Note: Important point to remember for VAM - Case of Tie
If the "smallest cost" in a row or column are repeating, then difference for that row or column is "0".
In VAM, we have to select the row or column which is having higher difference
- But if there is a tie in selection, then we have to select the row or column which contains minimum cost.
- In case there's a tie in minimum cost too, select the cell in which maximum allocation can be done.
The given problem is already balanced.
→ Select row/column with highest difference. In the same row/column, select the cell with minimum cost, then allocate smallest value of demand or supply in that cell.
→ Here, we have  as the highest difference. Selecting column with  as column difference and finding cell with minimum cost.
→ As we can see here "1" in the second row is the minimum cost in this last column with highest difference of .
→ So, allocating 10 to "1"(min. cost) with highest column difference.
→ Remove the row/column whose supply or demand is fulfilled and prepare new matrix as shown below.
→ Check that here, we have multiple highest difference as "".
→ [Tie] We have to select the row/column which has minimum cost included. (check note above for this step).
→ So, selecting first column with highest column difference as  and minimum cost as "1" and allocating same as we have done in third step above.
→ Repeat the procedure until all allocations are done.
→ You may get [Tie] again in this and further steps. Just repeat step 4 & 3 as above shown to get the answer.
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