  Round robin tournaments are omnipresent in sport competitions and beyond. We
propose two new integer programming formulations for scheduling a round robin
tournament, one of which we call the matching formulation. We analytically
compare their linear relaxations with the linear relaxation of a well-known
traditional formulation. We find that the matching formulation is stronger than
the other formulations, while its LP relaxation is still being solvable in
polynomial time. In addition, we provide an exponentially sized class of valid
inequalities for the matching formulation. Complementing our theoretical
assessment of the strength of the different formulations, we also
experimentally show that the matching formulation is superior on a broad set of
instances. Finally, we describe a branch-and-price algorithm for finding round
robin tournaments that is based on the matching formulation.
