# Northwest-corner solution

**DOI:**https://doi.org/10.1007/1-4020-0611-X_690

A procedure for finding a basic feasible solution to a transportation problem. For a problem with *m* origins and *n* destinations, the approach is to form an array with *m* rows and *n* columns, where a cell (*i*, *j*) of the array represents the shipment of goods from origin *i* to destination *j*. The algorithm starts with all shipments zero and first assigns the maxi-mum shipment possible to the most northwest cell (*i* = 1, *j* = 1). Each time an allocation is made, either a row or column of the array is crossed out. The algorithm continues to make the maximum possible shipments in the northwest corners of the reduced arrays, until the shipment is made in cell *i* = *m* and *j* = *n*. The resulting shipments form a basic feasible solution to the underlying linear-programming problem. A degeneracy avoiding procedure may have to be used in determining whether a row or column is to be crossed out in the intermediate steps.