Integer programming models for round robin tournaments

IP models for round robin tournaments

Generally speaking in sports competition a number of teams play against each other over a period of time according to a certain scheme. The round robin scheme is very popular in many team sports like soccer and basketball. In this paper we study several basic variants of round robin tournaments. Additionally, we examine real world issues that have to be considered when constructing a sports lea...

Scheduling asynchronous round-robin tournaments

We study the problem of scheduling asynchronous round-robin tournaments. We consider three measures of a schedule that concern the quality and fairness of a tournament. We show that the schedule generated by the well-known “circle design” performs well with respect to all three measures when the number of teams is even, but not when the number of teams is odd. We propose a different schedule th...

Win Sequences for Round-robin Tournaments

Each of n teams numbered 1, 2, · · · , n play each of the other n− 1 teams exactly one time for a total of ( n 2 ) = n(n − 1)/2 games. Each game produces a win for one team and a loss for the other team. Define (wi, li), i = 1, 2, · · · , n, to be the win-loss records for the teams. That is, team i, i = 1, 2, · · · , n, wins wi games and loses li games where wi + li = n− 1. Of course, n ∑

Integer and Constraint Programming Approaches for Round-Robin Tournament Scheduling

Round robin tournaments and three index assignments

Scheduling a sports league can be seen as 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 minimum cost round robin tournament is established by a reduction from the planar three-index assignment problem. Furthermore, we introduce integer p...