We seek methods which produce all the solutions of a transportation problem
and which are applicable to more complex transportation problems. It is argued
that direct methods should be considered. While the purest direct method is not
practical, a modification substitutes some simple techniques for the minimization
condition. With the methods of reduced matrices, we make subtractions from the
rows and columns of the transportation matrix to produce a transformed matrix
with all elements non-negative such that the non-negative integral Xij can be
assigned toX the zero terms so as to satisfy the specifications for origins, i, and
destinations, j.