Vogel’s Approximation Method (VAM) handles situations where supply or demand is exhausted before the entire transportation table is filled by adjusting the problem dynamically. When either supply or demand for a particular row (supply) or column (demand) becomes zero, that row or column is eliminated from further consideration. Here's how it works:

1. Exhausted Supply: If the supply for a row is exhausted before meeting all the demand in a column, the entire row is crossed out, and only the remaining columns are considered for future allocations.

2. Exhausted Demand: Similarly, if the demand for a column is met before all the supply in a row is allocated, the column is crossed out, and only the remaining rows are considered for future allocations.

3. Tied Exhaustion: If both the supply and demand are exhausted simultaneously (i.e., they both reach zero at the same time), either the row or the column can be crossed out, but the other is adjusted to show zero.

The method continues iterating until all the supplies and demands are allocated, ensuring that all constraints are satisfied while aiming to minimize the total transportation cost.