1. G.N.Khalsa College
BMM/BMS Department
A Project Report on
Operations Research
{Assignment Problem}
Group # 07
Under Prof Guide- Nimalan
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2. “
The essence of mathematics is not to make simple things complicated, but t
”
~Albert Einstein
ACKNOWLEDGEMENT
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3. It was an immensely pleasurable experience in
working on this project on the topic of,
“Assignment Problem ”
However, our efforts alone could not have been
sufficient for completion of this project.
Invaluable advice & suggestion from large
number of people have gone into this project.
The foremost among them in our guide and our
Prof in charge BMS/BMM Nimalan,
Guru Nanak Khalsa College (GNKC),
whose constant corrective guidance &
motivation enabled a focused effort towards
completion of the project. We are also very
grateful to our parents for being extremely
supportive.
Group Members
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5. Bird’s Eye View
Sr. # Topic Pg. #
1. Assignment Problem – Theory 5-6
2. Introduction 7
3. Hungarian Method 8
4. Minimization Case study 9-10
Example # 01
5 Example # 02 11-13
6. Alternate Solution Case study 14-16
Example # 03
ASSIGNMENT PROBLEMS
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6. What is an Assignment Problem?
• The assignment problem can be stated as a problem where
different jobs are to be assigned to different machines on the
basis of the cost of doing these jobs. The objective is to minimize
the total cost of doing all the jobs on different machines.
• The peculiarity of the assignment problem is only one job can be
assigned to one Machine i.e., it should be a one-to-one
assignment
• The cost data is given as a matrix where rows correspond to jobs
and columns to machines and there are as many rows as the
number of columns i.e. the number of jobs and number of
Machines should be equal
• This can be compared to demand equals supply condition in a
balanced transportation problem. In the optimal solution there
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7. should be only one assignment in each row and columns of the
given assignment table. one can observe various situations
where assignment problem can exist e.g., assignment of workers
to jobs like assigning clerks to different counters in a bank or
sales man to different areas for sales, different contracts to
bidders.
• Assignment becomes a problem because each job requires
different skills and the capacity or efficiency of each person with
respect to these jobs can be different. This gives rise to cost
differences. If each person is able to do all jobs equally efficiently
then all costs will be the same and each job can be assigned to
any person.
• When assignment is a problem it becomes a typical optimization
problem it can therefore be compared to a transportation
problem. The cost elements are given and are a square matrix
and requirement at each destination is one and availability at
each origin is also one.
INTRODUCTION
The assignment problem is one of the fundamental combinatorial
optimization problems in the branch of optimization or operations
research in mathematics. It consists of finding a maximum weight
matching in a weighted bipartite graph.
In its most general form, the problem is as follows:
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