anywhere between weeks 0 and 2) and
entire project can still be completed in 22 weeks.
62
17-63 Project Management
LATEST FINISH TIME RULE
 Using equation A the slack association with
activity C is LS-ES=5-5=0. thus activity C has no
slack time and must be held to the 5 weeks start
time schedule.
 Since this activity cannot be delayed without
affecting the entire project, it is a critical activity
and is on the critical path.
 In general the critical path activities are the
activities with ZERO SLACK.
63
17-64 Project Management
LATEST FINISH TIME RULE

64
17-65 Project Management
LATEST FINISH TIME RULE
 *The final assumption of PERT is that the duration
of the project completion time T follows a normal
or Bell-Shaped, distribution. Thus ‘T’ follows the
distribution shown
*The first assumption was
*The activities are independent in terms of their
variance (i.e. the completion times of the activities
are assumed to be independent)
65
17-66 Project Management
LATEST FINISH TIME RULE
Fig. PERT Normal Distribution of the Project Completion Time
Variation.
22 T
 = 1.66
weeks
Expected Completion Time (22
Weeks)
66
17-67 Project Management
LATEST FINISH TIME RULE
 With the assumption we can compute the probability
of meeting a specified project completion date.
 Suppose we want to finish the Coleman’s Project in
25 weeks.
 While we expect it to finish in 22 weeks.
Q: what is the probability that we will meet 25 weeks
deadline?
Using normal distribution from Fig. 17.9, we are asking
for the probability that T< 25 weeks.
This is shown graphically by shaded area in Fig. 17.10
67
17-68 Project Management
Fig. 17.9 LATEST FINISH TIME RULE
22 25
Time (Weeks)
(Prob.
T<25)
 =
1.66
T
0.4649
0.5
68
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LATEST FINISH TIME RULE

69
17-70 Project Management
Q. What is the time by which management can
be 95% confident of completing the project?
 The question asks for point “C” in the figure.
Then the area under the curve from te to C is
45% (i.e. 95% of the area is to the left of C)
te = 22 C
0.05
1.64 
0.5
0.45
Tim
e
70
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QUESTION 1
Given the information provided in the
accompanying network diagram, determine each of
the following:
a. The length of each path;
b. The critical path;
c. The expected length of the project;
d. Amount of slack time for each path;
e. Compute activity slack times for the precedence
diagram
17-72 Project Management
EARLIEST START AND EARLIEST
FINISH
 Consider the network in Fig (T), using the starting
time of O, compute an earliest start and earliest
finish time for each activity in the network.
Letting
ES = Earliest Start Time for a particular activity;
EF = Earliest Finish Time for a particular activity;
te = Expected activity time for the activity.
72
17-73 Project Management
 The following expression can be used to find the
earliest finish time for a given activity:
EF = ES + t
 e.g.; for activity A, ES=0, & t=3; the earliest finish
time for activity is EF=0+3=3.
 We write the earliest start and earliest finish times
directly on the network in brackets next to the
letter of the activity. Using activity A as an
example, we have:
73
17-74 Project Management
 
3
A [0, 3]
Activity
Earliest Start
Time Earliest Finish
Time
Expected Activity
Time
74
17-75 Project Management
EARLIEST START TIME RULE
 The earliest start time for an activity leaving a
particular node is equal to the largest value of the
earliest finish times for all activities entering the
node.
 Applying this rule to the portion of the network
involving node 1,2,3 and 4, we obtain the
following (on transparency):
 Note that after activity C, earliest start time is 5,
which is equal to the largest earliest finish times of
dummy and activity B.
75
17-76 Project Management
EARLIEST START TIME RULE
 Proceeding in a FORWARD PASS through the
network, we can establish first an earliest start and
then an earliest finish time for each activity. (see
fig. 3)
 Note that finish time for activity K, the last
activity, is 22 week. Thus the earliest completion
time for the entire project is 22 weeks.
76
17-77 Project Management
EARLIEST START TIME RULE
 We now continue the algorith for finding the
critical path by making a BACKWARD PASS
calculation.
 Starting at the completion point (node 10) and using
a latest finish time of 22 for activity K, we trace
back through the network computing a latest start
and latest finish time for each activity.
LS = Latest starting time for a particular activity;
LF = Latest finishing time for a particular activity
77
17-78 Project Management
EARLIEST START TIME RULE
 The following expression can be used to find the
latest start time for a given activity:
LS = LF-t
 Given and note that LF = EF for last activity
 Therefore LS = 22-2 = 20 Weeks
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LATEST FINISH TIME RULE
 The latest finish time for an activity entering a
particular node is equal to the smallest value of the
latest starting times for all activities leaving the
node.
 The calculation for LS and LF are given (in
transparency)
 After finding start and finish activity times as
summarized in the bottom figure of (transparency),
we can find the amount of slack or free time
associated with each of the activities.
79
17-80 Project Management
LATEST FINISH TIME RULE
 Slack is defined as the length of time and activity can
be delayed w/o affecting the completion date for the
project.
 The amount of slack for each activity is computed as
follows:
Slack = LS-ES = LF-EF (A1)
e.g. slack associated with activity A is LS-ES=2-0=2
weeks. This means that activity A can be delayed upto 2
weeks (start anywhere between weeks 0 and 2) and
entire project can still be completed in 22 weeks.
80
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LATEST FINISH TIME RULE
 Using equation A the slack association with
activity C is LS-ES=5-5=0. thus activity C has no
slack time and must be held to the 5 weeks start
time schedule.
 Since this activity cannot be delayed without
affecting the entire project, it is a critical activity
and is on the critical path.
 In general the critical path activities are the
activities with ZERO SLACK.
81
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LATEST FINISH TIME RULE

82
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LATEST FINISH TIME RULE
 *The final assumption of PERT is that the duration
of the project completion time T follows a normal
or Bell-Shaped, distribution. Thus ‘T’ follows the
distribution shown
*The first assumption was
*The activities are independent in terms of their
variance (i.e. the completion times of the activities
are assumed to be independent)
83
17-84 Project Management
LATEST FINISH TIME RULE
Fig. PERT Normal Distribution of the Project Completion Time
Variation.
