This paper introduces a framework for a highly constrained sports scheduling problem which is modeled from the requirements of various professional sports leagues. We define a sports scheduling problem, introduce the necessary terminology and detail the constraints of the problem. A set of artificial and real-world instances derived from the actual problems solved for the professional sports league owners are proposed. We publish the best solutions we have found, and invite the sports scheduling community to find solutions to the unsolved instances. We believe that the instances will help researchers to test the value of their solution methods. The instances are available online.

In this paper, we use operations research (OR) techniques to schedule the Second Division of the Chilean professional soccer league. The solution must satisfy a series of conditions requested by league officials. Because the teams generally travel long distances by bus, geographical restrictions are particularly important. We specify the scheduling problem and solve it using an integer linear programming (ILP) model that defines when and where each match is played, subject to constraints. For the most difficult instances, we formulate a second ILP model that generates home-away patterns and assigns them to the teams; we then run the model, which determines the match schedule. Chilean league officials have successfully used the models to schedule all five Second Division tournaments between 2007 and 2010, replacing the random scheduling methodology that they used previously. Since 2007, the two formulations have been adapted to various formats with which the Second Division has experimented; these include a quadruple round robin and a two-phase tournament with zonal and national phases. The application we present is one of a number of such projects that the authors and their colleagues developed over the past few years, and it represents an expansion of the use of OR techniques for managing tasks in Chilean soccer.

For the past 12 years, the Chilean Professional Soccer Association (ANFP) has applied operations research (OR) techniques to schedule soccer leagues in Chile. Using integer programming-based methods, the ANFP decides which matches are played in each round, taking into account various objectives, such as holding down costs and ensuring engaging tournaments for the fans. It has scheduled more than 50 tournaments using this approach, resulting in an estimated direct economic impact of about $59 million, including reductions in television broadcaster operating costs, growth in soccer pay-television subscriptions, increased ticket revenue, and lower travel costs for the teams. This application of OR has also had significant noneconomic impacts. First, the incorporation of team requirements and various sporting criteria has improved process transparency and schedule fairness, increasing fans’ interest in local professional tournaments; second, because of the high portability of these techniques, they have been used successfully to schedule sports leagues in other countries (examples include volleyball and basketball in Argentina, and the South American qualifiers for the 2018 Soccer World Cup). Furthermore, the models and methods used in this scheduling application have been disseminated widely, helping to promote OR as an effective tool for addressing practical problems. Our outreach activities have reached thousands of high school and university students in four countries and a more general audience of millions of television viewers and Internet users.

In 2007, the Department of Industrial Engineering at the University of Chile inaugurated a Master's degree in globalization management, in alliance with a major Chilean mining company. The new program aims to help meet the challenges currently facing the country in the development of human and social capital through the training of young professionals. This paper describes the use of mathematical programming models to applicant selection for the program in its first two years subject to equity criteria on gender, regional origin and socioeconomic background. The models generated robust solutions in a matter of minutes, an achievement practically impossible with manual methods. The success of this application demonstrates how Mathematical Programming and Operations Research can make a contribution on a social policy issue, in this case by generating a list of applicants that best fits the admission profile of a university degree program incorporating equity considerations. The mathematical tool developed also added transparency to the selection process.