This PPT of Assignment problem| Hungarian Method |Example of Assignment Problem

1. Unit-4
Assignment
Problem

2. • Assignment of a job to two different machine of two
different worker is another problem manager has to solve
• In any workshop there are number of workers number of
JOB to be completed by them by all workers are not
equal similarly all machines are not equally suitable for
the various job
• so the manager problem is how to select a best man or a
worker or a job and also the best machine for a job .
• How to assign a job to a man such that the total cost of
production is minimum or the profit is maximum that is
the assignment problem
•

3. BALANCEDASSIGNMENTPROBLEM -
ASSIGNMENTPROBLEMISSAIDTOBE BALANCEIFNUMBEROF
ROWSISEQUALTOTHENUMBEROFCOLUMNOTHERWISEISSAID
TO BEUNBALANCEASSIGNMENTPROBLEM.
Hungarian Method

4. Example
• Solve the following minimal assignment problem
I II III Iv
A 9 27 18 12
B 14 29 5 27
C 39 20 19 16
D 20 27 25 11

5. Row reduction
• Subtract the smallest entry in each row from all the entries of
its row
I II III Iv
A 9 27 18 12
B 14 29 5 27
C 39 20 19 16
D 20 27 25 11

6. I II III Iv
A 0 18 9 3
B 9 24 0 22
C 23 4 3 0
D 9 16 14 0

7. • Subtract the smallest entry in each Column from all the
entries of its column
I II III Iv
A 0 18 9 3
B 9 24 0 22
C 23 4 3 0
D 9 16 14 0

8. I II III Iv
A 0 14 9 3
B 9 20 0 22
C 23 0 3 0
D 9 12 14 0

9. I II III Iv
A 0 14 9 3
B 9 20 0 22
C 23 0 3 0
D 9 12 14 0

10. I II III Iv
A 9 27 18 12
B 14 29 5 27
C 39 20 19 16
D 20 27 25 11
Job Machine Cost
A I 9
B III 5
C II 20
D IV 11
Total Cost 45

11. Example
Solve the following minimal assignment problem
I II III IV
A 10 18 17 15
B 23 12 22 16
C 21 22 24 19
D 12 23 21 17

12. Row reduce
Subtract the smallest entry in each row from all the
entries of its row
I II III IV
A 10 18 17 15
B 23 12 22 16
C 21 22 24 19
D 12 23 21 17

13. I II III IV
A 0 8 7 5
B 11 0 10 4
C 2 3 5 0
D 0 11 9 5
Now ,Subtract the smallest entry in each Column
from all the entries of its column

14. I II III IV
A 0 8 7 5
B 11 0 10 4
C 2 3 5 0
D 0 11 9 5
I II III IV
A 0 8 2 5
B 11 0 5 4
C 2 3 0 0
D 0 11 4 5

15. The smallest uncovered element is 2, so it subtract from uncovered
element and add 2 to the element which are crossed by to lines
I II III IV
A 0 8 2 5
B 11 0 5 4
C 2 5 0 0
D 0 11 4 5

16. I II III IV
A 0 6 0 3
B 13 0 5 4
C 4 3 0 0
D 0 9 2 3

17. Job Machine Cost
A III 17
B II 12
C IV 19
D I 12
Total Cost 60