Lecture9 Basic Scheduling ForAON

arun kanda/pm/lecture9 1

PROJECT MANAGEMENT

Basic Scheduling with

A-O-N Networks


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


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.


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


PROJECT NETWORKEXAMPLE (A-O-N)

a c g

bd e h i

f

2 1 6

34

8

345


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


FORWARD PASS FOR EXAMPLE

a c g

bd e h i

f

2 1 6

34

8

345


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


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


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


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


CRITICAL PATH FOR EXAMPLE

a c g

bd e h i

f

2 1 6

34

8

345


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 ^^^^^^^^^


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


FLOAT INTERPRETATION

SUCCESSORS

Early Late

Early Free Total

PREDECESSORS

Late Independent Safety


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


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


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


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


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


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


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


START TO START LAG (SS)

u1

v1

u2

v2


FINISH TO FINISH LAG (FF)

u1

v1

u2

v2


START TO FINISH LAG (SF)

u1

v1

u2

v2


FINISH TO START LAG (FS)

u v


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


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.


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


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


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.

Documents

Lecture9 Basic Scheduling ForAON