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:

51	84	86	74
11	86	61	31
26	25	70	23
42	19	71	69

Subtract row minima

We subtract the row minimum from each row:

0	33	35	23	(-51)
0	75	50	20	(-11)
3	2	47	0	(-23)
23	0	52	50	(-19)

Subtract column minima

We subtract the column minimum from each column:

0	33	0	23
0	75	15	20
3	2	12	0
23	0	17	50
		(-35)

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

0	33	0	23	x
0	75	15	20	x
3	2	12	0	x
23	0	17	50	x

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

0	33	0	23
0	75	15	20
3	2	12	0
23	0	17	50

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

51	84	86	74
11	86	61	31
26	25	70	23
42	19	71	69

The optimal value equals 139.