The correct answer is option 'A' - Hungarian method.

Explanation:
- The transportation problem is a mathematical model that deals with the allocation and transportation of goods from sources to destinations. It involves finding the optimal solution for minimizing the total cost of transportation.
- Several methods have been developed to solve transportation problems, including the Northwest corner method, Least cost method, and Vogels approximation method.
- The Hungarian method, also known as the Kuhn-Munkres algorithm, is not a solution method for transportation problems. It is a combinatorial optimization algorithm used to solve assignment problems, where the goal is to find the best assignment of agents to tasks.
- Here is a brief explanation of the other three solution methods for transportation problems:

1) Northwest corner method:
- This method starts by allocating as much as possible to the cell in the top-left corner of the transportation table.
- Then, it moves horizontally to the next column and allocates the remaining supply to the respective cells until the supply is exhausted.
- After that, it moves vertically to the next row and allocates the remaining demand to the respective cells until the demand is satisfied.
- This process continues until all the demand is satisfied, and the transportation table is completely filled.

2) Least cost method:
- This method selects the cell with the lowest transportation cost and allocates as much as possible to that cell.
- It considers the cost matrix and chooses the cell with the minimum cost, breaking any ties arbitrarily.
- Then, it moves horizontally or vertically to the next cell with the lowest cost until the supply or demand is exhausted.
- This process continues until all the demand is satisfied, and the transportation table is completely filled.

3) Vogels approximation method:
- This method calculates the opportunity cost for each row and column in the cost matrix.
- The opportunity cost is the difference between the two lowest costs in each row or column.
- It selects the row or column with the highest opportunity cost and allocates as much as possible to the cell with the minimum cost in that row or column.
- It then updates the supply and demand and recalculates the opportunity costs.
- This process continues until all the demand is satisfied, and the transportation table is completely filled.

In summary, the Hungarian method is not a solution method for transportation problems, while the Northwest corner method, Least cost method, and Vogels approximation method are commonly used to solve transportation problems.