AOA and AON NETWORKS

In order to make project planning and control more effectively, various network techniques have been developed. Such as PERT(project evaluation and review technique) CPM (Critical Path Method) MAP(Manpower Allocation Procedure) LCS ( Least Cost Schedule) PCS (Project Control System) etc. Among these techniques, CPM and PERT are two important planning, scheduling and controlling network techniques.

Network Techniques

In order to make project planning and control more

effectively, various network techniques have been

developed Such as

1 PERT(project evaluation and review technique)

2 CPM (Critical Path Method)

3 MAP(Manpower Allocation Procedure)

4 LCS ( Least Cost Schedule)

5 PCS (Project Control System) etc.

Among these techniques, CPM and PERT are two important planning, scheduling and controlling network techniques.

BASIC SHCEDULING

WITH A-O-A and A-O-N

NETWORKS

The concept of the basic scheduling with

the time estimate of the project network or duration of project

ACTIVITY

Between the two nodes lies an arrow that represents the activity.

A-O-A: (Activity on Arrow)

Network drawing technique the start and end of each node or event is connected to an arrow.

A-O-N: (activity on Node)

Activity On Node (AON) is an activity sequencing tool and also known

as Precedence Diagramming Method (PDM) Activity sequence diagrams use boxes or rectangles to represent the activities which are called as nodes The nodes are connected with other nodes by arrows, which shows the dependencies between the connected activities.

Dummy Activity

Sometimes a "dummy task" is added, to represent a dependency between tasks, which does not represent any actual activity.

It is used when ,

(i) Two or more parallel activities in a project have the

same head and tail events

(ii) Two or more activities have some of their

immediate predecessors activities in common.

ACTIVITY DURATIONS

Deterministic (as in CPM)

When previous experience yields accurate estimate of activity duration, eg Construction activity, market survey

Probabilistic (as in pert)

When there is a uncertainity in times,as for instance in R & D activities, new activities being carried out for the first time

TIME ESTIMATES

Deterministic time estimate:

• A single time estimate is used for each activity, this is taken from experts who have prior knowledge and experience of the activity

Probabilistic time estimate:

• Three time estimate(optimistic, most likely, and pessimistic) are commonly used for each activity based on the consensus of the group

3 Merge and Burst Event

When more than one activity comes and joins an event,

When more than one activity leaves an event, such

An activity may be a merge and a burst event at same

Draw The network diagram for the project

Activity Description Duration(week) Immediate

Predecessor

A Obtain the budget approval 2

Project Network Diagramming

Steps to Follow:

1 Draw a project Network

2 Define EST and EFT (Forward Pass)

3 Define LST and LFT (Backward Pass)

4 Determine CPM (Critical Path Method)

5 Define three floats

Example - 1

Compute earliest start and finish times, latest start

and finish times and floats for the following project:

3

3 7

5

STEP – 2 Define EST and EFT (Forward Pass)

5

STEP – 3 Define LST and LFT (Backward Pass)

5

STEP – 4 Determine CPM (Critical Path Method)

5

Activities Duration EST EFT LST LFT TOTAL

LFT-EFT

LST-Duration Duration + EST

2-3 2 3 5 10 8 5 2-4 3 3 6 6 3 0 3-5 3 5 8 13 10 5 4-5 7 6 13 13 6 0 5-6 5 13 18 18 13 0

CRITICAL PATH METHOD

• The sequence of Critical Activities in a network is called CPM.

• The longest path in the network

• Lower bond on the project duration

• Selective control for management of project

Can be determine by:

1 Enumeration of all paths in the network

2 Event based computation(AOA)

3 Activity based computation(AON)

Path Enumeration

Level

0 -Level

1 -Level

2 -Level

3 -Level

4 -Level

5 -Path Enumeration

2 1

Forward Pass

Initialization:

• EI = 0 (or the project start time S)

(This applies to all source nodes)

• Ej = Max ( Ei + tij) for all I before node j

Backward Pass

 Initialization:

Ln (or the latest occurrence of all ending nodes)

o Project duration, T as determined in the forward pass

 Li = Min (Lj – tij) over all successor nodes j of the node i being investigated, (

Float Represent the flexibility in scheduling The concept of float is useful for the management in representing underutilized resources and flexibility of the schedule and the extent to which the resources will be utilized on different activities

Types of Floats

Total Float:

It is the amount of time by which completion of an activity can

be delayed beyond the earliest expected completion time without affecting the overall project duration time.

TF ij = (L j – E i ) – t ij

Free Float

It is the time by which the completion of an activity can be delayed beyond the earliest finish time without affecting the earliest start of a subsequent activity.

FF ij = (E j – E i ) - t ij

Types of Floats

Independent Float

It is the time by which the start of an activity can be delayed without affecting activities, assuming that the preceding activity has finished at its latest finish time

Example – 2

Compute Earliest Start and Finish Times, Latest Start and Finish Times and Floats for the following Project?

Activity 1-2 2-3 2-4 3-5 4-5 4-6 3-6 5-6

Programme Evaluation and Review Technique

The steps involved in PERT analysis are:

1 Development of project network

2 Time estimation

3 Determination of critical path, event slacks, and

activity floats.

4 Calculation of variability of project duration and

the probability of completion in a given time.

1 The project is divided into various activities

2 Draw the network

3 The events are numbered (fulkersons rule)

4 Time estimates for each activity is obtained using the following formula:

t e = (a+4m+b)/6

5 Determine the earliest and latest times for each activity

6 Identify the critical path

7 Compute the variance as follows (Critical Path)

σ = [b – a/b – a/ σ]2

8 Sum all the Variance

9 Compute the probability of completion of the project by a specified completion date using.

Z = Due date – Expected completion date / √Project variance

Steps of PERT

(1) Construct the PERT Network for the project

(2) Determine the critical Path and Expected duration, variance of the project (3) Project duration at 95% probability (z value 1.65)

Thank u