22 T
 = 1.66
weeks
Expected Completion Time (22
Weeks)
84
17-85 Project Management
LATEST FINISH TIME RULE
 With the assumption we can compute the probability
of meeting a specified project completion date.
 Suppose we want to finish the Coleman’s Project in
25 weeks.
 While we expect it to finish in 22 weeks.
Q: what is the probability that we will meet 25 weeks
deadline?
Using normal distribution from Fig. 17.9, we are asking
for the probability that T< 25 weeks.
This is shown graphically by shaded area in Fig. 17.10
85
17-86 Project Management
LATEST FINISH TIME RULE
22 25
Time (Weeks)
(Prob.
T<25)
 =
1.66
T
0.4649
0.5
86
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LATEST FINISH TIME RULE

87
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Q. What is the time by which management can
be 95% confident of completing the project?
 The question asks for point “C” in the figure.
Then the area under the curve from te to C is
45% (i.e. 95% of the area is to the left of C)
te = 22 C
0.05
1.64 
0.5
0.45
Tim
e
88
17-89 Project Management

89
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90
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91
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ADVANTAGES OF USING PERT AND
POTENTIAL SOURCE OF ERROR
PERT and similar project scheduling techniques can provide
important services for the project manager. Among the most
useful features are these:
 Use of these techniques forces the manager to organize and
quantify available information and to recognize where
additional information is needed.
 The techniques provide a graphic display of the project and
its major activities.
 The identify (a) activities that should be closely watched
because of the potential for delaying the project and (b)
other activities that have slack time and so can be delayed
without affecting project completion time. This raises the
possibility of reallocating resources to shorten the project.
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No analytical technique is without potential errors. Among the more
important sources of errors are:
 When developing the project network, managers may unwittingly
omit one or more important activities.
 Precedence relationships may not all the be correct as shown.
 Time estimates may include a fudge factor; mangers may feel
uncomfortable about making time estimates because they appear to
commit themselves to completion within a certain time period.
 There may be a tendency to focus solely on activities that are on the
critical path. As the project progresses, other paths may become
critical. Further, major risk events may not be on the critical path.
93
17-94 Project Management
17-95 Project Management
QUESTION 2
The network diagram for a project is shown in the
accompanying figure, with three time estimates for
each activity. Activity times are in months. Do the
following:
a. Compute the expected time for each activity and the
expected duration for each path;
b. Identify the critical path;
c. Compute the variance for each activity and the
variance for each path;
d. Find the probability that the project will be
completed within 17 months of its start;
17-96 Project Management
QUESTION 2
e. Find the probability that the project will take
longer than 18 months  2%;
f. Can the paths be considered independent? Why?
g. Determine the probability that the project will be
completed within 15 months of its start;
h. What is the probability that the project will not
be completed within 15 months of its start?
17-97 Project Management
17-98 Project Management
CPM NETWORKS & PROJECT
CRASHING
 CPM network is deterministic;
 CPM approach is useful when both time and cost
estimates are known with certainty;
 Two sets of time and cost figures are obtained for
each activity:
 Normal time and normal cost;
 Crash time and crash cost;
 Further, it is usually assumed that the relationship
between time and cost is linear;
17-99 Project Management
CPM NETWORKS & PROJECT
CRASHING

17-100 Project Management
 The idea of project crashing is that, under certain
circumstances, it is necessary and desirable to expedite
project completion even though it will result in higher
costs.
 In CPM we know both the minimum project completion
time and the cost-time relationships of all activities; our
objective is to design a program that will yield “minimum
project completion time with the least increase in costs
over the normal costs”. Let us consider these concepts
with the aid of the network shown in the figure (on
transparency).
17-101 Project Management
 Normal and crash times and cost data are shown;
 Note that cost/time will always yield a negative
slope;
 Normal time is without parenthesis; while the
crash time is within parenthesis. (This is the usual
convension to represent)
17-102 Project Management
THE MECHANICS OF CPM
 First four steps are the same as that of PERT network
i.e.;
 Step 1: Define the overall project, including the project
objective and target completion date;
 Step 2: Break down the project into well-defined
activities i.e. Identify beginning event (source event)
and Terminal Event;
 Step 3: Give serial nos. to each event and arrange then
in proper sequence as required by planning and
technological requirements; this establishes the
precedence relationships;
17-103 Project Management
 Step 4: Construct the actual CPM network, inter
connecting all the activities and events.
Next steps are the “Analysis Phase of CPM”
 Step 5: Identify the normal critical path and the
crash critical path;
 The network shown in the figure has got three
different paths as follows:
 The normal critical path is 1-3-6 (45 weeks) and
that, under normal conditions, the cost of the entire
project is $24,800.
17-104 Project Management
Length of Path (Weeks)
Path Normal Crash
1-3-6 45 30
1-2-5-6 42 32
1-2-4-5-6 44 34
– Crash critical path is 1-2-4-5-6 (34 weeks) and that, under
crash conditions, the cost of the entire project is $32,600.
– Our task, then, is to design a program that will complete the
project within 34 weeks with the least increase in cost
above $24,800.
– It is logical to start by crashing the least expensive activity
on the normal critical path.
17-105 Project Management
 Step 6: On the normal critical path, identify the
least expensive activity to crash;
 Crash this activity and note whether the critical path
has changed. If not, crash the next least expensive
activity on the critical path and so on. Until a new
critical path emerges, with its own least expensive
activity to crash.
Burning Time:
 Assumption of CPM is that “Normal and Crash”
estimates are linearly related
17-106 Project Management
 In many cases the
relationship is not linear.
Special computer
programs have been
developed to accept non-
linear time/cost tradeoffs,
but these are beyond the
scope of this text (course)
Cost
Time
Crash
Effort
Normal
Effort
17-107 Project Management
Finding the Minimum Time – Minimum Cost
Network:
 One of the principal questions CPM can answer is:
What is the least cost to complete a project in
minimum time?
 Continue this process until an “irreducible” critical
path on which all activities are on their crash times
has been obtained.
17-108 Project Management
FIRST CRASH
 Start our analysis with the normal critical path.
