Question 1

Can the assignment problem handle maximization?

Accepted Answer

Yes. To maximize, negate all costs (or subtract each entry from the matrix maximum) and then solve the resulting minimization problem. The optimal assignment is the same; only the sign of the objective changes.

Question 2

What if the number of workers and jobs is not equal?

Accepted Answer

The algorithm pads the smaller dimension with dummy rows or columns having zero cost. After solving, assignments to dummy entries indicate unassigned workers or jobs. This makes the method applicable to any rectangular cost matrix.