The Direct Solution of the Transportation Problem with Reduced Matrices

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Abstract
A discussion of the importance of a direct method in obtaining all the solutions of a transportation problem, and in obtaining solutions of more general problems, is followed by a discussion of methods of reduced matrices in which the transportation matrix is reduced, by a series of subtractions from rows and columns, to a transformed matrix to which the orthogonality condition is applicable. The direct method proceeds in a series of simple steps to the determination of zero terms having associated xij values which eventually satisfy the row and column equations. Formal and informal versions are presented and application is made to several general problems.

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