There are only two uncrashed activities on the
normal critical path (i.e.; 1-3 and 3-6);
 Activity 1-3 is the least expensive activity
($200/week), and hence crash it by 5 weeks. (see
transparency). This reduces path 1-3-6 to 40
weeks and changes the critical path to (1-2-4-5-6)
44 weeks.
17-109 Project Management
SECOND CRASH
 There are four uncrashed activities on (1-2-4-5-6)
the new critical path i.e.; (1-2, 2-4, 4-5, & 5-6).
 Of these activity 1-2 is the least expensive (i.e.;
$200/week); (see transparency). Hence we crash it
by 3 weeks.
 The critical path is still 1-2-4-5-6; but it has
decreased to 41 weeks.
17-110 Project Management
THIRD CRASH
 There are three uncrashed activities on the current
critical path (2-4, 4-5 and 5-6).
 Of these activities 2-4 and 5-6 are least expensive
$400/week). We can crash any of them; however,
we crash activity 5-6 as it yields a larger reduction
in completion time (3 weeks). As shown in table.
This changes the critical path to 1-3-6 (40 weeks).
17-111 Project Management
FOURTH CRASH
 There is only one uncrashed activity (i.e.; 3-6) the
current critical path. We crash it by 10 weeks (as
shown in the transparency) and the critical path is
again 1-2-4-5 (38 weeks).
 Of these activities 2-4 and 5-6 are least expensive
$400/week). We can crash any of them; however,
we crash activity 5-6 as it yields a larger reduction
in completion time (3 weeks). As shown in table.
This changes the critical path to 1-3-6 (40 weeks).
17-112 Project Management
FIFTH CRASH
 Now there are only two uncrashed activities on
the current critical path (3-4 and 4-5). Of these
activities 2-4 is least expensive $400/week) and
hence we crash it by 2 weeks. (as shown in table).
This means that we now have two critical paths (1-
2-5-6 and 1-2-4-5-6) of 36 weeks.
17-113 Project Management
SIXTH CRASH
 If we compare the two critical paths (1-2-5-6 and
1-2-4-5-6), we find that only two uncrashed
activities remain (2-5 and 4-5). Since activity 2-5
is least expensive $200/week), we crash it by 4
weeks. (as shown in transparency). This results in
making path 1-2-4-5-6 the critical path.
17-114 Project Management
SEVENTH CRASH
 There now remains only one uncrashed activity
on the current critical path (activity 4-5). We
crash it, and note that the critical path is still 1-2-4-
5-6, but it is irreducible (i.e.; all activities on this
path are at their crash times). Therefore, we have
completed step 2.
17-115 Project Management
Step 3: Examine the non-critical paths and uncrash
activities on such paths (beginning with the most
expensive activity) to the point after which further
uncrashing will create a longer critical path.
It has been observed uptill now:
1) The minimum completion time of 34 weeks has
been achieved;
2) The non-critical path 1-3-6 is 30 weeks long and
hence can be uncrashed by no more than 4
weeks; and
17-116 Project Management
3) The other non-critical path 1-2-5-6 is 32 weeks long
and hence can be uncrashed by no more than 2
weeks;
4)
i. Of the non-critical path 1-3-6, the activity 3-6 is the
most expensive ($240/week), hence we uncrash it by
4 weeks;
ii. Of the three activities on the non-critical path 1-2-5-
6, activities 1-2 and 5-6 cannot be uncrashed, as they
are included in the crash critical path 1-2-4-5-6.
However, we can uncrash activity 2-5 ($200/week),
and hence we uncrash it by 2 weeks.
17-117 Project Management
 We have now executed step 3, and our analysis of
CPM Network of Fig. is complete.
 We have obtained:
 Minimum completion time with the least increase in
costs above the normal project cost. The final time
status of the activities and their cost consequences
are summarized in table (transparency e.g.)
17-118 Project Management
Activity Normal Crash Cost ($)
1-2 7 1600
1-3 10 3000
2-4 6 2600
2-5 18 weeks total 4900
3-6 24 weeks total 8640
4-5 12 6000
5-6 9 4500
• It should be noted that the minimum project completion time
of 34 weeks has been obtained at a cost of 31,240, as
compared to the crash project cost of 32,600.
17-119 Project Management
 It should be emphasized that the CPM model is
well suited to accommodate the reality of
budgetary constraints. (e.g.; we can answer the
questions):
 What is the minimum project – completion time if
our budget for the network in figure is $27,000?
 To answer the question we start at the end of step
3 and, of the crashed activities at the stage, we
uncrash the most expensive activity first.
17-120 Project Management
 Then keeping an eye on the critical path, we keep
on uncrashing activities until the project cost is
reduced to the level of the budget constraints. For
H.W. find the new minimum project completion
time, assuming a budget of $27,000.
 We can also answer the question:
 What is the minimum cost to complete the project
in 39 days?

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Project-Management.ppt

  • 1. 17-1 Project Management William J. Stevenson Operations Management 8th edition
  • 2. 17-2 Project Management CHAPTER 17 Project Management McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
  • 3. 17-3 Project Management INTRODUCTION  Network: A network is a graphical representation of a project, depicting the flow as well as the sequence of well-defined activities and events.  Activity is the actual work to be performed.  An Event marks the beginning or end of an activity
  • 4. 17-4 Project Management  The purpose of this chapter is to present these models with specific examples. Network Models Developed during 1950s PERT (Program Evaluation & Review Technique) CPM (Critical Path Method)
  • 5. 17-5 Project Management PHILOSOPHICAL FOUNDATIONS OF PERT & CPM Planning and Control are two of the most important functions of management.  Planning involves the formulation of objectives and goals that are subsequently translated into specific plans and projects.  Control: The function of control is to institute a mechanism that shows actual performance (in terms of time, cost, or some other measure of effectiveness) is deviating from the plan. If such a deviation is unacceptable to the manager, he will take corrective action to bring performance in conformity with the plans.
  • 6. 17-6 Project Management EVOLUTION OF PERT AND CPM  PERT and CPM models are based upon, and have evolved from GANTT-TYPE bar charts and milestone charts.  GANTT CHART is a popular tool for planning and scheduling simple projects. It shows the start and finish times of overall project.
