The Direct Solution of the Transportation Problem with Reduced Matrices

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 x_ij values which eventually satisfy the row and column equations. Formal and informal versions are presented and application is made to several general problems.