information:filtering, information:classification
Step 1

For each row, its minimum element is subtracted from every element in that row. This causes all elements to have nonnegative values. Therefore, an assignment with a total penalty of 0 is by definition a minimum assignment.

This also leads to at least one zero in each row. As such, a naive greedy algorithm can attempt to assign all workers a task with a penalty of zero. This is illustrated below.

The zeros above would be the assigned tasks.

Worst-case there are n ! combinations to try, since multiple zeroes can appear in a row if multiple elements are the minimum. So at some point this naive algorithm should be short circuited.