  • 7. 17-7 Project Management GENERAL PURPOSE AND FRAMEWORK OF PERT & CPM  PERT & CPM models are useful for the purpose of planning, analyzing, scheduling and controlling the progress and completion of large and complex projects.  In PERT & CPM the working procedure consists of five steps: 1. Analyze and break down the project in terms of specific activities and/or events; 2. Determine the interdependence and sequence of activities and produce a network; 3. Assign estimates of time, cost or both to all the activities of the network;
  • 8. 17-8 Project Management GENERAL PURPOSE AND FRAMEWORK OF PERT & CPM 4. Identify the longest or critical path through the network; and 5. Monitor, evaluate and control the progress of the project by re-planning, rescheduling and reassignment of resources. The central task in these models is to identify the longest path through the network. It is also called the critical path of the project. If for some reason the project need to be completed in less time than the critical path time, additional resources must be devoted to expedite one or more activities of the critical path.
  • 9. 17-9 Project Management Paths other than critical path (i.e. non-critical or SLACK PATHS) offer flexibility in scheduling and transferring resources, because they take less time to complete than the critical path. PERT & CPM models are similar in basic structure, rationale, and mode of analysis. However, in general, two distinctions are made between PERT & CPM. 1. The way in which activity times are estimated; 2. The cost estimates for completing various activities
  • 10. 17-10 Project Management Project Management  What are the tools?  Work breakdown structure  Gantt charts  GANTT CHART is a popular tool for planning and scheduling simple projects. It shows the start and finish times of overall project. Figure 1  Milestone Charts  Network Diagram
  • 11. 17-11 Project Management Fig. 1 Gantt Chart MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Locate new facilities Interview staff Hire and train staff Select and order furniture Remodel and install phones Move in/startup Gantt Chart
  • 12. 17-12 Project Management Milestone Chart PERT NETWORK diagram  Milestone Chart (Fig 2) is an improvement on the bar chart because it identifies significant milestones or events and shows dependencies within tasks.  Milestone chart does not show inter-relationships and inter-dependencies of events among tasks. This deficiency is eliminated by the PERT NETWORK as shown in Figure 3.
  • 13. 17-13 Project Management MILESTONE CHART Task 1 Task 2 Task 3 Task 4 Figure 2
  • 14. 17-14 Project Management PERT NETWORK Task 1 Task 2 Task 3 Task 4 Figure 3
  • 15. 17-15 Project Management Difference between PERT & CPM PERT CPM Activity time estimates are probabilistic three different time estimates, based on the concept of probability of completing the activity are made for each activity. Activity times are deterministic. A single time estimate is made for each activity. Activity costs are not explicitly provided. CPM model gives explicit estimates of activity costs. Two sets of estimates are provided. One set gives normal time and normal cost required to complete each activity under normal condition. Second set gives crash time and crash cost required to complete each activity under condition to reduce project completion time by expending more money.
  • 16. 17-16 Project Management PERT  PERT was developed in 1958 by the special projects office of US Navy. The development was a result of the research conducted for the purpose of coordinating and expediting the work of several thousand contractors involved in the POLARIS MISSILE PROGRAM. It is claimed that, with the aid of PERT, the completion of the Polaris Missile Program was expedited by almost two years.
  • 17. 17-17 Project Management PERT & CPM  PERT WAS EVOLVED THROUGH THE JOINT EFFORTS OF Lockheed Aircraft, Booz, Allen & Hamilton in the effort to speed up the Polaris Missile Project.  CPM was developed by J.E. Kelly of the Remington Rand Corporation and M.R. Walker of DuPont in 1957 in connection with building and maintenance projects in chemical plants. As its name implies it identifies the critical (largest) path through the network and use it to exercise control on the progress of the project.
  • 18. 17-18 Project Management PERT AND CPM By using PERT OR CPM, managers are able to obtain: 1. A graphical display of project activities; 2. An estimate of how long the project will take; 3. An indication of which activities are the most critical to timely project completion; 4. An indication of how long any activity can be delayed without lengthening the project
  • 19. 17-19 Project Management PERT  As PERT is a probalistic model; and factor of uncertainties involved in the time required to complete work activities.  PERT’s originator decided three different time estimates: (a) Most Optimistic Time (this is short test time, assuming most favorable conditions) (m) Most likely time (most realistic time required to complete an activity); (b) Most pessimistic time (this is the longest time, assuming most unfavorable conditions) Three times can be represented by Beta Distribution and can be skewed to the right as shown in Figure 4.
  • 20. 17-20 Project Management Figure 4, Beta Distribution
  • 21. 17-21 Project Management Figure 17.2: Activity Time Distribution for the Activity B of the R.C. Coleman Project
  • 22. 17-22 Project Management Probabilistic Estimates, Another notations Activity start Optimistic time Most likely time (mode) Pessimistic time to tp tm te Figure 17.8
  • 23. 17-23 Project Management Discussion of the Beta Distribution for Activity Completion time and Probabilistic Time Estimates  a – most optimistic time estimate. Assume that a = 10 weeks, then the probability of completing the activity within “10 or less” weeks is 1/100.  m – most likely time. Assume m = 16 weeks means that most of the time this activity will take 16 weeks to complete.  b – most pessimistic time estimate. Assume b = 40 weeks; then the probability that the activity will take more than 40 weeks is 1/100.
