project scheduling and control with cpm & pert
DESCRIPTION
The best known and most widely used project scheduling and control method is called PERT, or Program Evaluation and ReviewTechnique. PERT is an analytical method which is designed to aid in the scheduling and control of complex projects which require that certain activities be performed in sequenceTRANSCRIPT
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LARGE SCALE PROJECTSProject scheduling and control with PERT / CPM
The best known and most widely used project scheduling and control method is called PERT, or Program Evaluation and ReviewTechnique. PERT is an analytical method which is designed to aid in the scheduling and control of complex projects which require that certain activities be performed in sequence .
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• PERT has been used for many kinds of construction activities, for building bridge and unusual buildings such as stadiums etc. Project planning method, also called network planning methods, were initially developed independently by two different groups.
• As an internal project for any companies , Critical Path Methods ( CPM ) were developed to plan and control the maintenance of chemical plant, assembly plant or any big projects.
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The immediate success of both the CPM and PERT methodologies may be gauged by the following facts. DuPont’s application of the CPM technique to a maintenance project works resulted in a resulted in a reduction in downtime for maintenance from 125 to 78 hours.
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The PERT technique was widely credited with helping to shorten by two years the time originally estimated for the completion of the engineering and development program.
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PERT and CPM are based substantially on the concepts. As originally developed, PERT was based on probabilistic estimates of activity times that resulted in a probabilistic path through a network of activities and a probabilistic project completion time.
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PERT CHARACTERISTICS AND DEFINITIONSACTIVIT
YAn activity is a part of the total work to be done; it consumes time and resources and has starting and ending points.
EVENT
An event is a “milestone”; it marks the beginning or the end of an activity. In drawing a PERT network, events are symbolized as circle or “nodes”. Events are also numbered, with those at the tail of an activity having lower numbers than events at the head of each activity arrow.
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Activity Time
PERT uses three estimates of the amount of time an activity might take to complete. These estimates are obtained from people who have knowledge about the work and how long it will probably take. They are:
Optimistic Time: The time the activity will take if everything goes well and no delays are encountered.
Or
The shortest time required for completion of the activity assuming that no hurdles or completions are encountered.
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• The most likely time or Realistic Time: The time the activity will most likely take under normal conditions, allowing for usual delays.
OR• The time in which the activity is most likely to be
completed .This estimate takes into consideration normal circumstances, making allowance for some unforeseen delays.
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Pessimistic Time The time the activity may take if more than usual delays are encountered.ORThe longest time required to complete the activity assuming that unusual complications and /or unforseen difficulties would arise.PERT weights these three estimates to obtain an “expected time” for an activity by:
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Expected activity time
= Optimistic Time + ( 4 x Realistic Time ) + Pessimistic Time
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Thus if an activity in a PERT network for building a building were “pour the concrete foundation” and it had estimates of 2, 4, and 12 days, its expected duration would be:
2 =Optimistic time,4 =Realistic time and 12 =Pessimistic time
Expected activity time = 2 + (4x4) + 12 / 6 = 5 days.
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FLOAT
• Activities that are not critical are called non-critical activities.
• These activities have a certain amount of spare time or float available.
• Thus, non critical activities can be delayed or advanced (depending on the extent of float availability)without affecting the overall completion date.
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• Earliest expected completion time of events (TE)
• Latest allowable time or latest finish time of events
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1 2 3 4 5 6 7 8 9 10Activity Immediate
Precedencerequirements
Event
Begin End
Opti-Mistictime
Real-Istictime
Pesi-Mistictime
Expected
time
Start
ES LS
Finish
EF LF
Totalslack
A None 1 2 3 4 5 4 0 0 4 4 0B A 2 3 4 7 10 7 4 16 11 23 12C B 3 7 2 7 12 7 11 23 18 30 12D A 2 4 3 5 13 6 4 19 10 25 15E D 4 7 1 5 9 5 10 25 15 30 15F A 2 5 7 8 21 10 4 4 14 14 0G F 5 6 1 7 7 6 14 14 20 20 0H G 6 7 --- --- --- --- 20 30 20 30 10I C, E, G 7 8 10 10 10 10 20 30 30 40 10J G 6 8 15 20 25 20 20 20 40 40 0K L, I, J 8 9 2 7 12 7 40 40 47 47 0L A 2 8 10 15 20 15 4 25 19 40 21
PERT data
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PERT DATA WITH EXPECTED TIME
(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20Expected time
= Optimistic Time + ( 4 x Realistic Time ) + Pessimistic Time
6
4 7 7 6 5 10 6 --- 10 20 7 15
4 7 7 6 5 10 6 --- 10 20 7 15
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PROJECT SCHEDULING
Data on the activities in the Print Project
ACTIVITY DESCRIPTION TIMEREQD.
