Scarf's Procedure for Integer Programming and a Dual Simplex Algorithm

Scarf has recently introduced an algorithm for integer programs based on the combinatorial concept of primitive set. We show that as the decision variables of the integer program become continuous and the integer program reduces to a linear program, the Scarf algorithm converges to a dual simplex algorithm for the limit linear programming problem. This result is robust in the sense that even before the limit is reached, the dual simplex path is contained in the path of primitive sets generated by the Scarf algorithm.