Solve an assignment problem online

Fill in the cost matrix of an assignment problem and click on 'Solve'. The optimal assignment will be determined and a step by step explanation of the hungarian algorithm will be given.

Fill in the cost matrix (random cost matrix):

Size: 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10

Don't show the steps of the Hungarian algorithm
Maximize the total cost

This is the original cost matrix:

45	38	98	97	26
32	99	22	79	88
53	41	81	93	82
42	81	79	56	40
45	38	38	28	35

Subtract row minima

We subtract the row minimum from each row:

19	12	72	71	0	(-26)
10	77	0	57	66	(-22)
12	0	40	52	41	(-41)
2	41	39	16	0	(-40)
17	10	10	0	7	(-28)

Subtract column minima

We subtract the column minimum from each column:

17	12	72	71	0
8	77	0	57	66
10	0	40	52	41
0	41	39	16	0
15	10	10	0	7
(-2)

Cover all zeros with a minimum number of lines

There are 5 lines required to cover all zeros:

17	12	72	71	0	x
8	77	0	57	66	x
10	0	40	52	41	x
0	41	39	16	0	x
15	10	10	0	7	x

The optimal assignment

Because there are 5 lines required, the zeros cover an optimal assignment:

17	12	72	71	0
8	77	0	57	66
10	0	40	52	41
0	41	39	16	0
15	10	10	0	7

This corresponds to the following optimal assignment in the original cost matrix:

45	38	98	97	26
32	99	22	79	88
53	41	81	93	82
42	81	79	56	40
45	38	38	28	35

The optimal value equals 159.