PREDECESSORS
A Widen access door 3 -----B Build compressor housing 3 AC Remove old printing press 1 -----D Move other machines to create
more space2 C
E Re-lay concrete floor 8 A,DF Upgrade factory power supply 4 -----G Lay new electrical cabling 1 FH Update and adjust pre-press
equipment4 ----
I Operators go on training course 12 CJ Install new printing press 6 B,E,F,G,K Commission new press 4 H,I,J,
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NETWORK DIAGRAM FOR PRINTING PRESS PROJECT
Nodes with activity
0
A
C D
H
B
3
3
1
F
K
E
G
8
4
6
1
1
4
J
I12
86
6
2
6
4
4
4
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NETWORK DIAGRAM FOR PRINTING PRESS PROJECT
Priority activity
0
1
3 4
8
2
A3
B3
6
12
5
7
E8
F4
J6
C1
G1
H4
11
10I12
E8J6
J6
D2
J6
K4
K4
K4
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FLOW OF CALCULATION FOR EARLY START, ES, AND EARLY FINISH, EF, TIMES.
20
EARLY FINISH
Priority Activities
0
1
3 4
8
2
A3
B3
6
12
5
7
E8
F4
J6
C1
G1
H4
11
10I12
E8 J6
J6
D2
J6
K4
K4
K4
40
84
30
10 31
113
113
63
131
1711
1713
126
40
54
104
115
2117
2121
EARLY START
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Precedence Chart Showing Activities Their Required Sequence, and Time Requirements for the New Product
Introduction ProjectActivityCode
Description ImmediateProcessor
Activity
Timeweeks
A Organize Sales Office ------ 6
B Hire Sales people A 4
C Train Sales People B 7
D Select advertising agency A 2
E Plan Advertising Campaign D 4
F Conduct Advertising Campaign E 10
G Design Package ---- 2H Set Up Packaging Facilities G 10
I Package initial Stocks H, J 6
J Order Stock from Manufacturer ---- 13
K Select Distributors A 9
L Sell Distributors C, K 3
M Ship Stock to Distributors I,L 5
Table
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Network Diagram for New Product Introduction Project
0
A
CB
6
47
D E
H
J
F
G
24 10
2
10
13
K
L
I
6
6
93
3
5
M
5
Nodes with activity
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Network Diagramming
A network is developed that takes account of the precedence relationships among the activities; it must be based on a complete, verified, and approved activity list.
The important information required for these network diagrams is generated by the following three questions:
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• Which activities must be completed before each activity can be started.
• Which activities can be carried out in parallel.
• Which activities immediately succeed other activities.
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ARCS NETWORK DIAGRAM FOR THE NEW PRODUCT INTRODUCTION PROJECT.
0 1
2
Start (0)A (6
)
3B (4) 4
C(7)
8D(2)
5
G(2)
6H(10)
J(13)
7
I(6)
K(9)L(3) 10
M(5)
9E(4)
F(10)
11FINISH(0)
Priority Activity
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FLOW OF CALCULATION FOR EARLY START, ES, AND EARLY FINISH, EF, TIMES.
