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7/29/2019 Assignment Problem 2
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HUNGARIAN METHOD
EXCEPTIONAL CASES
7/29/2019 Assignment Problem 2
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MAXIMIZATION
If the problem is of maximization
Hungarian method cannot be applicable
directly.
To apply the method first convert it into
minimization by subtracting all the
elements of the matrix from the largest
element of that matrix
7/29/2019 Assignment Problem 2
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Unbalanced A.P.
Any assignment problem is said to be
unbalanced if the cost matrix is not a square
matrix
i.e. the number of rows and the number ofcolumns are not equal.
To make it balanced we add a dummy row or
dummy column with all the entries as zero.
7/29/2019 Assignment Problem 2
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Practice problem
There are four jobs to
be assigned to the
machines. Only one job
could be assigned toone machine. The
amount of time in hours
required for the jobs in
a machine are given in
the following
matrix.Find an optimum
assignment.
A B C D E
1 4 3 6 2 7
2 10 12 11 14 16
3 4 3 2 1 5
4 8 7 6 9 6
7/29/2019 Assignment Problem 2
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Hungarian method
Since the cost matrix is
unbalanced we add a
dummy job 5 with
corresponding entrieszero.
Job number 5 is a
dummy job
A B C D E
1 4 3 6 2 7
2 10 12 11 14 16
3 4 3 2 1 5
4 8 7 6 9 6
5 0 0 0 0 0
7/29/2019 Assignment Problem 2
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HUNGARIAN METHOD
Step-1
Row minimization
Step-2
Column minimization
No.of lines = 4
No. of rows= 5
Go to next step
L3
2 1 4 0 5
L4 0 2 1 4 6
3 2 1 0 4
L2 2 1 0 3 0
L1 0 0 0 0 0
7/29/2019 Assignment Problem 2
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HUNGARIAN METHOD
STEP-3
Subtracting smallest
element 1 from
uncovered, adding 1 incross elements and
keeping the other
elements same the
modified matrix is No of lines=rows
Assignment is possible.
L5 1 0 3 0 4
L4 0 2 1 5 6
L3 2 1 0 0 3
L2 2 1 0 4 0
L1 0 0 0 1 0
7/29/2019 Assignment Problem 2
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HUNGARIAN METHOD
Different assignments are
1- B 1-B 1 - D
2- A 2- A 2 - A
3- D 3- D 3 - C
4- C 4- E 4 - E
5- E 5- C 5 - B Total minimum time = 20 min
7/29/2019 Assignment Problem 2
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HUNGARIAN METHOD
Five jobs are to beprocessed and fivemachines are available.Any machine can
process any job withthe resulting profit (inrupees) as follows:
What is the maximum
profit that may beexpected if an optimumassignment is made?
A B C D E
1 32 38 40 28 40
2 40 24 28 21 36
3 41 27 33 30 37
4 22 38 41 36 36
5 29 33 40 35 39
7/29/2019 Assignment Problem 2
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Hungarian method
Step1
Since the problem is of
maximization type
subtracting all elementsof the matrix from the
largest element the
modified matrix will
become
9 3 1 13 1
1 17 13 20 5
0 14 8 11 4
19 3 0 5 5
12 8 1 6 2
7/29/2019 Assignment Problem 2
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Hungarian method
Step 2
By row minimization the
matrix becomes 8 0 0 7 0
0 14 12 14 4
0 12 8 6 4
19 1 0 0 5
11 5 0 0 1
7/29/2019 Assignment Problem 2
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Hungarian method
Step-3
By column minimization
No of lines =4
No. of rows = 5
L2
L1 8 0 0 7 0
0 14 12 14 4
0 12 8 6 4
L3 19 1 0 0 8
L4 11 5 0 0 1
7/29/2019 Assignment Problem 2
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Hungarian method
Step-4
Selecting smallest
element 4 from
uncovered elementsand adding the same at
the intersection and
keeping the other
elements same themodified matrix
becomes
L4 L3 L2 L1
L5 12 0 0 7 0
0 10 8 10 0
0 8 4 2 0
23 1 0 0 8
15 5 0 0 1
7/29/2019 Assignment Problem 2
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Hungarian method
Different assignments are
1- B 1- B 1- B 1 - B
2- A 2- E 2- A 2 - E
3- E 3 A 3 - E 3 - A
4- C 4 D 4 D 4 - C
5- D 5 C 5 C 5 D
Total profit = 191 units
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