NETWORK ANALYSIS

CPM & PERT

IntroductionA network is graphic depiction of ‘activities’ and ‘events’.

By analyzing the network, the planning, scheduling and controlling becomes much easier.

CPM & PERT are most important techniques of network analysis

Generally, these techniques are used to handle very large & complex projects likeConstruction of a residential complexShips & aircraft projectsDevelopment of new drugSatellite developmentImplementation of computer systemDesigning & laying of a manufacturing plant ------& many more

PlanningThis phase involves setting the objectives of the project and the assumptions to be made. Also it involves the listing of tasks or jobs that must be performed to complete a project under consideration. In this phase, men, machines and materials required for the project in addition to the estimates of costs and duration of the various activities of the project are also determined.

Scheduling This consists of laying the activities according to the

precedence order and determining.

The start and finish times for each activity

The critical path on which the activities require special attention

The slack and float for the non-critical paths.

ControllingThis phase is exercised after the planning and scheduling,which involves the following:

Making periodical progress reports

Reviewing the progress

Analyzing the status of the project

Management decisions regarding updating , crashing and resource allocation etc.

CPM & PERTCPM & PERT helps in developing the overall layout of the project with estimate of time and resource required & scheduling of timing and sequencing of various jobs to be performed.

These techniques help the project managers todetermine the expected project completion date,The schedule start and completion time for the different activities of projectThe key activities of the project which must be completed at the scheduled timeThe period by which non-key activities may be delayed without causing a delay in the completion of the whole project

Difference between CPM & PERT PERT CPM

Probabilistic in nature, used in projects, in which the time for different activities as well as whole project is uncertain

Deterministic in nature, used in project scheduling, in which times needed as well as resources required are known with certainty.

Useful in new, non-repetitive and R & D projects

Useful in repetitive and standardized projects

Primary focus on time element and lesser significance to the cost

Primary focus on cost. Considers systematic reduction project duration along with cost savings

The First Step

The initial step in PERT/CPM project scheduling process is determination of all specific activities that comprises the project and their interdependence relationship.

Now, these activities portrayed by a network or an arrow diagram

Arrows and Nodes in a NetworkEach of the activities that make up a project consumes time and resources and has a definable beginning and ending are represented by an arrow.

The circle at the beginning and at the end of the arrow represent the nodes or events of beginning and completion, respectively. The events are points in time and can be considered as milestone of a project.

Whereas an activity is a recognizable part of project, involving mental or physical work and requiring time and resources for its completion; an event connotes an accomplishment occurring at an instantaneous point in time which neither requires any time for itself nor consumes any resources.

1 2

Activity begins Activity ends

A 3 days

Rules for Network Construction1. Each defined activity is represented by one and only one arrow

in the network2. Before an activity can be undertaken, all the activity preceding

it must be completed. The relation between predecessor and successor should be clearly laid.

3. The length of the arrows are of no significance. It is only logical presence of activities.

4. The direction of arrow indicates the general progression in time. The arrow tail represent the point in time at which the event ‘activity start’ occurs and the arrow head represent the point in time at which the ‘activity completion’ event takes place.

5. Events are identifies by numbers.6. The activities are identifies by the numbers of their starting and

ending events. For example A12

7. A network should have only one initial and one terminal node.

Dummy Activity

8. When two or more parallel activities in a project have same head and tail event , dummy activities are needed in constructing the network. The dummy activities do not consume time or resources

A

1 2

B

1

3

2A

B

looping9. Looping is not permitted in a network. If A precedes B, and B precedes

C, then C cannot precedes A.

1

3

2A

B

ExampleActivity Immediate

Predecessor

A ---

B A

C A

D B,C

E C

F D

G E

H F,G

1 2

6

7 8

5

4

3

A

B

D

CG

F

E

H

Time Analysis We shall use the following notation for basic scheduling

computations:

(i, j) = Activity (i, j) with tail event i and head

event j.

Tij = Estimated completion time of activity (i, j)

Esij = Earliest starting time of activity (i, j)

Efij = Earliest finishing time of activity (i, j)

Lsij = Latest starting time of activity (i, j)

Lfij = Latest finishing time of activity (i, j)

Forward Pass ComputationsBefore starting computations, the occurrence time of the initial network event is fixed. The forward pass computation yields the earliest start and earliest finish time for each activity (i, j) and indirectly the earliest occurrence time for each event namely Ei . This consists of the three steps.

ES & EFStep 1 The computations begin from the start node and move

towards the end node. Let zero be the starting time for the project.

Step 2 Earliest starting time (ES)ij = Ei is the earliest possible time when an activity can begin assuming that all of the predecessors are also started at their earliest starting time. Earliest finish time of activity (i, j) is the earliest starting time + the activity time.

(EF)ij = (Es)ij + tij

Step 3 Earliest event time for event j is the maximum of the earliest finish time of all the activities ending at that event.

Ej = Max (Ei + tij)

1

C 8

3 7 8

2

4

5

6

A 2

D3

G 4B 7

H 6

J 5

K 6

[0,7]

[8,14]

[2,5]

[15,21][7,11]

[0,2

]

[0,8]

[17,22]I 2

[13,15]

E 6

F 10[7,17][7

,13]

Forward Pass- ES & EF

Backward Pass ComputationsThe latest event time (L) indicates the time by which all activities entering into that event must be completed without delaying the completion of the project. These can be calculated by reversing the method of calculations used for earliest event time.

LS & LF

Step 1 For ending event assume E=L.

Step 2 Latest finish time for activity (i, j) is the target time for completing the project.

(Lfij) = Lj

Step 3 Latest starting time of the activity (i, j) = latest completion time of (i, j) – the activity time

Lsij = Lfij – tij

= Lj – tij

Step 4 Latest event time for event I is the minimum of the latest start time of all activities originating from the event.

Li = Min (Lj – tij)

1

C 8

3 7 8

2

4

5

6

A 2

D3

G 4B 7

H 6

J 5

K 6

[0,7]

[11,17]

[11,14]

[16,22][12,16]

[9,1

1]

[3,11]

[17,22]I 2

[14,16]

E 6

F 10[7,17][8

,14]

Backward Pass- LS & LF