Chapter 5- Net Work Final powe point for student

PROJECT MANAGEMENT AND
NETWORK MODEL
Chapter 5
1

PROJECT MANAGEMENT
What is project
A project is a temporary effort to create a unique
product or service. Projects usually include
constraints/limitations and risks regarding cost,
schedule or performance outcome.
Project management is the application of knowledge, skills, tools,
and techniques to project activities in order to meet or exceed
stakeholder needs and expectations from a project.
Meeting or exceeding stakeholder needs and expectations
invariably involves balancing competing demands among:
 Scope/capacity, time, cost, and quality
 Stakeholders with differing needs and expectations 2

BRIEF HISTORY OF CPM/PERT
CPM/PERT or Network Analysis as the technique is sometimes
called, developed along two parallel streams, one industrial and
the other military.
CPM was the discovery of M.R. Walker and J.E. Kelly in
1957.
 The first test was made in 1958, when CPM was applied to the
construction of a new chemical plant.
 Projects for which activity times were known.
PERT was devised in 1958 for the POLARIS missile program
by the Program Evaluation Branch of the Special Projects office
of the U.S. Navy.
 PERT was developed to handle uncertain activity times.
Both use same calculations, almost similar
Main difference is deterministic and probabilistic in
time estimation
3

 BY USING PERT/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 completion of the project.
4. An indication of how long any activity can be
delayed with out lengthening the project (slack).
4

BASIC DIFFERENCES BETWEEN PERT & CPM
 PERT: It assumes a probability distribution
for the duration of each activity
 It is used for one-time projects involving
activities of non-repetitive nature.
 CPM: was developed in connection with a
construction and maintenance project in
which duration of each activity was known
with certainty.
 It is used for completion of projects involving
activities of repetitive nature.
5

THE PROJECT NETWORK
Network analysis is the general name given to certain specific techniques which can be
used for the planning, management and control of projects.
Network:- Shows the sequential relationships among activities using nodes and arrows.

Use of nodes and arrows
Arrows an arrow leads from tail to head directionally. Indicate Activity.
 Activity:- A task or a certain amount of work required in the project which requires
time to complete

Nodes A node is represented by a circle
Indicate EVENT, a point in time where one or more activities start and/or
finish.
6

7
SITUATIONS IN NETWORK DIAGRAM
A
B
C
A must finish before either B or C can start
A
B
C both A and B must finish before C can start
D
C
B
A
both A and B must finish before either of C or
D can start
A
C
B
D
Dummy
A must finish before B can start both A and C must
finish before D can start

8
NETWORK EXAMPLE
Illustration of network analysis for shopping center expansion plan
The key question is: How long will it take to complete this project ?

9
FORWARD PASS
 Earliest Start Time (ES)
 earliest time an activity can start
 ES = maximum EF of immediate predecessors
 Earliest finish time (EF)
 earliest time an activity can finish
 earliest start time plus activity time
EF= ES + t
Latest Start Time (LS)
Latest time an activity can start without delaying critical
path time
LS= LF - t
Latest finish time (LF)
latest time an activity can be completed without delaying
critical path time
LF = minimum LS of immediate predecessors
BACKWARD PASS

10
CPM ANALYSIS
 Draw the CPM network
 Analyze the paths through the network
 Determine the float for each activity
 Compute the activity’s float
float = LS - ES = LF - EF
 Float/Slack is the maximum amount of time that
this activity can be delay in its completion before it
becomes a critical activity, (i.e., delays completion
of the project)
 Find the critical path is that the sequence of
activities and events where there is no “slack” i.e..
Zero slack
 Longest path through a network
 Find the project duration is minimum project
completion time

11
CPM CALCULATION
 Path
 A connected sequence of activities leading from the
starting event to the ending event
 Critical Path
 The longest path (time); determines the project
duration
 Critical Activities
 All of the activities that make up the critical path

