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Example 

Three workers to do Three task at the same time. Apply the Hungarian algorithm the cost matrix is,

Solution:

STEP 1: 

Identify minimum in each row (show in ‘green’)

Substract row mins from each element in their respective rows:

Identify minimum in each column (show in ‘green’).

Substract column mins from each element from their respective columns:

This is reduced cost matrix.

STEP 2: 

Find the minimum no of horizontal and vertical lines to cover all 0’s:

Since < 3 lines suffice, continue to step2.

Identify min of uncovered elements: uncovered min = 50

Substract min of uncovered matrix elements from the uncovered rows:

Add the min of the uncovered matrix elements to the covered columns:

STEP 3:

Find the minimum number of horizontal and vertical lines to cover all 0’s:

Since it takes 3 linkes to cover all zero’s, STOP: an assignment is possible.

Construct a valid assignment of row to column labels using only matrix zeros:

1. Worker_1 can only be assigned to task_A.
2. Worker_3 can only be assigned to task_C.
3. Worker_2 can only be assigned to task_B.