Pert cpm

Net work Analysis

CPM/PERT

Project “A project is a series of activities

directed to accomplishment of a desired objective.”

Plan your work first…..then work your plan

“Project can be splitted into small tasks with sequence of the their execution. This process is known as work break down structure “

Work break down structure

Network analysisNetwork analysis is the general name given to certain specific techniques which can be used for the planning, management and control of projects.

Main objectives are:

1. Complete the project within stipulated period..

2. Optimize resources utilization.

3. Better coordination in interdependent activities

C.P.M & P.E.R.T are two methodologies to analyze the network

PERT - Project Evaluation & Review Techniques

Definition: In PERT activities are shown as a network of

precedence relationships in which successive events are joined by arrows. – Probabilistic activity times– Optimistic time, pessimistic time, most likely time.– Event oriented diagram

USED IN : Project management - for non-repetitive jobs (research and development work), where the time and cost estimates tend to be quite uncertain. This technique uses probabilistic time estimates.

CPM - Critical Path Method

Definition: CPM activities are shown as a network of precedence relationships in which successive activities are represented by arrows. .also called PPS– Single estimate of activity time– Deterministic activity times– Activity oriented diagram

USED IN : Production management - for the jobs of repetitive in nature where the activity time estimates can be predicted with considerable certainty due to the existence of past experience.

Use of nodes and arrows

Arrows An arrow leads from tail to head directionally– Indicate ACTIVITY, a time or resource consuming effort

that is required to perform a part of the work.– Direction of the progress of the project

Nodes A node is represented by a circle- Indicate EVENT, a point in time where one or more

activities start and/or finish.- Some part of the project has been complete- Merge events, brust events.

Terminologies used in C.P.M

Terminologies used in C.P.M

Relation ship between Events: 1. Successor Events 2. Predecessor Events

Activity: 1. Successor Activity 2. Predecessor Activity 3. Dummy Activity 4. Concurrent Activity

Activity on Node & Activity on Arrow

Activity on Node

- A completion of an activity is represented by a node

Activity on Arrow

- An arrow represents a task, while a node is the completion of a task

- Arrows represent order of events

Rules to draw the network

1. Each event is presented by the nodes & activity by an arrow

2. The starting event should be represented by i3. The completion of project should be assigned

highest number in the network 4. The activities emerging from event i should have no

predecessor activities & event having highest number in diagram should have no successor activity

5. The activity must have highest number for its head (arrow) than its tail

6. Network diagram cannot have more than one starting node or end node

Rules to draw the network

7. 7. There should not be a loop in diagram8. 8. An event cannot occur or an activity cannot start unless all

its preceding activities have been completed (not applicable on dummy activity )

Fulkerson’s Rule

The starting event(having no predecessor activity is numbered as 1 ) other events are numbered in

increasing order from 1 to rightwards , if there are more then 1 initial event found in a diagram , anywhere they are to be numbered fro top to bottom in increase order no two events can have the same number in any case

Question 1

Activity Predecessor A ---

B AC BD C,EE B

F C,EG FH GI H,DJ I

Draw the network diagram

Question 2

A project consist of 7 activities .Activities P,Q,R run simultaneously . The relationship among the various activities is as follow

Activity successor P S

Q TR U

Activity V is the immediate successor to S, T, & U Draw the network diagram

Question 3

Activity Predecessor A ---

B ---C AD CE A

F EG BH GI C,EJ FK D,G,J

Draw the network diagram

Estimation activity time

Most optimistic completion time Most pessimistic completion time Most likely completion time te = a+4m+b

6

Where, a = Most optimistic completion time b = Most pessimistic completion time m = Most likely completion time

Q: Draw the network, labeling activities

Job Activity Immediate Optimistic time Most likely Pessimistic time Predecessor a m

b

A - 5 6 7 B - 2 5 8 C A 6 7 14 D B 1 2 3 E C, D 3 3

3 F B 6 8

10 G E 1 4 7 H F, G 4 5

6

Question 4

Activity Slack

- Earliest starting time (EST) , which is a calendar time when a event can occur when all the predecessor events completed at the earliest possible times

- Earliest finish time (EFT)-

* Preceding from start to finish

Activity Slack

- Latest starting time (LST): The latest time by which an activity is started with out delaying the total project completion.

- Latest finish time (LFT):

* Start working from finish to start

Determination of critical path

Critical Path: Critical path is the series of connecting activities

from starting to end for which the total time of completion of all activities is maximum

Critical activities /Bottle neck : All activities come in the way of critical path are

called critical activities Non Critical activities : All activities do not come in the

way of critical path are called non critical activities

Float/ Slacks

Slack is the amount of time an event can be delayed without delaying the project completion

Positive slack Negative slack Zero slack

Slack = LST – EST LFT – EFT

Question 4

Activities Predecessor activities Activity Time L ---- 3

M ---- 4N L 9O L 3P O 3Q N,M 6R N,M 4S R 2T R 5U P,Q,S 6

Draw the network diagram Calculate EST,EFT,LST,LFT ,activity slack & high light the critical path

Crash Time

Crash time = Crashed Cost – Normal Cost Normal Time – Crashed Time

Question 5Normal CrashNodes Time Cost Time Cost

1-2 3 300 2 400 2-3 3 30 3 30

2-4 7 420 5 5802-5 9 720 7 8103-5 5 250 4 300

4-5 0 0 0 0

5-6 6 320 4 4106-7 4 400 3 4706-8 13 780 10 9007-8 10 1000 9 1200

Project indirect cost is 50Rs. Per week. Draw the network diagram &

identify the critical path ? What are the normal project duration and

associated Cost ? Find total float associated with each activityCrash the relevant activities systemically and determine the

optimalproject completion and cost

Question 6 On May 1,Arnie Watson sent a memo to his boss,

the director of the project (6) management. Stating that the MX project would require 13 weeks for the completion. Arnie realized that customer wanted the job completed in less time, after discussions with the functional managers,Arnie developed the table shown.

According to the contract there is a penalty payment of $5,000 per week for every week over six. What is the minimum amount of additional funding that arnie should request.

Normal Crash

Job Activity Predecessor Time Cost ($.) Time Cost ($.)

Activity A - 3 6,000 2

8,000 B A 5 12,000 4

13,500 C A 5 16,000 3

22,000 D A 4 8,000 2

10,000 E C,D 2 6,000 1

7,500 F B,E 3 14,000 1

20,000

Benefits of CPM/PERT

Interdependencies of activity Project completion time Impact of late start Impact of early start “what if “ exercise Evaluation of performance

Questions Answered by CPM & PERT

Completion date? On Schedule? Within Budget? Critical Activities? How can the project be finished early at the

least cost?

Limitations to CPM/PERT

Clearly defined, independent and stable activities

Specified precedence relationships Over emphasis on critical paths

Thank you