Two algorithms to get strong Gomory cuts

The paper investigates two ways to get strong Gomory cuts. In Section 1 it gives an improved version of Nijenhuis’ dynamic programming method to solve the diophantine problem of Frobenius and applies it to determine the rank of a Gomory cut. In Section 2 a new method is given to find a strong cut among the multipliers of a cut. In the last section the paper illustrates on an example how deep the strong cuts can be. The example is that of Schrijver for showing that a cutting plane proof can have an arbitrary great length.