EXAMPLE: LISTED BELOW ARE ACTIVITIES TO BE
IMPLEMENTED FOR SHOPPING CENTER EXPANSION PLAN TO
MODERNIZE AND EXPAND THE CURRENT SHOPPING CENTER
COMPLEX.
Table 5.1. list of activities for shopping center project
12

EXAMPLE ...CONT’D
1. What is the total time to complete the project?
2. What are the scheduled start and finish dates for
each specific activity?
3. Which activities are “critical” and must be completed
exactly as scheduled to keep the project on schedule?
4. How long can “noncritical” activities be delayed
before they cause an increase in the total project
completion time?
CPM analysis answers the following questions
13

STEPS IN CPM
 Develop a list of the activities that make up the project
 Identify immediate predecessor(s) and the activity time (in weeks)
for each activity
 Activities that must be completed immediately prior to the start of that
activity
 Develop network of activities (find sequence of activities with
respective predecessor(s))
 Assign time (the number of weeks) required to complete each
activity.
 Determine total time required to complete the project
 Total project time is longest path time (critical path time)
14

15
CPM EXAMPLE:
Figure 5.1. CPM Network for shopping center project
activities

CPM EXAMPLE: …CONT’D
Figure 5.2. Shopping Center Project Network With Activity Times
16

DETERMINING THE CRITICAL PATH
 We begin by finding the
 earliest start (ES) time and a
 latest start (LS) time for all activities in the
network.
 Let
ES =earliest start time for an activity
EF =earliest finish time for an activity
t =activity time
EF = ES + t

Forward Pass Network
17

CRITICAL PATH…..CONT’D
 Activity A can start as soon as the project starts,
 So we set the earliest start time for activity A equal to 0.
i.e.
 ESA= 0
 With an activity time of 5 weeks, the earliest finish time
for activity A is
EF A = ESA + t A = 0+5 = 5
 EF A = 5
18

CRITICAL PATH…CON’D
We will write the earliest start and earliest finish times in the node to
the right of the activity letter. Using activity A as an example, we have
19

Figure 5.3. A Portion Of The Shopping Center Project Network, Showing
Activities A, B, C, And H
20

Figure 5.4. SHOPPING CENTER PROJECT NETWORK WITH EARLIEST
START AND EARLIEST FINISH TIMES SHOWN FOR ALL
ACTIVITIES
21

CRITICAL PATH…CONT’D
 We begin by finding the
 Latest start (LS) time and
 latest finish (LF) time for all activities in the
network.
 Let
LS =latest start time for an activity
LF =latest finish time for an activity
t =activity time
LS = LF – t
The latest finish time for an activity is the smallest of the latest start times for all
activities that immediately follow the activity.

Backward Pass Network
22

 Beginning the backward pass with activity I,
 we know that the latest finish time is
 LFI = 26 and
 activity time is tI = 2
 Thus, the latest start time for activity I is
 LSI = LFI - tI
26 - 2 = 24.
 We will write the LS and LF values in the node
directly below the earliest start (ES) and earliest
finish (EF) times.
23

Thus, for node I, we have
† The latest finish time for activity H must be the latest
start time for activity I.
† Thus, we set LF = 24 for activity H.
† Using equation (for LS), we find that LS = LF - t
 24 -12 =12 as the latest start time for activity H. 24

Figure 5.5. SHOPPING CENTER PROJECT NETWORK WITH LATEST
START AND LATEST FINISH TIMES SHOWN IN EACH
NODE
25

 Activity A requires a more involved application of the
latest start time rule.
 First, note that three activities (C, D, and E)
immediately follow activity A.
 latest start times for activities C, D, and E are:
 LS = 8, LS = 7, and LS = 5, respectively.
 The latest finish time rule for activity A states that
the LF for activity A is the smallest of the latest start
times for activities C, D, and E.
 With the smallest value being 5 for activity E,
we set the latest finish time for activity A to LF = 5.
26

