Round robin tournaments and three index assignment

In general scheduling a sports league is a difficult combinatorial optimization problem. We study some variants of round robin tournaments and analyze the relationship with the planar three index assignment problem. The complexity of scheduling a round robin tournaments is settled by a reduction from the planar three index assignment problem. Furthermore, integer programming models are introduced. We pick up a popular idea and decompose the overall problem in order to obtain two subproblems which can be solved sequentially. The latter subproblem can be represented as a planar three index assignment problem which makes corresponding Solution techniques amenable to sports league scheduling.