  • 24. 17-24 Project Management The Network Diagram  Network (precedence) diagram  Activity-on-arrow (AOA)  Activity-on-node (AON)  Activities  Events
  • 26. 17-26 Project Management Network Conventions a b c a b c a b c d a b c Dummy activity
  • 27. 17-27 Project Management The Network Diagram (cont’d)  Path  Sequence of activities that leads from the starting node to the finishing node  Critical path  The longest path; determines expected project duration  Critical activities  Activities on the critical path  Slack  Allowable slippage for path; the difference the length of path and the length of critical path
  • 28. 17-28 Project Management Expected Time for Completing the Activity, te
  • 29. 17-29 Project Management Variance 2 = (tp – to)2 36 2 = variance to = optimistic time tp = pessimistic time
  • 30. 17-30 Project Management Table 17.1: Activities for the Coleman Automated-Warehouse Project Activities Immediate Predecessors A Determine equipment needs – B Obtain vendor proposals – C Select vendor A, B D Order system C E Design new warehouse layout C F Layout warehouse E G Design computer interface C H Interface computer D, F, G I Install system D, F J Train system operators H K Test system I, J
  • 31. 17-31 Project Management Figure 17.1: PERT/CPM Network for the R.C. Coleman Project
  • 32. 17-32 Project Management Table 17.2: Optimistic, Most Probable, and Pessimistic Activity Time Estimates in Weeks for the R.C. Coleman Project Activity Optimistic a Most Probable m Pessimistic b A 2 3 4 B 3 4 11 C 1 2 3 D 4 5 12 E 3 5 7 F 2 3 4 G 2 3 10 H 2 3 4 I 2 3 10 J 1 2 3 K 1 2 3
  • 33. 17-33 Project Management Table 17.3: Expected Times and Variances for the R.C. Coleman Activities Activity Expected Time t (in Weeks) Variance 2 A 3 .11 B 5 1.78 C 2 .11 D 6 1.78 E 5 .44 F 3 .11 G 4 1.78 H 3 .11 I 4 1.78 J 2 .11 K 2 .11
  • 34. 17-34 Project Management Table 17.4: Activity Schedule in Weeks for the R.C. Coleman Project Activity Earliest Start Earliest Finish Latest Start Latest Finish Slack (LS-ES) Critical Path A 0 3 2 5 2 B 0 5 0 5 0  C 5 7 5 7 0  D 7 13 9 15 2 E 7 12 7 12 0  F 12 15 12 15 0  G 7 11 11 15 4 H 15 18 15 18 0  I 15 19 16 20 1 J 18 20 18 20 0  K 20 22 20 22 0 
  • 35. 17-35 Project Management   3 A [0, 3] Activity Earliest Start Time Earliest Finish Time Expected Activity Time 35
  • 36. 17-36 Project Management Figure 17.8: R.C. Coleman Project with Latest Start and Latest Finish Times in Parentheses
  • 37. 17-37 Project Management Project Network – Activity on Arrow 1 2 3 4 5 6 Locate facilities Order furniture Furniture setup Interview Hire and train Remodel Move in Figure 17.4 AOA
  • 38. 17-38 Project Management Project Network – Activity on Node 1 2 3 5 6 Locate facilities Order furniture Furniture setup Interview Remodel Move in 4 Hire and train 7 S Figure 17.4 AON
  • 39. 17-39 Project Management Time Estimates  Deterministic  Time estimates that are fairly certain  Probabilistic  Estimates of times that allow for variation
  • 40. 17-40 Project Management Example 1 1 2 3 4 5 6 8 weeks 6 weeks 3 weeks 4 weeks 9 weeks 11 weeks 1 week Move in Deterministic time estimates Figure 17.5
  • 41. 17-41 Project Management Example 1 Solution Path Length (weeks) Slack 1-2-3-4-5-6 1-2-5-6 1-3-5-6 18 20 14 2 0 6 Critical Path
  • 42. 17-42 Project Management  Network activities  ES: early start  EF: early finish  LS: late start  LF: late finish  Used to determine  Expected project duration  Slack time  Critical path Computing Algorithm
  • 43. 17-43 Project Management Example 5 3-4-5 d 3-5-7 e 5-7-9 f 2-4-6 b 4-6-8 h Optimistic time Most likely time Pessimistic time
  • 44. 17-44 Project Management Path Probabilities Z = Specified time – Path mean Path standard deviation Z indicates how many standard deviations of the path distribution the specified time is beyond the expected path duration.
  • 46. 17-46 Project Management Time-cost Trade-offs: Crashing  Crash – shortening activity duration  Procedure for crashing  Crash the project one period at a time  Only an activity on the critical path  Crash the least expensive activity  Multiple critical paths: find the sum of crashing the least expensive activity on each critical path
  • 47. 17-47 Project Management Time-Cost Trade-Offs: Crashing Total cost Shorten Shorten Cumulative cost of crashing Expected indirect costs Optimum CRASH Figure 17.11
  • 49. 17-49 Project Management Advantages of PERT  Forces managers to organize  Provides graphic display of activities  Identifies  Critical activities  Slack activities 1 2 3 4 5 6
  • 50. 17-50 Project Management Limitations of PERT  Important activities may be omitted  Precedence relationships may not be correct  Estimates may include a fudge factor  May focus solely on critical path 1 2 3 4 5 6 142 weeks
  • 51. 17-51 Project Management  Computer aided design (CAD)  Groupware (Lotus Notes)  Project management software  CA Super Project  Harvard Total Manager  MS Project  Sure Track Project Manager  Time Line Technology for Managing Projects
  • 52. 17-52 Project Management  Imposes a methodology  Provides logical planning structure  Enhances team communication  Flag constraint violations  Automatic report formats  Multiple levels of reports  Enables what-if scenarios  Generates various chart types Advantages of PM Software
  • 53. 17-53 Project Management  Risk: occurrence of events that have undesirable consequences  Delays  Increased costs  Inability to meet specifications  Project termination Project Risk Management
  • 54. 17-54 Project Management  Identify potential risks  Analyze and assess risks  Work to minimize occurrence of risk  Establish contingency plans Risk Management
  • 55. 17-55 Project Management EARLIEST START AND EARLIEST FINISH  Consider the network in Fig (T), using the starting time of 0, compute an earliest start and earliest finish time for each activity in the network. Letting ES = Earliest Start Time for a particular activity; EF = Earliest Finish Time for a particular activity; te = Expected activity time for the activity.