 After we complete the forward and backward passes, we
can determine the amount of slack associated with each
activity.
 Slack is the length of time an activity can be delayed
without increasing the project completion time.
 The amount of slack for an activity is computed as follows:
 Slack = LS - ES = LF – EF
 For example,
 the slack associated with activity C is LS - ES = 8 -5 = 3
weeks.
27

TABLE 5.2. ACTIVITY SCHEDULE FOR THE WESTERN HILLS
SHOPPING CENTER PROJECT
28

PROJECT SCHEDULING WITH UNCERTAIN
ACTIVITY TIMES
The preceding analysis on CPM assumed that activity times
were known and not subject to variation. Although that
assumption is appropriate in some situation, there are many
other in which it is not.
Consequently, those situations require a probabilistic
approach. PERT uses this approach.
The probabilistic approach involves three time estimates for
each activity instead of one:
1.Optimistic time: - the length of time require under optimum
condition. It is represented by the letter “a”.
2.Pessimistic time: - the amount of time that will be required
under the worst condition. It is represented by the letter “b”.
3.Most likely time: - the most probable amount of time
required. It is represented by letter ”m”.
These time estimate should be made by managers or other
who have knowledge about the project. 29

PERT …CONT’D
The important issue in network analysis is the average of
expected time for each activity, teand the variance of each
activity time, δ2
.
30

 To find the expected activity time (t), the beta
distribution weights the estimates as follows
 To compute the dispersion or variance of
activity completion time, we use the formula
6
4m b
+
+
a
=
t
2
6
Variance 




  a
b
=
31

EXAMPLE:
A SMALL IS COMPOSED OF 8 ACTIVITIES WHOSE TIME
ESTIMATES ARE LISTED IN THE TABLE BELOW
32
Activity Predecessors
Estimated Duration (Weeks)
Optimistic Most Likely Pessmistic
A - 1 1 7
B - 1 4 7
C - 2 2 8
D A 1 1 1
E B 2 5 14
F C 2 5 8
G D, E 3 6 15
H F, G 1 2 3

CONT……….
REQUIRED:
a) Draw the project network and identify all the paths.
b) Compute the expected time for each activity and the
expected duration for each path.
c) Determine the expected project length.
d) Identify the critical path and critical activities.
e) Compute the variance for each activity and the variance for
path .
33

PERT CRITICAL PATH…CONT’D
SOLUTION
A)
34

CONT…..
Solution B): Expected time calculation
Path Activity
Times
a m b
te = a+4m+b
6
Path
total
1-2-5-8
a
d
g
1 3 4
3 4 5
2 3 6
2.83
4.00
3.33
10.16
1-3-6-8
b
e
h
2 4 6
3 5 7
4 6 8
4.00
5.00
6.00
15.00
1-4-7-8
c
f
i
2 3 5
5 7 9
3 4 6
3.17
7.00
4.17
14.34
35

CONT…..
Solution C): Variance calculation
Path Activity
Times
a m b
δ=activity=(b-a)2
36
δ2
path δ path
1-2-5-8
a
d
g
1 3 4
3 4 5
2 3 6
(4-1)2
/36=9/36
(5-3)2
/36=4/36
(6-2)2
/36=16/36
29/36=0.8055 0.898
1-3-6-8
b
e
h
2 4 6
3 5 7
4 6 8
(6-2)2
/36=16/36
(7-3)2
/36=16/36
(8-4)2
/36=16/36
48/36=1.33 1.155
1-4-7-8
c
f
i
2 3 5
5 7 9
3 4 6
(5-2)2
/36=9/36
(9-5)2
/36=16/36
(6-3)2
/36=9/36
34/36=0.944 0.972
36

