This document discusses the Hungarian method for solving assignment problems. It explains the steps of the Hungarian method which include subtracting the smallest elements from rows and columns to reduce the matrix, drawing lines to cover zeros, marking squares around uncovered zeros while cancelling others in the same row or column, and subtracting from uncovered elements and adding to intersections if the solution is not optimal. The goal is to obtain an optimal solution where the number of assignments equals the number of rows or columns. Real-life business situations where assignment problems could be applied are also discussed.

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Unit No.2.
DECISION SCIENCE
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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302-DECISION SCIENCE
Unit No.2. Transportation &
Assignment
2.16 Hungarian Method in
Assignment
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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TRANSPORTATION & ASSIGNMENT
 At the End of the Session Student will be able to find-
A. Hungarian Method in Assignment

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Hungarian Method in Assignment
1. In the given n*n matrix, subtract the smallest element in
each row from every element in that row.
2. Subtract then, the smallest element in each column from
every element of that column.
3. Draw minimum number of vertical and horizontal lines
necessary to cover all the zeros in the reduced matrix, by
inspection.
Now,
a. If the number of lines= number of rows/columns, solution
is optimum.
b. If the number of lines is less than the total number of
rows/columns the solution is not optimum and needs
improvement.

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Hungarian Method in Assignment
4. Make the assignment as follows-
i. Check the rows successively. Mark a Square around a single
unmarked zero in a row (if present) and cancel all the other
zeros in its column.
ii. Check the columns successively, Mark a square around a
single unmarked zero in a column (if present) and cancel all
other zeros in its row.
iii. Repeat steps (i) and (ii) above until all the zeros in the
matrix are either marked with square or cancelled out.
Now the squared zeros represent the assignments and if
there is exactly one assignment in each row and column, it
indicates an optimum solution.

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Hungarian Method in Assignment
5. If the solution is not optimum, then
i. Select the smallest element among all the uncovered
elements of the reduced matrix.
ii. Subtract it from all the uncovered elements and add it to
the elements at the intersection of the lines, keeping
other elements unchanged.
Then go to step 3 and repeat the procedure until the number
of assignments is equal to number of rows or columns i.e. the
optimum solution is obtained.

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EXERCISE
 List down the areas whereby knowledge of Assignment
could be used to solve the real life business situations.

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in

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Thank You