there . Cross × ( ) all other zeros in its row. Continue this until all the columns have been examined. Step : If each row and each column contains exactly one assignment, then the solution is optimal.
Hungarian method provides optimum assignment schedule in an assignment problem. Example . Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the machines I, II, III and IV.
machines I II III IV jobs XII Std - Business Maths & Stat EM Chapter - - Operations Research 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.
I II III IV Look for atleast one zero in each row and each column.Otherwise go to step . Step : Select the smallest element in each column and subtract this from all the elements in its column. I II III IV Since each row and column contains atleast one zero, assignments can be made. Step (Assignment): Examine the rows with exactly one zero.
First three rows contain more than one zero. Go to row D . There is exactly one zero. Mark that zero by (i.e) job D is assigned to machine I.
Mark other zeros in its column by × . I II III IV Step : Now examine the columns with exactly one zero. Already there is an assignment in column I. Go to the column II.
There is exactly one zero. Mark that zero by . Mark other zeros in its row by × . I II III IV Column III contains more than one zero.
Therefore proceed to Column IV, there is exactly one zero. Mark that zero by . Mark other zeros in its row by × . I II III IV Step : Again examine the rows.
Row B contains exactly one zero. Mark that zero by I II III IV Thus all