operatin research

1. Hemant Sharma (Applied Operation Research-MB301)
Can be reached at sharma.hemant@ymail.com
Applied Operations Research – MB301
Handout-1 Critical Path Method-1
Definitions-
1. Project – A project is a temporary endeavor with a defined beginning and end (usually
time constrained, and often constrained by funding or deliverables), undertaken to meet
unique goals and objectives, typically to bring about beneficial change or added value.
Checklist (project definition checklist)
Endeavor
Temporary
Endeavor
Defined
Beginning
Define
d End
Undertake
n to meet
unique
goals and
objectives
Leads to
value
addition
Project
/ Not
Construction
of House (for
its owner)
Yes
(non-repetitive,
a home can be
build only once)
Yes
(Buying of
Plot)
Yes
(White-
wash
and
Floorin
g)
Yes
(To create
a place of
residence)
Yes
(benefit of
shelter)
Project
Preparation of
Maggi
Yes
(a single packet
can be made
only once
Yes
(Starting
to boil the
water)
Yes
(Servin
g it)
Yes
(To satisfy
hunger)
Yes
(hunger
satisfied)
Project
Every project can be sub-divided into smaller parts for various reasons –
Specialization
Planning and Management
Economies of Scale
2. Activity (or a task or a job) – any portion of the project which consumes time or
resources, and has a definable beginning and end
Example- Preparation of Maggi can be divided into many smaller steps/portions
i. Boil water
ii. Break the noodle cakes and put them in boiling water
iii. Add tastemaker, once the noodles are soft
iv. Mix well and wait for it to evenly dissolve
v. Serve hot

2. Hemant Sharma (Applied Operation Research-MB301)
Can be reached at sharma.hemant@ymail.com
Each step has well definable beginning and end, and No Activity can start until all previous
activities in the same chain a re complete i.e. activity (ii) cannot start before activity (i) is
complete.
Types of Activities-
Predecessor Activities – the activities which immediately come before another
activity without any intervening activities
Successor Activities – activities which follow another activity without any
intervening activities
Activities Predecessor Activities
(immediately before)
Successor Activities
(immediately after)
Boil water -
Break the noodle cakes
and put them in boiling
water
Break the noodle cakes
and put them in boiling
water
Boil water
Add tastemaker, once the
noodles are soft
Add tastemaker, once the
noodles are soft
Break the noodle cakes
and put them in boiling
water
Mix well and wait for it to
evenly dissolve
Mix well and wait for it to
evenly dissolve
Add tastemaker, once the
noodles are soft
Serve hot
Serve hot
Mix well and wait for it to
evenly dissolve
-
3. Event- the starting and finishing point of an activity or a group of activities
Types of Events-
Head Event – marks the beginning of the activity
Tail Event – marks the end of the activity
Merge Event – an event which represents the joint completion of more than one
activity
Burst Event- an event which represents the joint starting of more than one activity
4. Dummy Activities- A hypothetical activity which requires zero effort and zero resources
for completion
5. Network – it is a graphical representation of a project, depicting the flow as well as the
sequence of well defined activities and events.

3. Hemant Sharma (Applied Operation Research-MB301)
Can be reached at sharma.hemant@ymail.com
6. Network Path- it consists of a set of activities that connects the networking beginning
event to the network terminal event
7. Critical Path – the longest path through the network is called critical path, it determines
the minimum duration in which the said project can be finished.
Problems to be discussed in class-
1. Draw the network form the following and find the critical path (and project duration)
Activity Duration (days)
1-2 2
1-3 4
1-4 3
2-5 1
3-5 6
4-6 5
5-6 7
2. Draw the network form the following and find the critical path (and project duration)
Activity Duration (days) Activity Duration (days)
1-2 5 5-9 3
1-3 8 6-10 5
2-4 6 7-10 4
2-5 4 8-11 9
2-6 4 9-12 2
3-7 5 10-12 4
3-8 3 11-13 1
4-9 1 12-13 1
3. Draw the network form the following and find the critical path (and project duration)
Activity Immediate Predecessor Duration (Days)
A - 10
B - 9
C A 9
D A 8
E B 7
F B 11
G D,E 5