Project

A project is an endeavour to create a unique product or service. Projects are a part of an overall programme are broken down into well defined activities, all of which must be completed within a specified time along with minimum cost.Example: Construction of a bridge, residential complex, mall, highway etc.

Planning, Scheduling and Controlling:Before starting a project, it is necessary to schedule the required activities in an efficient manner so as to complete it on or before a specified time limit at a minimum cost of its completion. Hence, before starting, a project, it is necessary to prepare a plan for scheduling and controlling the various activities. Network Analysis/Scheduling Techniques:Techniques of operations research are used for planning, scheduling and controlling of project. Out of these two techniques are PERT and CPM.

Basic Concepts of Network Analysis:• Activity

All projects may be viewed as being composed of operations or tasks called activities. An activity is depicted by a single arrow (→) on the project network. The activity arrows are called Arcs.

1. Predecessor Activity: An activity that must be completed immediately prior to the start of another activity.

2. Successor Activity: An activity which starts immediately after one or more of other activities are completed.

3. Dummy Activity: Many activities can be performed simultaneously. It is possible that two activities could be drawn by same beginning and end event. In such situations, dummy activity is introduced.

By convention, dummy activities are represented by a dashed arrow on the project network and is inserted in the network to clarify activity pattern in the following situations:

• When two or more activities run exactly in parallel such that they would both start at the same event and finish at the same event, a dummy would be inserted between the end of one of the activities and the common finishing event.

• In some situations, a dummy activity is necessary to fully and accurately represent the logic of a series of activities. For example, if activity C follows activity A and activity D follows both activities A and B, this cannot be represented without the aid of a dummy.

Dummy Activity

• Case II

A C

BD

• (B) EVENT:- An event represents the start or the completion of an activity.

EVENTACTIVITY

MERGE EVENT

BRUST EVENT

Types of Event

• Merge Event: When more than one activity comes and joins, the event is known as merge event.

• Burst Event: When more than one activity leaves an event, the event is known as a burst event.

• Merge and Burst Event: An activity may be a merge and burst event simultaneously as with respect to some activities it can be a merge event and with respect to some other activities it may be burst event.

Common errors in Network Diagramming

• There are three types of errors which are most common in Network:

(a) Dangling: To disconnect an activity before the completion of all activities in a project network diagramming is known as Dangling.

• Dangling

• Looping: Looping is also known as Cycling error in a network diagram. Drawing an endless loop in a network diagram is known as error of looping.

• Looping

• Redundancy: To provide unnecessary the Dummy activity in a network logic is known as the error of redundancy.

• Redundancy:

• Example:Activity Predecessor activity

A None

B None

C A

D A

E B

F C

G D and E

A company has decided to redesign its electronic components. The project involves several activities which are listed in the following table. First, the electronic engineering staff must finish the design of the component. Second, the marketing program for promoting the component must be developed.Third, a new manufacturing process must be designed. Fourth, advertising media must be selected. Fifth, an initial production run must be successfully completed. Sixth, the component must be released to the market.

Activity Name of the Activity

Pre-requisites Estimated time

1-2 A None 3

1-3 B None 5

1-4 C None 4

2-5 D A 2

3-5 E B 3

4-6 F C 9

5-7 G D, E 8

3-6 H B 7

6-7 I H, F 9

Time estimates in Critical Path AnalysisThe basic objective of the time analysis is to get a planned schedule of the project for which the following factors should be known:

(i) Total completion time of the project.(ii) Earliest time when each activity can begin.(iii) Latest time when each activity can be started,

without delaying the total project completion time.(iv) Float for each activity, i.e., amount of time by which

the completion of an activity can be delayed without delaying the total project completion time.

(v) Identification of critical activities and critical path.

TIME ANALYSIS IN CRITICAL PATH METHOD(CONTD….)

• Earliest occurrence time for each event

Step1: the computations begins from start node and move towards the end node. Assume earliest occurrence time for initial event is zero

Step2:(Es)ij=Ei (Ef)ij=Ei+Dij

Ej=max(Ei+Dij)

Ei=Earliest time of event i(Es)ij=earliest starting time

of activity i,j Dij=Duration time of activity

i,j(Ef)ij=Earliest finish time of

activity i,jEj=Earliest time of event j

Forward pass computations (earliest event time):

TIME ANALYSIS IN CRITICAL PATH METHOD (Contd….)

Latest event time indicates the time by which all activities entering into that event must be completed without delaying the total project completion time

Step1:for ending event assume E=L

Step2:(Lf)ij=LjStep3:(Ls)ij=Lj-DijStep4:(Li)=min((Lf)ij-Dij)

(Lj)=Latest time of event j

(Lf)ij= Latest finish time of activity I,j

(Ls)ij= Latest starting time of activity I,j

(Li)= Latest time of event i

Backward pass computation (latest event time):-

SLACK:-

Slack of an event is difference between the latest time and earliest time of an event

Tail slack=Li-Ei (for tail event) Head slack=Lj-Ej (for head event)

Float of an Activity

There are mainly three types of floats as given below:

1. Total Float. This is the most important type of float as it is concerned with overall project-duration. It may be defined as “the amount of time by which completion of an activity could be delayed ”.

Total Float = LSij – ESij

2. Free Float:This is concerned with commencement of subsequent activity. 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.”

Free Float = (Ej - Ei) - tij

3. Independent Float: It is the amount of time by which the start of an activity can be delayed without affecting the earliest start time of any immediately successor activities, assuming that the preceding activity has finished at its latest finish time.

Independent Float = (Ej - Lj) - tij

Critical Path MethodCPM (Critical Path Method), was developed by M.R.Walker. They were concerned with the problem of improving the scheduling techniques or projects. They came up with arrow diagram as the most logical representation of the interrelationship between the jobs in a project to be executed in a well defined sequence.CPM emphasizes the relationship between applying more resources to shorten the duration of given jobs in a project and the increased cost of these additional resources.

Critical Event

The slack of an event is the difference between the latest and earliest event times or

slack (i) = Li –Ei.The events with zero slack time are known as critical events.

Critical Activities

The difference between the latest start time and earliest start time of an activity will indicate the amount of time by which the activity can be delayed without affecting the total project duration. This difference is called as total float. Activities with zero total float are known as critical activities.

Critical Path

The sequence of critical activities in a network is called critical path. The critical path is longest “path in the network from the starting event to ending event and defines the minimum time required to complete the project.”If the activities on critical path are delayed by a day, the project also would be delayed by a day unless the times of the future critical activities are reduced by a day by different means.