The Northwest Corner Rule is a method used to find an initial feasible solution for transportation problems in operations research. It involves filling the transportation table starting from the top-left corner (the "northwest" corner) of the matrix. The process begins by allocating as much supply as possible to that cell without exceeding the supply available at the source or the demand required at the destination. After making an allocation, the corresponding supply or demand is adjusted, and if either is fully satisfied, the next step moves either down to the next row or across to the next column, depending on which side still has remaining supply or demand.

The Northwest Corner Rule is a method used in the transportation problem to find an initial basic feasible solution. It starts at the top-left (northwest) corner of the transportation tableau, allocating as much as possible to that cell without exceeding the supply or demand constraints. After making an allocation, the algorithm moves either down to the next row or right to the next column, depending on whether the supply or demand has been satisfied, and continues this process until all supplies and demands are met. This rule provides a straightforward and systematic way to generate an initial solution for optimization.

the Northwest Corner Rule is a method for initializing allocations in transportation problems by starting at the top-left cell of the cost matrix and allocating resources until supply or demand is met