The Hungarian assignment algorithm is used to solve assignment problems to maximize total profit or minimize total cost. It involves 9 steps: 1) add dummy rows or columns if needed, 2) subtract smallest row elements from each row, 3) subtract smallest column elements from each column, 4) examine rows/columns for single zeros and cross out other zeros, 5) check if number of assigned cells equals rows/columns, 6) draw lines through zeros, 7) check if minimum lines equals rows/columns, 8) revise matrix by subtracting smallest covered element and adding to line intersections, 9) repeat steps 4-8 until optimum solution is found.