A Summation Constraint Method for Linear Programming

The idea of the summation constraint method consists in summation of the constraints of the original problem to obtain a new problem with one constraint. One basis optimum variable is the solution of this new problem. The index of this variable is the index of the optimal basis variable of the original problem. We exclude the variable with this index from the original problem. Thus dimension of the original problem decreased by one variable and one constraint. Similarly, we can find other optimal basis variables of the original problem. This computational procedure is the non-iteration algorithm of the summation constraint method. A numerical example illustrates the usefulness of the non-iteration algorithm.