A Transportation Problem where the summation of Supply is not equal to summation of Demand is called Unbalanced Transportation Problem.
Here, BFS means Basic Feasible Solution. This is also sometimes referenced as IBFS, meaning Initial Basic Feasible Solution.
This problem can also be solved using Vogel's Approximation Method, North West Corner Method or Least Cost Method. But as mentioned in the problem statement we'll be solving it using Least Cost Method.
In the given problem:
The given problem is not balanced as .
To balance this, a dummy row is added with supply of 30 units in order to balance the problem.
In this step, we'll start by selecting the lowest cost from the entire matrix and allocate the minimum value from Supply or Demand to it.
Note: When selecting the lowest cost we should NOT consider the dummy row that we added to balance the problem.
Now we shall remove the row or column for which the demand or supply has been fulfilled and prepare a new matrix.
Now prepare a new matrix:
Now that we have completed all the allocations as done above, we'll use all the allocations and calculate the transportation cost.
In the problem above we have seen that , so we added a Dummy row 'D1' to balance the problem. Likewise, if then, we should add a Dummy column and then solve the problem.
Later the problem can be solved by any of the following methods: