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 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 BASIC SHCEDULING WITH A-O-A and A-O-N NETWORKS CONCEPT The concept of the basic scheduling with A-O-A and A-O-N networks is to identify the time estimate of the project network or duration of project DEFINATIONS 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 Types of Activities Predecessor Activity Successor Activity Concurrent Activity Dummy Activity Activity that must be completed immediately prior to the start of another activity are called predecessor activity Activity that cannot be started until one or more of other activities are completed is called successor activities Activities that can be accomplished simultaneously are known as concurrent activities is called concurrent activity 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 Types of Events Event represent the start or the completion of an activity (task) Merge Event Burst Event Merge and Burst Event When more than one activity comes and joins an event, such event is known as merge event When more than one activity leaves an event, such event is known as burst event An activity may be a merge and a burst event at same time, such activity is called merge and burst event Draw The network diagram for the project Activity Description Duration(week) Immediate Predecessor A Obtain the budget approval - B Obtain the Machine A C Hire the Operator A D Install the Machine B E Train the operator C f Produce the goods D,E STEP – Determine CPM (Critical Path Method) E L 6 E E L L E E 13 2 3 E L 10 L L 18 18 13 Activities Duration EST EFT LST LFT TOTAL LFT-EFT LST-Duration Duration + EST 1-2 (3+0)=3 0 2-3 10 2-4 3 6 3-5 13 10 4-5 13 13 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: Enumeration of all paths in the network Event based computation(AOA) Activity based computation(AON) Path Enumeration Level Level Level Level Level Level - Path Enumeration LEVEL -1 LEVEL -2 5 LEVEL -4 6 LEVEL -5 LEVEL -3 Forward Pass Initialization: • EI = (or the project start time S) (This applies to all source nodes) • Ej = Max ( Ei + tij) for all I before node j Backward Pass Floats 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 Free float Independent Float Interfering Float 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 TFij = (Lj – Ei) – tij 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 FFij = (Ej – Ei) - tij 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 IFij = (Ej – Li) – tij Interfering Float It is that part of total float which causes reduction in float of successor activities InFij = TFij - FFij Example – 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 Duration 3 PERT Programme Evaluation and Review Technique The steps involved in PERT analysis are: Development of project network Time estimation Determination of critical path, event slacks, and activity floats Calculation of variability of project duration and the probability of completion in a given time Steps of PERT The project is divided into various activities Draw the network The events are numbered (fulkersons rule) Time estimates for each activity is obtained using the following formula: te = (a+4m+b)/6 Determine the earliest and latest times for each activity Identify the critical path 11.Compute the variance as follows (Critical Path) σ = [b – a/ σ]2 Sum all the Variance 14.Compute the probability of completion of the project by a specified completion date using Z = Due date – Expected completion date / √Project variance Z = T –Te/σT PERT -Example – Activity Days a m b 1-2 1.5 2-3 2-4 3-5 4-5 4-6 5-7 6-7 7-8 7-9 8-10 9-10 (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) T hank u