## Solve the Following Minimal Assignment Problem : - Mathematics and Statistics

Solve the following minimal assignment problem :

## Solution Show Solution

Step 1 : We introduce a dummy machine M 2  with time zero for each job and replace '-' by ∞

Step 2: Subtracting minimum element of each row from all its elememts

As minimum number of lines = 4 ≠ order of the matrix. . . Optimal solution is not reached. Step 3 : We subtract minimum element (from uncovered elements) from each uncovered element and add to intersection elements.

Minimum number of lines= 5 = order of matrix. :. Optimum solution is reached. Step 4 : Making assignment at single zero of the row and of the column.

. . The optimal assignment of jobs to machines is

M 1 → B       M 2 → D     M 3 → E      M 4 → C     M 5 → A

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## Solve the following minimal assignment problem Jobs Machines I II III M 1 1 4 5 M 2 4 2 7 M 3 7 8 3

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