A Lagrangian approach for minimum cost tournaments

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. Since matches are carried out at one of both opponents venues matches may be forbidden in certain periods due to unavailability of stadiums. The goal is to find the minimum cost tournament among those having no forbidden match. We employ a Lagrangian relaxation approach in order to obtain tight lower bounds. Moreover, we develop a cost-oriented repair mechanism yielding a feasible tournament schedule to each Solution of the relaxed problem.