0 1
2
Start (0)A (6
)
3
B (4)
4C(7)
8D(2)
5
G(2)
6H(10)
J(13) 7
I(6)
K(9)
L(3) 10M(5)
9E(4)
F(10)
11
FINISH(0)00
20122
130 1913
60
86
128
2212
106 1710
156
2017
2520 2525
EARLY
0;00;0
EARLY
Priority Activities
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FLOW OF CALCULATION FOR LATE START, LS, AND LATE FINISH, LF, TIMES.
0 1
2
Start (0)A (6
)
3
B (4)
4C(7)
8D(2)
5
G(2)
6H(10)
J(13) 7
I(6)
K(9)
L(3) 10M(5)
9E(4)
F(10)
11
FINISH(0)0;00;0
2;40;2
0;00;0
LATEEARLY
Start Finish
EARLY LATE
12;142;4
13;140;1
6;60;0
10;106;6
14;1410;10
8;116;9
12;158;11
15;176;8
22;2512;15
25;2525;25
20;2017;17
25;2520;20
19;2013;14
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PROJECT GRAPH OF ACTIVITIES ON NODES
A,6 B,4 C,7 L,3 M,5
K,9
D,2 E,4 F,10
J,13
G,2 H,10
I,6Finish,0
A,6
Critical Path
Activity Code
Time, Weeks
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1 2
3
4
7
5
6
89
A 4
B 7
C 7
D 6
E 5
F 10 G 6
H 0
I 10
J 20
K 7
PERT NETWORK WITH ACTIVITY TIME
Continue from slide # 38
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PERT data
(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
4 7 7 6 5 10 6 --- 10 20 7 15
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1 2
3
4
7
5
6
89
A 4
B 7
C 7
D 6
E 5
F 10 G 6
H 0
I 10
J 20
K 7
PERT NETWORK WITH EARLY START ( ES )
ES 0 ES 4
ES 11
ES1 0
ES 14
ES 20
ES 20
ES 40ES 47
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(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
ES0 4 11 4 10 4 14 20 20 20 40 4
PERT DATA WITH EARLY START ( ES )
0 4 11 4 10 4 14 20 20 20 40 4
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(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
ES0 4 11 4 10 4 14 20 20 20 40 4
PERT DATA WITH EARLY START / EARLY FINISH ( ES ) / (EF )
4 11 18 10 15 14 20 20 30 40 47 19
EARLY FINISH (EF) = ES + Expected time
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
4 11 18 10 15 14 20 20 30 40 47 19
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1 2
3
4
7
5
6
89
A 4
B 7
C 7
D 6
E 5
F 10 G 6
H 0
I 10
J 20
K 74747
4040
30202311
2020
2510
1414
4 4
0 0
ES LF
PERT NETWORK WITH EARLY START / LATE FINISH ( ES ) / ( LF )
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(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
LF0 4 11 4 10 4 14 20 20 20 40 4
PERT DATA WITH EARLY START / EARLY FINISH LATE FINISH ( ES ) / (EF ) / ( LF )
LATE FINISH (LF) = From the end time
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
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(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
PERT DATA WITH EARLY START / EARLY FINISH / LATE FINISH / TOTAL SLACK ( ES ) / (EF ) / ( LF ) ( TS)
Slack time = LF - Expected Time - ES
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
4 - 4 - 0 = 0 23- 7 - 4 = 12 30- 7-11 = 12
25-6-4 = 15
30-5-10 = 15 14-10-4 = 0 20-6-14 = 0 30-0-20 = 10
40-10-20 = 10 40-20-20 = 0 47-7-40 = 0 40-15-4 = 21
0 12 12 15 15 0 0 10 10 0 0 21
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
0 12 12 15 15 0 0 10 10 0 0 21
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(1)
Activity
(2) Immediate
precedence requirement
(3) Events
Begins End
(4) Optimistic time
(5) Realistic time
(6) Pessimistic time
(7) Expected time
(8)
Start
ES LS
(9)
Finish
EF LF
(10)
Total slack
A B C D E F G H I J K L
None A B A D A F G
CEG G LIJ
A
1 2 3 2 4 2 5 6 7 6 8 2
2 3 7 4 7 5 6 7 8 8 9 8
3 4 2 3 1 7 1 -- 10 15 2 10
4 7 7 5 5 8 7 --- 10 20 7 15
5 10 12 13 9 21 7 ---- 10 25 12 20
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
PERT DATA WITH EARLY START / EARLY FINISH / LATE FINISH / TOTAL SLACK LATE START ( ES ) / (EF ) / ( LF ) / ( TS) / ( LS )
LATE START ( LS ) = Total Slack + ES
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
0 12 12 15 15 0 0 10 10 0 0 21
0 16 23 19 25 4 14 30 30 20 40 25
4 7 7 6 5 10 6 --- 10 20 7 15
0 4 11 4 10 4 14 20 20 20 40 4
4 11 18 10 15 14 20 20 30 40 47 19
4 23 30 25 30 14 20 30 40 40 47 40
0 12 12 15 15 0 0 10 10 0 0 21
0 16 23 19 25 4 14 30 30 20 40 25
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CRITICAL PATHThe critical path is the largest through the network.
