Transportation Method of Linear programming

Definition: The Transportation Method of linear programming is applied to the problems related to the study of the efficient transportation routes i.e. how efficiently the product from different sources of production is transported to the different destinations, such as the total transportation cost is minimum.

Here origin means the place where the product is originated or manufactured for the ultimate sales while the places where the product is required to be sold is called destination. For solving the transportation problem, the following steps are to be systematically followed:

1. Obtaining the initial feasible solution, which means identifying the solution that satisfies the requirements of demand and supply. There are several methods through which the initial feasible solution can be obtained; these are:
   • North-West Corner
   • Least Cost Method
   • Vogel’s Approximation Method

Note: It is to be ensured that the number of cells occupied should be equal to m+n-1, where “m” is the number of rows while “n” is the number of columns.

2. Testing the optimality of the initial feasible solution. Once the feasible solution is obtained, the next step is to check whether it is optimum or not. There are two methods used for testing the optimality:
   • Stepping-stone Method
   • Modified Distribution Method (MODI)
3. The final step is to revise the solution until the optimum solution is obtained.

The two most common objectives of transportation problem could be: i) maximize the profit of transporting “n” units of product to the destination “y”, ii) Minimize the cost of shipping “n” units of product to the destination “y”.