The NW corner rule described earlier considers only the availability and supply requirements in making assignments. It takes no account of the shipping costs given in the tableau. It is therefore not a sound methods as it ignores the very factor (cost ) which is sought to be minimized. The least cost methods and the Vogel Approximation methods consider the transportation costs while making allocations.
As the name suggests of all the routs ( that is combination of sources and destination) select the one where transportation cost is the least. Now consider the supply available at the corresponding source and demand at the corresponding destination and put the lower of the two as the quantity to be transported through that route. After this delete the source destination whichever is satisfied. Consider the remaining routes and again choose the one with the smallest cost and make assignments. Continue in this manner until all the unit are assigned.