  • 56. 17-56 Project Management  The following expression can be used to find the earliest finish time for a given activity: EF = ES + te  e.g.; for activity A, ES=0, & te =3; the earliest finish time for activity is EF=0+3=3.  We write the earliest start and earliest finish times directly on the network in brackets next to the letter of the activity. Using activity A as an example, we have:
  • 57. 17-57 Project Management EARLIEST START TIME RULE  The earliest start time for an activity leaving a particular node is equal to the largest value of the earliest finish times for all activities entering the node.  Applying this rule to the portion of the network involving node 1,2,3 and 4, we obtain the following (on tran:  Note that after activity C, earliest start time is 5, which is equal to the largest earliest finish times of dummy and activity B. 57
  • 58. 17-58 Project Management EARLIEST START TIME RULE  Proceeding in a FORWARD PASS through the network, we can establish first an earliest start and then an earliest finish time for each activity. (see fig. 3)  Note that finish time for activity K, the last activity, is 22 week. Thus the earliest completion time for the entire project is 22 weeks. 58
  • 59. 17-59 Project Management EARLIEST START TIME RULE  We now continue the algorith for finding the critical path by making a BACKWARD PASS calculation.  Starting at the completion point (node 10) and using a latest finish time of 22 for activity K, we trace back through the network computing a latest start and latest finish time for each activity. LS = Latest starting time for a particular activity; LF = Latest finishing time for a particular activity 59
  • 60. 17-60 Project Management EARLIEST START TIME RULE  The following expression can be used to find the latest start time for a given activity: LS = LF-t  Given and note that LF = EF for last activity  Therefore LS = 22-2 = 20 Weeks 60
  • 61. 17-61 Project Management LATEST FINISH TIME RULE  The latest finish time for an activity entering a particular node is equal to the smallest value of the latest starting times for all activities leaving the node.  The calculation for LS and LF are given (in transparency)  After finding start and finish activity times as summarized in the bottom figure of (transparency), we can find the amount of slack or free time associated with each of the activities. 61
  • 62. 17-62 Project Management LATEST FINISH TIME RULE  Slack is defined as the length of time and activity can be delayed w/o affecting the completion date for the project.  The amount of slack for each activity is computed as follows: Slack = LS-ES = LF-EF (A1) e.g. slack associated with activity A is LS-ES=2-0=2 weeks. This means that activity A can be delayed upto 2 weeks (start anywhere between weeks 0 and 2) and entire project can still be completed in 22 weeks. 62
  • 63. 17-63 Project Management LATEST FINISH TIME RULE  Using equation A the slack association with activity C is LS-ES=5-5=0. thus activity C has no slack time and must be held to the 5 weeks start time schedule.  Since this activity cannot be delayed without affecting the entire project, it is a critical activity and is on the critical path.  In general the critical path activities are the activities with ZERO SLACK. 63
  • 64. 17-64 Project Management LATEST FINISH TIME RULE  64
  • 65. 17-65 Project Management LATEST FINISH TIME RULE  *The final assumption of PERT is that the duration of the project completion time T follows a normal or Bell-Shaped, distribution. Thus ‘T’ follows the distribution shown *The first assumption was *The activities are independent in terms of their variance (i.e. the completion times of the activities are assumed to be independent) 65
  • 66. 17-66 Project Management LATEST FINISH TIME RULE Fig. PERT Normal Distribution of the Project Completion Time Variation. 22 T  = 1.66 weeks Expected Completion Time (22 Weeks) 66
  • 67. 17-67 Project Management LATEST FINISH TIME RULE  With the assumption we can compute the probability of meeting a specified project completion date.  Suppose we want to finish the Coleman’s Project in 25 weeks.  While we expect it to finish in 22 weeks. Q: what is the probability that we will meet 25 weeks deadline? Using normal distribution from Fig. 17.9, we are asking for the probability that T< 25 weeks. This is shown graphically by shaded area in Fig. 17.10 67
  • 68. 17-68 Project Management Fig. 17.9 LATEST FINISH TIME RULE 22 25 Time (Weeks) (Prob. T<25)  = 1.66 T 0.4649 0.5 68
  • 69. 17-69 Project Management LATEST FINISH TIME RULE  69
  • 70. 17-70 Project Management Q. What is the time by which management can be 95% confident of completing the project?  The question asks for point “C” in the figure. Then the area under the curve from te to C is 45% (i.e. 95% of the area is to the left of C) te = 22 C 0.05 1.64  0.5 0.45 Tim e 70
  • 71. 17-71 Project Management QUESTION 1 Given the information provided in the accompanying network diagram, determine each of the following: a. The length of each path; b. The critical path; c. The expected length of the project; d. Amount of slack time for each path; e. Compute activity slack times for the precedence diagram
  • 72. 17-72 Project Management EARLIEST START AND EARLIEST FINISH  Consider the network in Fig (T), using the starting time of O, compute an earliest start and earliest finish time for each activity in the network. Letting ES = Earliest Start Time for a particular activity; EF = Earliest Finish Time for a particular activity; te = Expected activity time for the activity. 72
  • 73. 17-73 Project Management  The following expression can be used to find the earliest finish time for a given activity: EF = ES + t  e.g.; for activity A, ES=0, & t=3; the earliest finish time for activity is EF=0+3=3.  We write the earliest start and earliest finish times directly on the network in brackets next to the letter of the activity. Using activity A as an example, we have: 73
  • 74. 17-74 Project Management   3 A [0, 3] Activity Earliest Start Time Earliest Finish Time Expected Activity Time 74
  • 75. 17-75 Project Management EARLIEST START TIME RULE  The earliest start time for an activity leaving a particular node is equal to the largest value of the earliest finish times for all activities entering the node.  Applying this rule to the portion of the network involving node 1,2,3 and 4, we obtain the following (on transparency):  Note that after activity C, earliest start time is 5, which is equal to the largest earliest finish times of dummy and activity B. 75
  • 76. 17-76 Project Management EARLIEST START TIME RULE  Proceeding in a FORWARD PASS through the network, we can establish first an earliest start and then an earliest finish time for each activity. (see fig. 3)  Note that finish time for activity K, the last activity, is 22 week. Thus the earliest completion time for the entire project is 22 weeks. 76
  • 77. 17-77 Project Management EARLIEST START TIME RULE  We now continue the algorith for finding the critical path by making a BACKWARD PASS calculation.  Starting at the completion point (node 10) and using a latest finish time of 22 for activity K, we trace back through the network computing a latest start and latest finish time for each activity. LS = Latest starting time for a particular activity; LF = Latest finishing time for a particular activity 77
  • 78. 17-78 Project Management EARLIEST START TIME RULE  The following expression can be used to find the latest start time for a given activity: LS = LF-t  Given and note that LF = EF for last activity  Therefore LS = 22-2 = 20 Weeks 78
