Column generation, combined with an appropriate integer programming technique, has shown to be a powerful tool for solving huge integer programmes arising in various applications. In these column generation approaches, the master problem is often of a set partitioning type.

The integral simplex method for set partitioning problems allows only pivots-on-one to be made, which results in a primal all-integer method. In this technical note we outline how to tailor the column generation principle to this method. Because of the restriction to pivots-on-one, only local...