spring 2008, king saud university arrow diagramming dr. khalid al-gahtani 1 network schedule...

Spring 2008, King Saud University

Arrow DiagrammingDr. Khalid Al-Gahtani

1

Network Schedule

• Predominant Network Scheduling Techniques:– Critical Path Method (CPM)– Program Evaluation and Review Technique

(PERT)



2

Critical Path Method (CPM)

• CPM is a graphical network-based scheduling techniques that when applied intelligently and honestly can be an excellent tool in project management.

• The CPM uses a graphic presentation of the planned sequence of activities of a project.



3

CPM Network

• Diagrammatically illustrates all interdependencies of the project’s activities.

• Used as a basis for:– Scheduling the total project time– Establishing priorities.



4

CPM Network

• Can be used for integrating:– Time– Cost– Available resources

• Establishes a critical path for efficient use of resources

• Determine how much time each of the project activities may be delayed without affecting the completion time of the project as determined in objective number one.



5

CPM Network Drawing Schemes

• Arrow Diagramming

(Activity-On-Arrow, AOA).• Node Diagramming

(Activity-On-Node, AON)



6

Activity-On-Arrow Method

• Arrows:– Original Network Scheduling Technique– Uses a 2 nodes scheme– Diagram easily time scaled.

• Nodes:– Commonly called events– Mark points in time– Represent the beginning or end of the time

available for a given activity.• Links:

– Represent activities



7


• Dummy Activities:– Dummy Activity is a fictitious activity that has

no time duration and requires no resource utilization.

– Dummy activities used to develop correct representation.

– Always break up a dummy activity at the tail, not at the head of the arrow.



8


– Remove redundant dummy activities– Use unique numbering system for events.– Allow for addition of future activities– Try to number events such that the “i” node is

less than the “j” node.



9

Drawing AOA Networks

• Prerequisites:– List of all activities comprising the project– Order of precedence of each activity– Duration estimate of each activity



10

Drawing AOA Networks

• Basic Rules of Network Logic1. Before an activity may begin, all activities

preceding it must be completed. (Activities with no predecessors are self-actuating when the project begins.)

2. Arrows imply logical precedence only. Neither the length of the arrow not its “compass” direction on the drawing have any significance.



11

Example:

Activity Depends on

(Immediate Predecessor(s)) Duration (Day)

(Time to perform) a ─ 14 b ─ 3 c ─ 7 d a, b 4 e b, c 10



12

Bar Chart

a b c d e

14

3

18

17

7



13

a

b

c

d

e

Dummy

Activity on arrow



14

Common Errors in AOA

• Dangling (AOA only).• Looping.• Redundancy (AOA only)• Unique Activity Designation• Possible of showing Improper Logic



15

Dangling

6 7

9

10

8

11

12

13

(8) and (9) are left dangling as they are not the last activities.



16

Looping

a

f g

i

e h

b d

c

Looping error results when an endless loop is shown in the diagram and you can not progress beyond it.



17

Redundancy

2 3

4

Dummy

Dummy 2-4 is unnecessary as it is not needed for network analysis.



18

Unique Activity Designation

10 15

11

10 15

a)

b)



19

Possible of showing improper Logic

15 30

20 a)

10 25

Activity A Place Concrete Slab in garage

Activity C Install prefinished

shop cabinets

Activity B Install garage

door

Activity D Install garage

opener

15 30

20 b)

10 25

20



shop cabinets


door


opener

In a) Activity D depends on A and B

In b) Activity D depends on B only.



20


15 30

20 a)

10 25



shop cabinets


door


opener

15 30

20 b)

10 25

20



shop cabinets


door


opener

In a) Activity D depends on A and B

In b) Activity D depends on B only.



21

15 45

25 a)

10 40

Activity A Install Wallboard Activity D

Paint Wall

Activity B Install vinyl

flooring Activity E

Install base trim 30

20 50

Activity C Install Carpet

Activity F Install floor registers 35

In a) Activity F depends on A, B, and C.

15 45

25 b)

10 40


Paint Wall


flooring Activity E


20 50


Activity F Install floor registers

35

30

In b) Activity F depends only on B and C.




22

15 45

25 a)

10 40


Paint Wall


flooring Activity E


20 50


Activity F Install floor registers 35

In a) Activity F depends on A, B, and C.

15 45

25 b)

10 40


Paint Wall


flooring Activity E


20 50


Activity F Install floor registers

35

30

In b) Activity F depends only on B and C.




23

Disadvantages of Arrow Notation

• We may need to use “dummy activities”• Project Management is done on activity

basis• Does not give all details of the activity on

network diagram• Arrow would be very long, and don’t

relate to time. The network is not time scaled



24

Disadvantages of Arrow Notation

3

A 6

B

C 2

9

5

Dangling possible if B dos not have successors, B dangles.



25

Class work#1:

Activity Depends upon Activity Depends upon A G F B A I F F A J H H A K I, J, F C B, A L G, D, E D B M K E C N L, M



26

Class work#1:

A

B

F

H

C

D

E

G

I

J K

L

M

N

spring 2008, king saud university arrow diagramming dr. khalid al-gahtani 1 network schedule...

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