Operations Research: North-West Corner Method

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For the transportation problem given by the following tableau, find an initial basic feasible solution by the North-West corner method and then find an optimal solution.

North West Method:

We need to start off with a feasible (but not necessarily optimal) solution. One simple way is to use the Northwest (NW) Corner method. Start at the top left (NW) corner, and ship the maximum number of units possible along that route. In our example, that would be 15 units. This eliminates the first column and we need to change the first supply to 20-15=5. Now the block with 10, we can only provide a maximum of 5 units, since there is only 5 left in column 1. Thus, there is only 20 units left in row 2. Find the top left cell of the remaining cells and do the same. Continue doing this until you get to the bottom right cell. You should now have all the demands met exactly, and all the supplies used up completely. The top row should contain 15, and two blank cell, a second row should be 5, 19, and 1, and the third row should be two blank cells, and a 15.
Therefore, the initial basic feasible solution is = ...