SOLUTION B:
EXPECTED TIME (TE) AND VARIANCE (2
)
CALCULATIONS
37
Activity
Sequence
Activity
Times
to tm tp
1 - 2 A 1 1 7 2 1
1 - 3 B 1 4 7 4 1
1 - 4 C 2 2 8 3 1
2 - 5 D 1 1 1 1 0
3 - 5 E 2 5 14 6 4
4 - 6 F 2 5 8 5 1
5 - 6 G 3 6 15 7 4
6 - 7 H 1 2 3 2 0.33
 
t
t
t
t p
m
o
e


 4
6
1
 






 t
t o
p
6
1
2
2


PROBABILITY FOR PERT/UNCERTAIN TIME
PROJECT
 Variability leading to a longer-than-expected total time for the
critical activities will
always extend the project completion time, and
 Conversely, variability that results in a
shorter-than-expected total time for the critical activities will reduce
the project completion
time, unless other activities become critical.
 Let us now use the variance in the critical activities to determine the
variance in the project completion time.
 Let T denote the total time required to complete the project. The
expected value of T, which is the sum of the expected times for the
critical activities, is
 E(T) =tc + tf + ti
=3.17+ 7+4.17 = 14.34weeks
38

PROBABILITY FOR PERT…CONT’D
 The variance in the project completion time is the sum
of the variances of the critical path activities.
 Thus, the variance (2
) for this project completion time
is
2
= 2
c +2
f +2
i
= 0.25+0.44+0.25 = 0.94
Where: 2
c , 2
f , and 2
i are variances of critical activities
 Knowing that the standard deviation is the square root
of the variance, we compute the standard deviation ()
for this project completion time as
39

 In order to obtain the probability of completing the
project for less or equal to 20 weeks is
 From standard normal distribution table probability
of Z = +5.83 i.e. p(Z≤+5.83) is more than 0.999
 Therefore, we have more than 0.999 or 99.9%
probability to complete the project within 20 weeks 40

 Assuming that the distribution of the project
completion time T follows a normal, or bell-shaped,
distribution
 With this distribution, we can compute the probability
of meeting a specified project completion date.
 For example, suppose that management allotted 20
weeks for the project under analysis. What is the
probability that we will meet the 20-week deadline?
 Using the normal probability distribution from
statistical probability distribution table
 We are asking for the probability that T ≤ 20; this
probability is the area of z-value for the normal
cumulative probability for less than or equal to 20 41

CONT….
Knowledge of the expected path time and their standard
deviation enables a manager to make probabilistic estimate
of the project complementation time.
It is assumed that the path time is of independent to each
other. This requires two things:
Activity times are independent of each other, and each
activity is only on one path
A project is not completed until all of its activities, not just
those on the critical path, have been completed.
42

TIME-COST TRADE-OFFS
_CRUSHING:
 In many situations it is possible to reduce the
length of a project by injecting additional
resources.
 Managers often have certain options at their
disposal that allow them to shorten, or crush,
certain activities.
 Among the most obvious options are using
additional personnel or more efficient equipment
and relaxing work specifications. 43

CONTD
…
 a project manager may be able to shorten a
project, there by realizing a savings on indirect
project cost by increasing direct expenses to
speed up the project.
 The goal in evaluating time-cost trade-offs is to
identify a plan that will minimize the sum of the
indirect and direct project costs.
44

 In order to make a rational decision about
which activities (If any) to crush and the
extent of crushing desirable, a manager needs
the following information:
1. Regular time and crushing time estimates for
each activity
2. Regular cost and crush cost estimates for each
activity
3. A list of activities that are on the critical path
45

 Activities on the critical path are potential candidates
for crushing because shortening non critical activities
would not have an impact on total project duration.
Optimum
Expected
indirect cost
Cost
Cumulative
cost of crushing
Shorten
Total cost
Shorten
Shorten
crush
Project
length
46

THE GENERAL PROCEDURE FOR
CRUSHING IS:
1. Obtain estimates of regular and crush times
and costs for each activity.
2. Determine the length of all paths and path
slack times.
3. Determine which activities are on the critical
path.
4. crush critical activities, in order of increasing
costs, as long as crushing costs do not exceed
benefits.
47

CRUSHING COST CALCULATION
Table 5.2. NORMAL AND CRUSH ACTIVITY DATA FOR THE TWO- MACHINE
MAINTENANCE PROJECT
48

Chapter 5- Net Work Final powe point for student

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