A head of department has four teachers to be assigned to
four different courses. All of the teachers have taught the courses in the past
and have been evaluated by the students. The rating for each teacher for each
course is given in the table below a perfect score is 100. The head of
department wants to know the optimal assignment of teachers to courses that
will maximise the overall average evaluation.
ABCD185808075275857881383817074481828378Use the Hungarian
algorithm to solve this assignment problem.SUMMARY OF KEY POINTS1 The Hungarian
algorithmStep 1 Find the
opportunity cost matrix.Step 2Test for
an optimal assignment. If an optimal assignment can be made make it ans stop.Step 3 Revise the
opportunity cost matrix and return to step 2.2 Testing for an optimal assignmentIf the minimum number of straight lines (vertical and horizontal)
required to cover all the zeroes in the opportunity cost matrix is equal to
the number of rows and columns in the matrix then an assignment can bemade.3 Revising the
opportunity cost matrixTo revise the opportunity cost matrix(i) Subtract the smallest number not covered by a line from
all numbers not covered by a straight line.(ii) Add this number to every number (including zeros) lying
at the intersection of any two lines.