For problems associated with finding of solutions, it is important that a feasible solution be found that is useful for every sum in regards to this transportation problem.

There are 3 methods that are to be followed while finding out the initial feasible solution. This include:

• Vogel’s approximation method
• North west corner method
• Least cost method

With these methods followed in a particular manner, this whole process of getting correct solution is eased to a great extent.

Vogel’s approximation method:

In this case,difference associated with each row and columnar unit of a matrix is taken into consideration. This arithmetic difference is found as a difference of the smallest with the next to the smallest element that is present in that particular column or row. Thus, with this, the minimum amount can be seen.

North west corner method:

In this method, there are multiple steps that are to be followed. Once these steps are successfully completed an ideal solution can be found.

Initially, the top left-hand corner is to be taken into consideration, where the maximum feasible amount that is there is placed. Now as per supply, cell has to be moved either in the right direction or downward and solution can be obtained.

Give in this case,unit cost of transportation is not taken, so solution may not be optimal. But as an initial solution, this acts as a base for improvement.

Least cost method:

In this case, as well, certain steps are to be followed to get the minimal feasible solution. Here a transportation table is given from where the least cost has to be determined.  Allocation of the maximum feasible quantity is to be made in regards to that column which already has the least cost associated with it. Finally, after removing that row which has the allocation costs, the first 2 points are to be repeated.

Thus, with the help of these methods, an ideal feasible solution can be found in the best possible manner.  