Geodesic
The determination of necessary and sufficient conditions for the existence of a solution to the $3\times3\times3$ multi-index problem
Applications of Mathematics, Tome 24 (1979) no. 3, pp. 201-208.

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Modifications to a procedure for determining necessary and sufficient conditions for the existence of a solution to the multi-index problem are described. These modifications reduce the computation required to such an extent that necessary and sufficient conditions for the existence of a solution to the 3x3x3 multi-index problem can now be determined. These conditions are given in this paper.
DOI : 10.21136/AM.1979.103797
Classification : 90C05, 90C08
Keywords: necessary and sufficient conditions; existence of a solution; 3x3x3 multi-index problem; existence conditions; existence of feasible solutions; convex polyhedron; multi-index-problems; surrogate linear program 
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Smith, Graham; Dawson, Jeremy. The determination of necessary and sufficient conditions for the existence of a solution to the $3\times3\times3$ multi-index problem. Applications of Mathematics, Tome 24 (1979) no. 3, pp. 201-208. doi : 10.21136/AM.1979.103797. http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103797/

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