  • 79. 17-79 Project Management LATEST FINISH TIME RULE  The latest finish time for an activity entering a particular node is equal to the smallest value of the latest starting times for all activities leaving the node.  The calculation for LS and LF are given (in transparency)  After finding start and finish activity times as summarized in the bottom figure of (transparency), we can find the amount of slack or free time associated with each of the activities. 79
  • 80. 17-80 Project Management LATEST FINISH TIME RULE  Slack is defined as the length of time and activity can be delayed w/o affecting the completion date for the project.  The amount of slack for each activity is computed as follows: Slack = LS-ES = LF-EF (A1) e.g. slack associated with activity A is LS-ES=2-0=2 weeks. This means that activity A can be delayed upto 2 weeks (start anywhere between weeks 0 and 2) and entire project can still be completed in 22 weeks. 80
  • 81. 17-81 Project Management LATEST FINISH TIME RULE  Using equation A the slack association with activity C is LS-ES=5-5=0. thus activity C has no slack time and must be held to the 5 weeks start time schedule.  Since this activity cannot be delayed without affecting the entire project, it is a critical activity and is on the critical path.  In general the critical path activities are the activities with ZERO SLACK. 81
  • 82. 17-82 Project Management LATEST FINISH TIME RULE  82
  • 83. 17-83 Project Management LATEST FINISH TIME RULE  *The final assumption of PERT is that the duration of the project completion time T follows a normal or Bell-Shaped, distribution. Thus ‘T’ follows the distribution shown *The first assumption was *The activities are independent in terms of their variance (i.e. the completion times of the activities are assumed to be independent) 83
  • 84. 17-84 Project Management LATEST FINISH TIME RULE Fig. PERT Normal Distribution of the Project Completion Time Variation. 22 T  = 1.66 weeks Expected Completion Time (22 Weeks) 84
  • 85. 17-85 Project Management LATEST FINISH TIME RULE  With the assumption we can compute the probability of meeting a specified project completion date.  Suppose we want to finish the Coleman’s Project in 25 weeks.  While we expect it to finish in 22 weeks. Q: what is the probability that we will meet 25 weeks deadline? Using normal distribution from Fig. 17.9, we are asking for the probability that T< 25 weeks. This is shown graphically by shaded area in Fig. 17.10 85
  • 86. 17-86 Project Management LATEST FINISH TIME RULE 22 25 Time (Weeks) (Prob. T<25)  = 1.66 T 0.4649 0.5 86
  • 87. 17-87 Project Management LATEST FINISH TIME RULE  87
  • 88. 17-88 Project Management Q. What is the time by which management can be 95% confident of completing the project?  The question asks for point “C” in the figure. Then the area under the curve from te to C is 45% (i.e. 95% of the area is to the left of C) te = 22 C 0.05 1.64  0.5 0.45 Tim e 88
  • 92. 17-92 Project Management ADVANTAGES OF USING PERT AND POTENTIAL SOURCE OF ERROR PERT and similar project scheduling techniques can provide important services for the project manager. Among the most useful features are these:  Use of these techniques forces the manager to organize and quantify available information and to recognize where additional information is needed.  The techniques provide a graphic display of the project and its major activities.  The identify (a) activities that should be closely watched because of the potential for delaying the project and (b) other activities that have slack time and so can be delayed without affecting project completion time. This raises the possibility of reallocating resources to shorten the project. 92
  • 93. 17-93 Project Management No analytical technique is without potential errors. Among the more important sources of errors are:  When developing the project network, managers may unwittingly omit one or more important activities.  Precedence relationships may not all the be correct as shown.  Time estimates may include a fudge factor; mangers may feel uncomfortable about making time estimates because they appear to commit themselves to completion within a certain time period.  There may be a tendency to focus solely on activities that are on the critical path. As the project progresses, other paths may become critical. Further, major risk events may not be on the critical path. 93
  • 95. 17-95 Project Management QUESTION 2 The network diagram for a project is shown in the accompanying figure, with three time estimates for each activity. Activity times are in months. Do the following: a. Compute the expected time for each activity and the expected duration for each path; b. Identify the critical path; c. Compute the variance for each activity and the variance for each path; d. Find the probability that the project will be completed within 17 months of its start;
  • 96. 17-96 Project Management QUESTION 2 e. Find the probability that the project will take longer than 18 months  2%; f. Can the paths be considered independent? Why? g. Determine the probability that the project will be completed within 15 months of its start; h. What is the probability that the project will not be completed within 15 months of its start?
  • 98. 17-98 Project Management CPM NETWORKS & PROJECT CRASHING  CPM network is deterministic;  CPM approach is useful when both time and cost estimates are known with certainty;  Two sets of time and cost figures are obtained for each activity:  Normal time and normal cost;  Crash time and crash cost;  Further, it is usually assumed that the relationship between time and cost is linear;
  • 99. 17-99 Project Management CPM NETWORKS & PROJECT CRASHING 
  • 100. 17-100 Project Management  The idea of project crashing is that, under certain circumstances, it is necessary and desirable to expedite project completion even though it will result in higher costs.  In CPM we know both the minimum project completion time and the cost-time relationships of all activities; our objective is to design a program that will yield “minimum project completion time with the least increase in costs over the normal costs”. Let us consider these concepts with the aid of the network shown in the figure (on transparency).
  • 101. 17-101 Project Management  Normal and crash times and cost data are shown;  Note that cost/time will always yield a negative slope;  Normal time is without parenthesis; while the crash time is within parenthesis. (This is the usual convension to represent)
  • 102. 17-102 Project Management THE MECHANICS OF CPM  First four steps are the same as that of PERT network i.e.;  Step 1: Define the overall project, including the project objective and target completion date;  Step 2: Break down the project into well-defined activities i.e. Identify beginning event (source event) and Terminal Event;  Step 3: Give serial nos. to each event and arrange then in proper sequence as required by planning and technological requirements; this establishes the precedence relationships;
  • 103. 17-103 Project Management  Step 4: Construct the actual CPM network, inter connecting all the activities and events. Next steps are the “Analysis Phase of CPM”  Step 5: Identify the normal critical path and the crash critical path;  The network shown in the figure has got three different paths as follows:  The normal critical path is 1-3-6 (45 weeks) and that, under normal conditions, the cost of the entire project is $24,800.
