# Assignment Method

If it's not a square matrix, we make it one by adding dummy rows/columns with entries equal to the highest cost in the matrix.

Then the steps of the Hungarian Algorithm are as follows: Once you're able to stop the algorithm, you choose a set of zeros so that there is just one selected in each row and column, then take out the dummy rows and columns.

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Once we are able to stop like this, we choose a set of zeros in the matrix so that each row and column only has one zero selected. The minimum cost is 421 407 411 = \$1,239, and it happens when you assign job 1 to employee 2, job 2 to employee 3, and job 3 to employee 4.

Looks like employee 1 is out of luck, but at least you know how to assign the jobs in order to minimize your cost.

The selected zeros correspond to the ideal assignment in the original matrix.

Once you get used to the process, the Hungarian Algorithm is a cinch, so keep practicing. We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities.

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