A branch-and-price algorithm for scheduling sport leagues

Abstract

A single round robin tournament 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 period resulting in a set P of n−1 periods. Matches are carried out at one of the stadiums of both opponents. 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. There is a vast field of requests arising in real-world problems. For example, the number of breaks is to be minimized due to fairness reasons. 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 cost of arranged matches. Then, sports league scheduling can be seen as a hard combinatorial optimization problem. We develop a branch-and-price approach in order to find optimal solutions.