the four assignments have been made. The optimal assignment schedule and total cost is Job Machine cost II III IV I Total cost XII Std - Business Maths & Stat EM Chapter - - The optimal assignment (minimum) cost = ` Example . Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows.
Determine the optimum assignment schedule. Person Job E Here the number of rows and columns are equal. ∴ The given assignment problem is balanced. Now let us find the solution.
Step : Select a smallest element in each row and subtract this from all the elements in its row. The cost matrix of the given assignment problem is Person Job E Column contains no zero. Go to Step . Step : Select the smallest element in each column and subtract this from all the elements in its column.
Person Job E Since each row and column contains atleast one zero, assignments can be made. Step (Assignment): Examine the rows with exactly one zero. Row B contains exactly one zero. Mark that zero by (i.e) PersonB is assigned to Job .
Mark other zeros in its column by × . Person Job E Now, Row C contains exactly one zero. Mark that zero by . Mark other zeros in its column by × .
Person Job E XII Std - Business Maths & Stat EM Chapter - - Operations Research Now, Row D contains exactly one zero. Mark that zero by . Mark other zeros in its column by × . Person Job E Row E contains more than one zero, now proceed column wise.
In column , there is an assignment. Go to column . There is exactly one zero. Mark that zero by .
Mark other zeros in its row by × . Person Job E There is an assignment in Column and column . Go to Column . There is exactly one zero.
Mark that zero by . Mark other zeros in its row by × .