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 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
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