Assignment Problem by using Hungarian Method

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 I n 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 . H ow 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. BALANCED ASSIGNMENT PROBLEM - Assignment Problem is said to be balance if number of rows is equal to the number of column otherwise is said to be unbalance assignment problem. 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 18 9 3 B 9 24 22 C 23 4 3 D 9 16 14

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

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

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

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 8 7 5 B 11 10 4 C 2 3 5 D 11 9 5 Now ,Subtract the smallest entry in each Column from all the entries of its column

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

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

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