  • 104. 17-104 Project Management Length of Path (Weeks) Path Normal Crash 1-3-6 45 30 1-2-5-6 42 32 1-2-4-5-6 44 34 – Crash critical path is 1-2-4-5-6 (34 weeks) and that, under crash conditions, the cost of the entire project is $32,600. – Our task, then, is to design a program that will complete the project within 34 weeks with the least increase in cost above $24,800. – It is logical to start by crashing the least expensive activity on the normal critical path.
  • 105. 17-105 Project Management  Step 6: On the normal critical path, identify the least expensive activity to crash;  Crash this activity and note whether the critical path has changed. If not, crash the next least expensive activity on the critical path and so on. Until a new critical path emerges, with its own least expensive activity to crash. Burning Time:  Assumption of CPM is that “Normal and Crash” estimates are linearly related
  • 106. 17-106 Project Management  In many cases the relationship is not linear. Special computer programs have been developed to accept non- linear time/cost tradeoffs, but these are beyond the scope of this text (course) Cost Time Crash Effort Normal Effort
  • 107. 17-107 Project Management Finding the Minimum Time – Minimum Cost Network:  One of the principal questions CPM can answer is: What is the least cost to complete a project in minimum time?  Continue this process until an “irreducible” critical path on which all activities are on their crash times has been obtained.
  • 108. 17-108 Project Management FIRST CRASH  Start our analysis with the normal critical path. There are only two uncrashed activities on the normal critical path (i.e.; 1-3 and 3-6);  Activity 1-3 is the least expensive activity ($200/week), and hence crash it by 5 weeks. (see transparency). This reduces path 1-3-6 to 40 weeks and changes the critical path to (1-2-4-5-6) 44 weeks.
  • 109. 17-109 Project Management SECOND CRASH  There are four uncrashed activities on (1-2-4-5-6) the new critical path i.e.; (1-2, 2-4, 4-5, & 5-6).  Of these activity 1-2 is the least expensive (i.e.; $200/week); (see transparency). Hence we crash it by 3 weeks.  The critical path is still 1-2-4-5-6; but it has decreased to 41 weeks.
  • 110. 17-110 Project Management THIRD CRASH  There are three uncrashed activities on the current critical path (2-4, 4-5 and 5-6).  Of these activities 2-4 and 5-6 are least expensive $400/week). We can crash any of them; however, we crash activity 5-6 as it yields a larger reduction in completion time (3 weeks). As shown in table. This changes the critical path to 1-3-6 (40 weeks).
  • 111. 17-111 Project Management FOURTH CRASH  There is only one uncrashed activity (i.e.; 3-6) the current critical path. We crash it by 10 weeks (as shown in the transparency) and the critical path is again 1-2-4-5 (38 weeks).  Of these activities 2-4 and 5-6 are least expensive $400/week). We can crash any of them; however, we crash activity 5-6 as it yields a larger reduction in completion time (3 weeks). As shown in table. This changes the critical path to 1-3-6 (40 weeks).
  • 112. 17-112 Project Management FIFTH CRASH  Now there are only two uncrashed activities on the current critical path (3-4 and 4-5). Of these activities 2-4 is least expensive $400/week) and hence we crash it by 2 weeks. (as shown in table). This means that we now have two critical paths (1- 2-5-6 and 1-2-4-5-6) of 36 weeks.
  • 113. 17-113 Project Management SIXTH CRASH  If we compare the two critical paths (1-2-5-6 and 1-2-4-5-6), we find that only two uncrashed activities remain (2-5 and 4-5). Since activity 2-5 is least expensive $200/week), we crash it by 4 weeks. (as shown in transparency). This results in making path 1-2-4-5-6 the critical path.
  • 114. 17-114 Project Management SEVENTH CRASH  There now remains only one uncrashed activity on the current critical path (activity 4-5). We crash it, and note that the critical path is still 1-2-4- 5-6, but it is irreducible (i.e.; all activities on this path are at their crash times). Therefore, we have completed step 2.
  • 115. 17-115 Project Management Step 3: Examine the non-critical paths and uncrash activities on such paths (beginning with the most expensive activity) to the point after which further uncrashing will create a longer critical path. It has been observed uptill now: 1) The minimum completion time of 34 weeks has been achieved; 2) The non-critical path 1-3-6 is 30 weeks long and hence can be uncrashed by no more than 4 weeks; and
  • 116. 17-116 Project Management 3) The other non-critical path 1-2-5-6 is 32 weeks long and hence can be uncrashed by no more than 2 weeks; 4) i. Of the non-critical path 1-3-6, the activity 3-6 is the most expensive ($240/week), hence we uncrash it by 4 weeks; ii. Of the three activities on the non-critical path 1-2-5- 6, activities 1-2 and 5-6 cannot be uncrashed, as they are included in the crash critical path 1-2-4-5-6. However, we can uncrash activity 2-5 ($200/week), and hence we uncrash it by 2 weeks.
  • 117. 17-117 Project Management  We have now executed step 3, and our analysis of CPM Network of Fig. is complete.  We have obtained:  Minimum completion time with the least increase in costs above the normal project cost. The final time status of the activities and their cost consequences are summarized in table (transparency e.g.)
  • 118. 17-118 Project Management Activity Normal Crash Cost ($) 1-2 7 1600 1-3 10 3000 2-4 6 2600 2-5 18 weeks total 4900 3-6 24 weeks total 8640 4-5 12 6000 5-6 9 4500 • It should be noted that the minimum project completion time of 34 weeks has been obtained at a cost of 31,240, as compared to the crash project cost of 32,600.
  • 119. 17-119 Project Management  It should be emphasized that the CPM model is well suited to accommodate the reality of budgetary constraints. (e.g.; we can answer the questions):  What is the minimum project – completion time if our budget for the network in figure is $27,000?  To answer the question we start at the end of step 3 and, of the crashed activities at the stage, we uncrash the most expensive activity first.
  • 120. 17-120 Project Management  Then keeping an eye on the critical path, we keep on uncrashing activities until the project cost is reduced to the level of the budget constraints. For H.W. find the new minimum project completion time, assuming a budget of $27,000.  We can also answer the question:  What is the minimum cost to complete the project in 39 days?