# Northwest corner rule

This constructs a feasible shipment for the transportation problem, from the cost table ($LaTeX: c_{ij}$ = unit cost from source $LaTeX: i$ to destination $LaTeX: j$), as follows. Start at the NW corner (source 1, destination 1), and allocate the most possible: the min of the supply and demand. If supply exceeds the demand, proceed to the next destination, and continue until all of supply 1 is allocated. Then, go to source 2 and repeat the allocation process, starting with the first (lowest index) destination whose demand has not been fulfilled. If demand exceeds the supply, proceed to the next source, and continue until all of demand 1 is allocated. Then, go to destination 2 and repeat the allocation process. Eventually, all demand must be fulfilled if the problem is feasible (i.e., total supply $LaTeX: \ge$ total demand).