Scheduling Sport Leagues using Branch-and-Price

Sports league scheduling is a hard combinatorial optimization problem. There is a vast field of requests arising in real world problems, e.g., organizational, attractiveness and fairness constraints. A single round robin tournament (SRRT) can be described as a league of a set T of n teams (n even) to be scheduled such that each team plays exactly once against each other team and such that each team plays exactly once per matchday (MD) resulting in a set P of n − 1 MDs. Matches are carried out at one of opponents’ stadiums. A team playing twice at home or twice away in two consecutive periods is said to have a break in the latter of both periods. The number of breaks is to be minimized. It is well known that at least n− 2 breaks must occur. We focus on schedules having the minimum number of breaks. Costs corresponding to each possible match are given and the objective is to minimize the sum of matches’ cost. This can be formulated as a cost minimization IP as follows: