Post on 24-Oct-2014
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PROJECT MANAGEMENT
Basic Scheduling with
A-O-N Networks
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ALTERNATIVE PROJECT REPRESENTATIONS
• Activity on Arc
(A-O-A)• Arrow diagrams• Event oriented
networks
• Activity on Node
(A-O-N)• Precedence networks• Activity oriented
networks
i j aactivity, a
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SCHEDULING WITH A-O-N NETWORKS
• Basic scheduling computations can be done on both A-O-A or A-O-N networks.
• A-O-N networks are simpler to draw, though they lack intuitive work flow interpretation of A-O-A networks.
• There are no float anomalies in A-O-N networks.• A-O-N networks are becoming more popular, in
computer packages,• Lead easily to PDM with expanded precedence
relations FS , FF, SS, SF.
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EXAMPLE Job Predecessors Duration (days)a -- 2b -- 3c a 1d a, b 4e d 5 f d 8 g c, e 6h c, e 4i f, g, h 3
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PROJECT NETWORKEXAMPLE (A-O-N)
a c g
bd e h i
f
2 1 6
34
8
345
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FORWARD PASS(A-O-N Networks)
• Initialization: Early start(ES) for all beginning activities = 0 (or the start date, S for the project)• Early finish (EF) for activity = ES+
duration• ES(j)= Max (EF all predecessors)
i1
i2j
ip
ES/ EFES/EFES/EF
ES/EF
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FORWARD PASS FOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
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BACKWARD PASS (A-O-N Networks)
• Initialization Project duration,T = Max (EF of ending jobs).
LF(all ending jobs) =T
• LS = LF- Duration
• LF = Min (LS of successors)LS/LF
LS/LF
LS/LF
LS/LF
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BACKWARD PASSFOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
0 / 2
0 / 3
2 / 3
3 / 7 7 / 12
12 / 18
12 / 16
7 / 15
18 / 21
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EARLY & LATE SCHEDULE FOR EXAMPLE
Job duration ES EF LS LF TF
a 2 0 2 1 3 1
b 3 0 3 0 3 0
c 1 2 3 11 12 9
d 4 3 7 3 7 0
e 5 7 12 7 12 0
f 8 7 15 10 18 3
g 6 12 18 12 18 0
h 4 12 16 14 18 2
i 3 18 21 18 21 0
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CRITICAL PATHFOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
0 / 2
0 / 3
2 / 3
3 / 7 7 / 12
12 / 18
12 / 16
7 / 15
18 / 21
18 /21
10 / 18
14 / 18
12 /1811 / 12
7 / 12 3 / 7
1 / 3
0 / 3
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CRITICAL PATH FOR EXAMPLE
a c g
bd e h i
f
2 1 6
34
8
345
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GANTT CHART SHOWING ACTIVITY SCHEDULE
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
a *** ]
b ^^^^^^
c ** ]
d ^^^^^^^^^
e ^^^^^^^^^^^^^
f ****************** ]
g ^^^^^^^^^^^^^^^
h ********** ]
i ^^^^^^^^^
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INTERPRETATION OF FLOATS
• An activity , in general, has both predecessors and successors. Each of the four kinds of float depends on how these accommodate the activity.
activity
Predecessors Successors
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FLOAT INTERPRETATION
SUCCESSORS
Early Late
Early Free Total
PREDECESSORS
Late Independent Safety
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COMPUTATION OF FLOATS
j
k1
k2
i1
i2 ES/EF
LS/LF
LS/LF
LS/LF
ES/EF
ES/EF
ES/EF
Slack on preceding node= Max (LF of predecessors) -ESSlack on succeeding node = LF- Min (ES of successors) (in the corresponding A-O-A representation)
imLS/LF kn
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FLOATS FOR EXAMPLE
Job Total Safety Free Independenta 1 1 0 0b 0 0 0 0c 9 8 9 8d 0 0 0 0e 0 0 0 0f 3 3 3 3g 0 0 0 0 h 2 2 0 0i 0 0 0 0
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FLOAT COMPUTATIONS FOR ACTIVITY a
Total Float = LS - ES = LF - EF =1Safety float = Total Float - [Max (LF of predecessors)-ES] = 1- (0 - 0) = 1Free float = Total Float -[LF -Min(ES of successors)] = 1 - (3-2) = 0Independent float = Total float - both the latter terms = 1 - (0+1) = 0
a c
d
0 / 2
1 / 3
2 / 3
3 / 7
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FLOAT COMPUTATIONS FOR ACTIVITY c
Total Float = LS - ES = LF - EF =9Safety float = Total Float - [Max (LF of predecessors)-ES] = 9- (3 -2) = 8Free float = Total Float -[LF -Min(ES of successors)] = 9 - (12-12) = 9Independent float = Total float - both the latter terms = 9 - (1+0) = 8
a c g
h
2 / 3
11 / 12
12 / 18
12 / 161 / 3
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FLOAT COMPUTATIONS FOR ACTIVITY f
Total Float = LS - ES = LF - EF =3Safety float = Total Float - [Max (LF of predecessors)-ES] = 3- (7 -7) = 3Free float = Total Float -[LF -Min(ES of successors)] = 3 - (18 - 18) = 3Independent float = Total float - both the latter terms = 3 - (0+0) = 3
d f i7 / 15
10 / 18
18 / 21
3 / 7
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Total Float = LS - ES = LF - EF =2Safety float = Total Float - [Max (LF of predecessors)-ES] = 2- (12 - 12) = 2Free float = Total Float -[LF -Min(ES of successors)] = 2 - (18 - 18) = 2Independent float = Total float - both the latter terms = 2 - (0+0) = 2
FLOAT COMPUTATIONS FOR ACTIVITY h
c
e h i12 / 16
14 / 18
18 / 2111 / 12
7 / 12
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PRECEDENCE DIAGRAMMMING METHODS• Generalized precedence relations
– Start to Start (SS)– Finish to Finish (FF)– Start to Finish (SF)– Finish to Start (FS)
• Permit partial or complete overlap of activities
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START TO START LAG (SS)
u1
v1
u2
v2
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FINISH TO FINISH LAG (FF)
u1
v1
u2
v2
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START TO FINISH LAG (SF)
u1
v1
u2
v2
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FINISH TO START LAG (FS)
u v
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PDM EXAMPLE COMPUTATIONS
A10
E12
F14
G2
C20
B 8
D6
SS 3
FF 2 SS 10
FS 0
SS 2FF 5
FS 0
SF 4
FF 5
FS 4
SS 3
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PDM EXAMPLE SCHEDULE 1 2 3 4 5 6 7 8 91011121314151617181920212223242627A^^^^^^^^^^^^^^^^] B ^^^^^^^^^^^^^^ ] C^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ]D ^^^^^^^^ ] E ^^^^^^^^^^^^^^^^^^^^^^^^] F ^^^^^^^^^^^^^^^^^^^^^^^^^^^]G ^^^^^ ]
Notice that the critical path now is A E F, with F being finish critical owing to the FF 5 relationship between E & F.
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SUMMARY - I
• A-O-N network as an alternative to the
A-O-A network– Simplified representation – Activity rather than event orientation– No float anomalies– Permits expanded relationships, SS, SF, FF, FS– Lacks intuitive work flow interpretation
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SUMMARY- II
• Basic scheduling with A-O-N networks– Network or Tabular computations– Forward pass to compute ES and EF of all jobs– Backward pass to compute LF and LS of all
jobs– Total float computations and identification of
the Critical Path– Safety, free and independent float computations
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SUMMARY - III
• Extensions to Precedence Diagramming Methods– Start to Start Lag (SS)– Finish to Finish Lag (FF)– Start to Finish Lag (SF)– Finish to Start Lag (FS)
• Examples to illustrate the procedures.