Abstract
It is known that the d-dimensional axial transportation (assignment) problem can easily be solved by a greedy algorithm if and only if the underlying cost array fulfills the d-dimensional Monge property. In this paper the following question is solved: Is it possible to find d permutations in such a way that the permuted array becomes a Monge array? Furthermore we give an algorithm which constructs such permutations in the affirmative case. If the cost array has the dimensions n 1× n 2×⋯× n d with n 1⩽ n 2⩽⋯⩽ n d , then the algorithm has time complexity O( d 2 n 2⋯ n d ( n 1+log n d )). By using this algorithm a wider class of d-dimensional axial transportation problems and in particular of the d-dimensional axial assignment problems can be solved efficiently.
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