1, 2, 8, 9 4 + 15 + 7 = 26
1, 2, 3, 7, 8, 9, 4 + 7 + 7 + 10 + 7 = 35
1, 2, 4, 7, 8, 9 4 + 6 + 5 + 10 + 7 = 32
1, 2, 5, 6, 7, 8, 9, 4 + 10 + 6 + 0 + 10 + 7 = 37
1, 2, 5, 6, 8, 9, 4 + 10 + 6 + 20 + 7 = 47
The critical path will be 1, 2, 5, 6, 8, 9 = 47
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1 2
3
4
7
5
6
89
A 4
B 7
C 7
D 6
E 5
F 10 G 6
H 0
I 10
J 20
K 74747
4040
30202311
2020
2510
1414
4 4
0 0
ES LF
CRITICAL PATH NETWORK
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EXAMPLE : In this example the finish-start (F-S) links have zero duration. A network will be developed for the project represented by the data in table:
Activity Duration (wks) Precursor activity (ies)A 4 ---B 3 ---C 6 A,BD 1 BE 7 DF 2 CG 5 C,E,H 8 EJ 4 GK 5 F,G,L 6 J,H,M 3 L,K,
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START
E
H FINISH
L M
J
F
G
KC
B
A
D
0 4 26
3
5
1
5
7
4
8 0
6 3
Duration
31
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0 0
0 0START
4 11
E
11 19
H29 29FINISH
20 26
L26 29
M
16 20J
10 12
F
11 16
G
16 21
K4 10
C
0 3
B
0 4
+ A
3 4
D
0 4 26
3
5
1
5
7
4
8 0
6 3
Duration
Early Start
32
Early Finish
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0 0
0 0START
4 11
4 11E
11 19
12 20 H
29 29
29 29FINISH
20 26
20 26L
26 29
26 29M
16 20
16 20J
10 12
19 21F
11 16
11 16G
16 21
21 26K
4 10
5 11C
0 3
0 3B
0 4
1 5 A
3 4
3 4D
0 4 26
3
5
1
5
7
4
8 0
6 3
Duration
Early Start
33
Early Finish
Late Start
Late Finish
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Path with maximum duration or Critical Path Mean ( CPM )
Start + A+C+F+K+M = 4+6+2+5+3 = 20
Start + A+C+G+J+L+M = 4+6+5+4+6+3 = 28
Start + B+C+G+K+M = 3+6+5+5+3 = 22
Start + B+C+G+J+L+M = 3+6+5+4+6+3 = 27
Start + B+D+E+G+K+M = 3+1+7+5+5+3 = 24
Start + B+D+E+G+J+L+M = 3+1+7+5+4+6+3 = 29 ( CPM )
Start + B+D+E+H+L+M = 3+1+7+8+6+3 = 28
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0 0
0 0START
4 11
4 11E
11 19
12 20H 29 29
29 29FINISH
20 26
20 26L
26 29
26 29M
16 20
16 20J
10 12
19 21F
11 16
11 16G
16 21
21 26K
4 10
5 11C
0 3
0 3B
0 4
1 5 A
3 4
3 4D
0 4 26
3
5
1
5
7
4
80
6 3
Duration
Early Start
35
Early Finish
Late Start
Late Finish
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Activity-on-node diagrams in which finish-to-start (F-S) links have duration's, and in which there are start-to-start (S-S) and finish-to-finish (F-F) links will now be considered.
