This document outlines the steps to solve an assignment problem using the Hungarian algorithm. It presents an example with 4 jobs (A, B, C, D) and 4 workers (1, 2, 3, 4). The costs of assigning each worker to each job are given in a table. The steps then show subtracting rows and columns to arrive at a solution with all zeros except the optimal assignment. The optimal assignment pairs worker 1 with job A, worker 2 with job C, worker 3 with job B and worker 4 with job D, with a total cost of 22. The document provides an example of applying the Hungarian algorithm to solve an assignment problem by iteratively subtracting rows and columns until an optimal solution is reached.

1. -
–
-

2. assignment problem


3. assignment problem


4. 
1
A
2
B
4
C
B
C
1
3
A
50
36
16
2
28
30
18
3
35
32
20
4
25
25
14

5. 
D
1
A
2
B
C
4
D
B
C
D
1
3
A
50
36
16
0
2
28
30
18
0
3
35
32
20
0
4
25
25
14
0

6. 
A
B
C
D
1
50 -0
36 -0
16-0
0 -0
2
28 -0
30 -0
18-0
0 -0
3
35 -0
32 -0
20-0
0 -0
4
25 -0
25 -0
14 -0
0 -0

7. 
A
B
C
D
1
50 -25
36-25
16 -14
0-0
2
28 -25
30-25
18 -14
0-0
3
35 -25
32-25
20 -14
0-0
4
25 -25
25-25
14 -14
0-0

8. 
A
B
C
D
1
25
11
2
0
2
3
5
4
0
3
10
7
6
0
4
0
0
0
0

9. 
A
B
C
D
1
25
11
2
0
2
3
5
4
0
3
10
7
6
0
4
0
0
0
0

10. 
A
B
C
D
1
25
11
2
0
2
3
5
4
0
3
10
7
6
0
4
0
0
0
0

11. 
A
B
C
D
1
25-2
11-2
2-2
0
2
3-2
5-2
4-2
0
3
10-2
7-2
6-2
0
4
0
0
0
0+2

12. 
A
B
C
D
1
23
9
0
0
2
1
3
2
0
3
8
5
4
0
4
0
0
0
2

13. 
A
B
C
D
1
23
9
0
0
2
1
3
2
0
3
8
5
4
0
4
0
0
0
2

14. 
A
B
C
D
1
23 -1
9 -1
0
0
2
1 -1
3 -1
2
0
3
8 -1
5 -1
4
0
4
0
0
0 +1
2 +1

15. 
A
B
C
D
1
22
8
0
0
2
0
2
2
0
3
7
4
4
0
4
0
0
1
3

16. 
C&D
A&D
D
A&B
D
C
A
B

17. 

18. 


19. The End
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