The dual of a transportation problem is not a transportation problem.

by George Bernard Dantzig

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A proof that the dual of the classical transportation problem-after elimination of the variables unrestricted in sign-cannot by row operations be reduced to transportation format, nor can it be so reduced by augmenting the system with k additional variables and equations. The dual of the transportation problem possesses the unimodular property that every subdeterminant has value 0, 1, or -1. Therefore, extreme point solutions have integer values if the constant terms are integer valued. The question is undetermined whether unimodular systems exist which are more general than those derived from transportation (distribution) problems.

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