Home away table classification and carry-over effect values minimization under restricted breaks for round-robin tournament

Abstract

Sports scheduling is the research region that concerns making a reasonable game schedule, especially a round-robin tournament, for sports competitions. One of the important factors in game scheduling is fairness. Based on the fairness of the schedule, the two elements of the break and the carry-over effect are considered in this study. First, three types of home-away tables that are limited to a small number of breaks, i.e., the number of two consecutive home/away games are evaluated, and these tables are characterized by introducing a number sequence called space-sequence. The space-sequences also clarify the property of feasibility, which helps to enumerate feasible home-away tables. Next, the carry-over effect value minimization problem with a small number of breaks was solved by using an integer programming problem. Adding some valid inequalities and converting the quadratic objective function into linearization slightly improve the calculation of the minimum carry-over effect values, but it still cannot obtain the solution for a large number of teams. Since it is difficult to calculate the entire integer programming model, isomorphic home-away tables obtained by rotation of rounds are defined and the candidates home-away tables are reduced. By solving the problem for each of the nonisomorphic home-away tables enumerated, better carry-over effect values can be found for the small number of teams.

Keywords

• round-robin tournament
• integer programming
• carry-over effect
• home-away table
• space-sequence