A branching scheme for minimum cost tournaments with regard to real world constraints

Single round robin tournaments are a well known class of sports leagues schedules. We consider leagues with a set T of n teams where n is even. Costs are associated to each possible match. Moreover, stadium availability, fixed matches, and regions' capacities are taken into account. The goal is to find the minimum cost tournament among those having the minimum number of breaks and being feasible with regard to these additional constraints. A branching scheme is developed where branching is done by fixing a break for a team. Thus, the focus is on identifying breaks leading to an infeasible home away pattern set in order to avoid the resulting infeasible subtrees of a branch and bound tree.