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Article Excerpt
Since 2005, Chile's professional soccer league has used a game-scheduling system that is based on an integer linear programming model. The Chilean league managers considered several operational, economic, and sporting criteria for the final tournaments' scheduling. Thus, they created a highly constrained problem that had been, in practice, unsolvable using their previous methodology. This led to the adoption of a model that used some techniques that were new in soccer-league sports scheduling. The schedules they generated provided the teams with benefits such as lower costs, higher incomes, and fairer seasons. In addition, the tournaments were more attractive to sports fans. The success of the new scheduling system has completely fulfilled the expectations of the Asociacion Nacional de Futbol Profesional (ANFP), the organization for Chilean professional soccer.
Key words: Chilean soccer league; integer programming; sports scheduling; recreation/sports; OR/MS implementation; scheduling.
History: This paper was refereed.
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Soccer is "the passion of multitudes" worldwide. The World Cup 2006, which was held in Germany, amply demonstrated this phenomenon. Beyond the purely sporting and emotional aspects of the game, managing soccer increasingly requires the application of scientific criteria. In Chile, soccer has faced competition from the international leagues, other televised sports, and different forms of entertainment such as shopping malls, cinema, video games, and the Internet. Organizers of professional sports in many countries are facing similar situations.
This competition has caused a reduction in Chileans' interest in soccer and a resulting decline in the revenue the sport generates. To reverse this decline and reduce costs, professional league officials are facing the challenge of having to increase the attractiveness of the league season. The planning of league game schedules is critical to achieving this objective. Considering the many aspects of developing a game calendar that is simultaneously fair to the teams, economically beneficial, and attractive to sports fans, the task of scheduling each regular-season match-up would be nearly impossible if attempted manually.
Beginning with the first tournament of 2005, the Asociacion Nacional de Futbol Profesional (ANFP), the organizing body for Chilean soccer, employed the services of the Centro de Gestion de Operaciones (CGO), a unit of the Industrial Engineering Department at the University of Chile, to assist in the planning of the main league's game schedule. We integrated sporting, operational, and economic criteria within an integer programming model to develop a schedule that meets the ANFP criteria and makes the season more interesting to soccer fans.
Our work falls within the area known as sports scheduling. In this paper, we present the criteria we used to define an efficient season schedule. We address sporting fairness or equity, the introduction of operational and economic considerations into the scheduling process, and how the model and its implementation provide a flexibility that was previously absent in Chilean soccer schedules. In addition to increasing the season's attractiveness, these factors combine to put the scheduling process on a more scientific basis, making it more transparent and more acceptable to team managers.
We organize the paper as follows. We begin with a description of the Chilean soccer tournaments and a review of the sports-scheduling literature. In the Conditions Imposed on the Problem section, we explain the conditions considered in the 2006 opening tournament. In The Mathematical Model and Computational Solution section, we describe the model and its computational solution. In the Results section, we discuss some recent statistics and qualitative factors of our model that have satisfied the ANFP and soccer teams and fans. In the Conclusions section, we summarize and provide guidelines for future work. Finally, in the appendix, we show the formulation of the mathematical model.
Background
The Chilean professional soccer league is composed of the First Division and the Second Division. The First Division has 20 teams and divides its annual playing calendar into two tournaments--the opening championship and the closing championship. Each championship comprises two phases: the regular season, which consists of 19 playing dates or rounds, and the playoffs. The teams are organized into four groups of five teams each. Each team must play once against each of the other 19 teams. The ANFP sets the date of each round and the composition of the groups in advance. Following the regular season, the two top teams in each group advance to the playoffs to determine the champion. The Mexican soccer-league system inspired this structure.
The Second Division has 12 teams. Each year the last two teams (measured by the sum of points in both tournaments) of the First Division are relegated to the Second Division; the best two teams of the Second Division are promoted to the First Division.
The country is geographically divided into 12 Regions and the Metropolitan Region (Santiago), which is located between Regions V and VI. We have classified the 20 teams of the First Division into three clusters by geographic location: North with five teams, Center with 10 teams, and South with five teams (Figure 1).
Prior to 2005, the method used to schedule the First Division was a random draw of teams and venues using a preset template; almost all soccer leagues in South America and Europe use this system. While it facilitated manual scheduling, it did not take into account most of the criteria (e.g., fairness and economic considerations to provide greater revenue and lower costs for the teams) that are needed for efficiency. To ensure fairness, each team should play a balanced mix of home and away games against the strongest teams. Games against the strongest teams should not be scheduled consecutively; each team should play against two of its group opponents at home and against the other two opponents away. Scheduling two consecutive away games (e.g., Sunday-Wednesday or Wednesday-Sunday) for a given team in different opponents' venues, which are located relatively close to each other but far from the team's home venue, is an example of an economic consideration; it would spare the team a second long trip. Other examples include setting "attractive" games for appropriate dates, such as summer home games for teams located in popular beach towns against the most popular teams, and scheduling classic rivalries or matches between teams of the same group in the second half of the tournament when the stakes are higher. In addition, we can distribute weekday home games fairly; such dates are less attractive to the teams because attendance is lower than on weekends (revenue for any specific game goes entirely to the home team).
In previous years, scheduling based on these criteria was woefully deficient. Examples included classic match-ups on inappropriate dates, weaker teams scheduled to play all their games against stronger ones away from home, and unbalanced distribution of weekday, home games.
Because a season calendar that meets these standards of efficiency would be nearly impossible to develop manually, operations research can make a substantial contribution by allowing the application of technology to give more flexibility to the season-scheduling process. To help the reader appreciate the scale of the complexity involved, we note that for a tournament in which six teams play a simple round-robin, there are 720 different possible schedules (this does not even consider whether the games are at home or away); for a...
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