The nature and duration of each links will be shown against each arrow. Showing in the figure illustrates the case in which activity F cannot start until one week after the finish to activity X, and activity C cannot commence until two weeks after the completion of activity F.
X0
F CF - S (1) F - S (2)
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EXAMPLE A project consists of activities A, B and C with links as shown in the tables
Activity DurationWeeks
PrecursorActivity
Link Type Link Duration
A 4 ------B 24 A F - S 0C 12 B S –S 6
F - F 3
0
A4
4
4
B28
24
10
C31
12
F - S (0)
S - S (6)
F - F (3)
Start for B (4) plus S - S(6) = 10
Finish for B(28) plus F-F(3)=31
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0
0 4A
4
4
4
4 28B
28
24
10
19 31C
31
12
F - S (0)
S - S (6)
F - F (3)
Block B and Block C are independent with Late finish and Late start
Late Finish
Late Start
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EXAMPLE A project data are given to find out all the respectful information for every individual block.
Activity Duration weeks Precursor activity Link type Link DurationA 4 ------ F--S 0B 3 ------ F--S 0C 6 A,B F--S 0D 1 B F--S 6E 12 D S--S 4F 2 C F--S 0G 5 E,F F--S 0H 8 E S--S 3
F--F 2J 4 G F--S 1K 5 F,G F--S 0L 6 J,K F--S 0M 3 L,K F--S 0
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START0
A4
C6
F2
K5
B3
G5
J4
M3
L6 E
12 D
1
S-S (4)
H8
S-S (3)
F-F (2)
F-S (1)
F-S (6)
FINISH0
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PERT DATA WITH DURATION
ACTIVITY
DURATION(WEEK)
PRECURSORACTIVITY
ABCDEFGH
JKLM
4361
12258
4563
--------
A,B,BDC
E,F,E
GF,G,J,H,L,K,
ES LSSTART
EF LF
FINISH
SLACK
TOTAL
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0 0
START0
0 4
A4
4 10
C6
10 12
F2
30 35
K5
0 3
B3
25 30
G5
31 35
J4
41 44
M3
35 41
L6
13 25
E129 10
D1
S-S (4)
16 27
H8
S-S (3)
F-F (2)
F-S (1)
F-S (6)
44 44
FINISH0
Early Start
EarlyFinish
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PERT DATA WITH ES & EF
ACTIVITY
DURATION(WEEK)
PRECURSORACTIVITY
ABCDEFGH
JKLM
4361
12258
4563
--------
A,B,BDC
E,F,E
GF,G,J,H,L,K,
ES
0049
13102516
31302541
LSSTART
EF LF
FINISH
43
101025123027
35354144
SLACK
TOTAL
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0 0
0 0START
0
0 4
13 17 A
4
4 10
17 23 C
6
10 12
23 25 F
2
30 35
36 41 K
5
0 3
0 3 B
3
25 30
25 30 G
5
31 35
31 35 J
4
41 44
41 44 M
3
35 41
35 41 L
613 25
13 25 E
129 10
9 10 D
1
S-S (4)
16 27
27 35 H
8
S-S (3)
F-F (2)
F-S (1)
F-S (6)
44 44
44 44FINISH
0
Late Start
LateFinish
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PERT DATA WITH LS & LF
ACTIVITY
DURATION(WEEK)
PRECURSORACTIVITY
ABCDEFGH
JKLM
4361
12258
4563
--------
A,B,BDC
E,F,E
GF,G,J,H,L,K,
ES
0049
13102516
31302541
LSSTART
130
179
13232527
31363541
EF LF
FINISH
43
101025123027
35354144
173
231025253035
35414144
SLACK
TOTAL
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PERT DATA WITH TOTAL SLACK
ACTIVITY
DURATION(WEEK)
PRECURSORACTIVITY
ABCDEFGH
JKLM
4361
12258
4563
--------
A,B,BDC
E,F,E
GF,G,J,H,L,K,
ES
0049
13102516
31302541
LSSTART
130
179
13232527
31363541
EF LF
FINISH
43
101025123027
35354144
173
231025253035
35414144
SLACK
TOTAL
130
1300
130
11
06
100
Total Slack = LS - ES
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A+C+F+K+M = 4+6+2+5+3 = 20
A+C+F+G+J+L+M =4+6+2+5+4+6+3 = 30
A+C+F+G+K+M = 4+6+2+5+5+3 = 25
B+C+F+K+M = 3+6+2+5+3 = 19
B+C+F+G+J+L+M = 3+6+2+5+4+6+3 = 29
B+C+F+G+K+M = 3+6+2+5+5+3 = 24
B+C+F+G+J+L+M = 3+6+2+5+4+6+3 = 30
B+D+E+G+J+L+M = 3+1+12+5+4+6+3 = 34
B+D+E+G+K+M =3+1+12+5+5+3 = 29
B+D+E+G+J+L+M = 3+1+15+5+4+6+3 = 37
B+D+E+H+L+M = 3+1+12+8+6+3 = 33
