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Northwest corner Rule to serve transportation problem

Northwest corner Rule: The idea is to find an initial to find an initial basic feasible solution i.e., a set of allocations that satisfied the row and column totals. This method simply consists of making allocations to each row in turn, apportioning as much as possible to its first cell and proceeding in this manner to its following cells until the row total in exhausted.

The algorithm involved under north-west corner rule consists for the following steps:

1. Before allocation ensure that the total of availability and requirement is equal. If not then make same equal.
2. The first allocation is made in the cell occupying the upper left hand corner of the matrix. The assignment is made in such a way that either the resource availability is exhausted or the demand at the first destination is satisfied.

3. (a) If the resource availability of the row one is exhausted first, we move down the second row and first column to make another allocation which either exhausts the resource availability of row two or satisfies the remaining destination demand of column one. 

(b) If the first allocation completely satisfies the destination demand of column one, we move to column two in row one, and make a second allocation which either exhausts the remaining resource availability of row one or satisfies the destination requirement under column two.

4. The above procedure is repeated until all the row availability and column requirements are satisfied. Consider, for example, the following sample problem. This method does not use transportation costs which we shall bring in later in the other method.
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