The Northwest corner rule revisited

Under which conditions can one permute the rows and columns in an instance of the transportation problem, such that the Northwest corner rule solves the resulting permuted instance to optimality? And under which conditions will the Northwest corner rule find the optimal solution for every possible permutation of the instance? We show that the first question touches the area of NP-completeness, and we answer the second question by a simple characterization of such instances. (C) 2011 Published by Elsevier B.V.