What are the three methods of transportation models?

Three Methods of Transportation Models

Transportation models are mathematical tools used to optimize the movement of goods and people. They are used to design and evaluate transportation systems, such as highways, railways, and airports.

There are three main methods of transportation models:

1. The Northwest Corner Method
2. The Least Cost Cell Method
3. Vogel's Approximation Method

The Northwest Corner Method is the simplest of the three methods. It starts by assigning the northwest corner cell of the transportation table to the maximum amount possible. The remaining amount is then assigned to the cell below, and so on. This method is easy to use, but it does not always produce the optimal solution.

The Least Cost Cell Method is more complex than the Northwest Corner Method, but it produces a more optimal solution. It starts by identifying the cell with the lowest transportation cost. The maximum amount possible is then assigned to this cell. The remaining amount is then assigned to the cell with the next lowest transportation cost, and so on.

Vogel's Approximation Method is a heuristic method that is used to find a good initial solution for the transportation problem. It starts by finding the row or column with the largest difference between the highest and lowest transportation costs. The maximum amount possible is then assigned to the cell in this row or column with the lowest transportation cost. The remaining amount is then assigned to the cell with the next lowest transportation cost, and so on.

All three of these methods can be used to find a feasible solution to the transportation problem. However, the Least Cost Cell Method and Vogel's Approximation Method are more likely to produce an optimal solution.

Once a feasible solution has been found, it can be improved using techniques such as the stepping-stone method. The stepping-stone method is a systematic way of finding the optimal solution to the transportation problem. It starts by identifying a cycle of cells that can be used to reduce the total transportation cost. The maximum amount possible is then assigned to the cells in this cycle, and the remaining amount is assigned to the other cells in the transportation table.

The stepping-stone method can be used to find the optimal solution to any transportation problem. However, it can be a time-consuming process, especially for large transportation problems.