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OBSERVATION
PROBLEM DEFINITION
MODEL CONSTRUCTION
SOLUTION
IMPLEMENTATION
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Mathematical Linear
Programming (MLP)
Probabilistic
Inventory
Networks
Others
Critical Path Method (CPM)
Program Evaluation and
Review Technique (PERT)
Network Flow
Obtain Stamp
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Write a
Letter
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Obtain
Envelope
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Put in
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Address
& Stamp
Post
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The first step in the application of
CPM is to develop a network
representation of the project plan.
A 'network' is a graphic representation with a flow of some type in
its branches. It represents nodes
and branches.
Rules For Construction
of Networks
(a) Each activity is represented by one and
only one arrow. This means that no single
activity can be represented twice in a network
(b) No two activities can be identified by the
same end events. This means that there
should not be loops in the network
…
(c) Time flows from left to right. All the
arrows point in one direction. Arrows
pointing in opposite direction must be
avoided.
(d) Arrows should not cross each other.
(e) Every node must have at least one
activity preceding it and at least one
activity following it, except for the nodes
at the very beginning and at the very end
of the network.
Dummy Activities
There is a need for dummy
activities when the project
contains groups of two or
more jobs which have
common predecessors. The
time taken for the dummy
activities is zero.
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B
E
D
D1
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F
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D2
D3
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D
1
A
2
B
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7
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Looping
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Dangling
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Merge Node
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Burst Node
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Example
15
2
8
10
3
12
16
20
3
15
7
16
1
30
11
15
2
8
Example
10
3
12
16
20
3
15
7
EVENT
1 0
2 16
3 20
7 20 + 15
8 16 + 15, OR 20 + 10 OR 20 + 15
+3
11 30, OR 35 + 16, OR 38 + 12
16
1
30
11
15
2
8
Cont!
10
3
12
16
20
3
15
7
16
1
30
EARLIEST TIME:By Longest Chain
LATEST TIME: Backward Pass
51, 39, 35, 20, 24, 0
11
TIMES (ACTIVITY)
EARLIEST START TIME
Earliest possible time at
which an activity can start
and is given by the earliest
time of the Tail Event.
TIMES (ACTIVITY)
EARLIEST FINISH TIME
Earliest possible time at
which an activity can finish
and is given by adding the
duration time to the earliest
start time.
TIMES (ACTIVITY)
LATEST FINISH TIME
Latest Event Time of the
Head Event.
TIMES (ACTIVITY)
LATEST START TIME
Latest possible time by which
an activity start and is given by
subtracting the duration time
from the Latest Finish Time.
Example
E=16
E=38
15
2
8
L=39
L=24
10
16
E=20
1
L=0
12
E=35
3
20
E=0
3
L=20
15
7
L=35
30
16
E=51
11
L=51
Cont!
ACTIVITY DURATION
START
E
L
FINISH
E
L
1-2
1-3
1-11
2-8
3-7
3-8
7-8
7-11
8-11
0
0
0
16
20
20
35
35
38
16
20
30
31
35
30
38
51
50
16
20
30
15
15
10
3
16
12
8
0
21
24
20
29
36
35
39
24
20
51
39
35
39
39
51
51
Notations
Earliest Time of Tail Event i= iE
Latest Time of Tail Event i = iL
Earliest Time of Head Event j= jE
Latest Time of Head Event j = jL
FLOATS
INDEPENDENT FLOAT
Time by which an activity can
expand without affecting other
(PREV or SUBSEQ)
I = jE - iL - D
If Negative, take I = 0
Cont !
FREE FLOAT
Time by which an activity
can expand without affecting
subsequent activity.
F = jE - iE - D
Cont !
TOTAL FLOAT
Time by which an activity can
expand without affecting the
overall duration of the project.
T = jL - iE - D
Example
E=16
2
L=24
E=38
15
E=51
8
11
L=39
2-8
T = jE – iE – D = 39 – 16 – 15 = 9
F = jE – iE – D = 38 – 16 – 15 = 7
I = jE – iL – D = 38 – 24 – 15 = -1
L=51
Note
TARGET TIME > PROJECT TIME
 POSITIVE FLOAT
TARGET TIME < PROJECT TIME <
 NEGATIVE FLOAT
 REDUCE THE ASSOCIATED
ACTIVITY