Row family inequalities for the set covering polyhedron

From the polyhedral point of view the set covering polyhedron (SCP) and the set packing polyhedron (SPP) associated with clutter matrices (i.e. 0, 1 matrix without dominating rows and zero columns) have strong similarities. Thus, many key concepts have been transferred from SPP to SCP by Balas and Ng (1989), Cornuéjols and Sassano (1989), Nobili and Sassano (1989) and Sassano (1989). s work, we present a new class of valid inequalities for the SCP associated with general clutter matrices, called row family inequalities, that can be viewed as the counterpart of the valid clique family inequalities introduced by Oriolo (2004) for SPP. w that many valid inequalities for SCP belong to this class. In particular, all the inequalities with coefficients in { 0 , 1 , 2 } studied by Balas and Ng (1986).