CRITICAL PATH MEAN (CPM)
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THE BAR CHARTThe bar chart can be drawn. All activities with float have been shown as starting at their earliest start time.
A B C D F E H G K J L
M
0 10 20 30 40 50Weeks
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EXAMPLEAs part of a large computer net work system project of MAN (Metropolitan Area Network) is to be installed in the city. Cabling and work station will be carried out by a civil engineering group. Setting out the networking with cabling for communication which connect one or more telephones and computers and associated devices. Installation of networking was carried out by Computer Engineering group. Non destructive testing (NDT) for the networking will be carried out by independent assessors for statuary purpose, and once this has been finishes, the Civil Engineering group will place for constructing the building as required according to the networking. The different groups have been asked to provide estimates of their rates of progress . The area covering is 120 km square. Each group assumes that it has one team working, starting at one end and proceeding to the other.The initial plan provides for all operation to be at least 4 km apart. The following data are given on the next slide.
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Group Activity Estimated rate ofworking (km/day)
Duration(days)
Civil Engg. X-Building 2 60
Suppliers P-Placing 4 30Computer
Engg.W-Network
setup1 120
NDTassessors
N-NDT 2 60
Civil Engg. B-Sub-bldg. 4 30
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0 0
0 0START
0
0 60
0 118 X
60
2 61
2 119 P
30
S-S (2)
F-F(1)
3 123
3 123 W
120
S-S(1)
7 125
65 125 N
60
S-S(4)
F-F(2)
9 126
96 126 B
30S-S(2)
F-F(1)
126 126
126 126FINISH
0
F-F (4)
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PROBLEMS # 1The following information covers part of a large PERT :
Starting Event Following event Expected timeweeks
A C 11A D 6B D 5C E 7C F 5D F 9D G 10D H 12E F 2F H 8F I 12G H 4H I 8
What is the critical path and how many weeks will it take to complete this work. Also construct a data for ES, LS, EF, LF and slack weeks.
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KEY POINTS
• Straight lines connecting circles represent tasks that take time or resources; these lines are called activities.
• The circles are called events and represent a point in time .
• A dotted line is called a dummy activity.
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• The critical path through a network is the chain of activities whose times determine the overall duration of the project.
• Activities on the critical path are known as critical activities.
• The top right of each event records its earliest finish time.
• The bottom right of the event records the latest finish time.
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• Events whose earliest time equals their latest time are on the critical path.
• Spare time for an activity is called a float.• Total float=latest finish time-earliest start
time-activity duration.• The float is used to identify whether any
delay in starting or carrying out an activity will cause a delay in the project completion time.
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• The latest finish time for each of the previous events is obtained by subtracting the activity durations from the preceding events along the backward route, taking the minimum value where there is more than one route back into an event.
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Data Flow Diagrams – Relationship Grid