The reduced matrix method to solve the transportation problem

This paper presents the reduced matrix method to solve the standard transportation problem. It consists of systematic transformation of the original cost matrix by a sequence of operations involving only subtraction and/or addition of positive constants to all the elements of a row or a column until a feasible solution is found by making positive assignments to the zero-containing cells of the transformed matrix. The transformed matrix contains only non-negative elements and is called the reduced matrix. Computing experience on small scale problems indicates that this method is faster than most of the other conventional methods.