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.