Note: The Northwest corner rule revisited

Authors:
Bettina Klinz;Gerhard J. Woeginger
Affiliations:
Institut für Optimierung und diskrete Mathematik, TU Graz, Steyrergasse 30, 8010 Graz, Austria;Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600 MB Eindhoven, Netherlands
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

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.