A mathematical optimisation model can save significant time in scheduling training sessions for sports clubs and help them make better use of their facilities. These are the first results of a research project led by Professor Tómas Philip Rúnarsson at the School of Engineering and Natural Sciences at the University of Iceland. He is joined by three recent graduates of industrial engineering; Bjartur Berg Baldursson, Jóhann Steinn Miiller Ólafsson, and Margrét Rán Rúnarsdóttir, who received a grant from the Icelandic Student Innovation Fund last March to work on the project over the summer.
Scheduling timetables is one of society’s most complex puzzles, whether in education, healthcare, transportation, or sports. Much of our daily lives is about balancing different needs and times, where many parties must be accommodated. This is also true for sports clubs, which must regularly schedule numerous training sessions for different sports and age groups. The process is often manual and time-consuming, making it difficult to optimize both time and facilities and avoid conflicts.
“The research is about developing a mathematical optimization model that arranges training sessions for sports clubs more efficiently than traditional manual methods. The aim is to maximize the use of sports facilities, reduce conflicts between groups, and make planning easier and more flexible for coaches and athletes,” says Tómas.
Inspired by exam timetable at the University of Iceland
According to Tómas, the idea for the project came after a conversation with Arnar Gíslason, a gender studies expert and equality officer at the university, who had also been on the parents’ council at KR sports club and noticed the challenges of scheduling training sessions. “He knew I had been involved in developing mathematical solutions for exam timetables and class scheduling at the university.”
Arnar suggested exploring whether KR’s training timetables could be organised in the same way as the university’s exam timetable using a mathematical optimisation model. He also pointed out that, in addition to easing scheduling and avoiding conflicts, such a model could be used as a tool to ensure equality between genders in terms of training times and facilities.
“The exam and class scheduling projects at the university were carried out in close collaboration with industrial engineering students and colleagues at the School of Engineering and Natural Sciences,” Tómas explains. “Currently, many timetables at the university are simply copied from previous years and then manually adjusted based on feedback from teachers or students. This results in inconsistent quality and underutilization of classrooms.”
There are hopes that this technology will be implemented throughout the university to improve opportunities for interdisciplinary study. “Although the university has purchased scheduling systems, adapting them to its real needs has proven difficult, if not impossible,” Tómas adds.
Using data from KR and Breiðablik
The research is based on developing a mixed-integer programming (MIP) optimization model that places training sessions on a timetable while considering constraints such as facilities, session length, conflicts, and workload balance. According to Tómas, the scientific novelty of the research lies in using a continuous time model and open-source optimization software, which has not been applied to this extent before, neither in Iceland nor abroad. “The model is being tested with data provided by the football clubs KR and Breiðablik to ensure practical use and reliability. Such data provides insight into real-world scheduling, and the aim is to expand the project by including more clubs,” he explains.
An app is also being developed and will be hosted on the university’s servers for the duration of the project. The app allows training organizers to enter and adjust constraints through a conversational interface. Tómas plans to use this technology in another project funded by the Icelandic Research Fund, titled Automatic Learning of Decision Models. “In that project, I also use sports training schedules as an example, where the clubs themselves shape the optimization model interactively through an AI-based interface. The goal is for organizers to ‘talk their way through’ the scheduling process with the help of generative AI and mathematical optimization.”
Importance of real-world projects for students
Tómas emphasizes using real-world projects that students can relate to in teaching, which is why he introduced this project. As mentioned, he is supported by three industrial engineering graduates in the research. Bjartur, Jóhann Steinn, and Margrét Rán have spent the summer developing the model, processing data, and designing the user interface.
“We first encountered the project in a course taught by Tómas. In that course, he presented an assignment to develop a mixed-integer optimization model to schedule training sessions for football and basketball at KR, which sparked our interest in further development,” explain Bjartur and Jóhann Steinn. They continued the project in a follow-up course on operations research under Tómas’s supervision.
To better connect the project to a real problem requiring a solution, Tómas brought in Íunn Eir Gunnarsdóttir, KR’s sports officer. “Íunn and the coaches at KR prepared the first draft of the dataset we could use in the course. Íunn also came to class and answered students’ questions. Finally, Bjartur and Jóhann got the chance to continue with the project as their bachelor’s thesis in industrial engineering.”
Exciting to work on practical solutions for sports clubs
Bjartur and Jóhann Steinn were highly motivated by the project, so it was natural for them to apply for a grant from the Student Innovation Fund to continue its development over the summer. After receiving the grant, they invited Margrét Rán to rejoin the project.
“I found the optimization model we developed with Tómas very interesting, and I saw both the potential and the impact it could have. When the opportunity came to continue working on it, I was excited to take part,” says Bjartur.
Jóhann Steinn agrees, highlighting that the project was both practical and challenging: “It was exciting to work on a solution that directly benefits sports clubs.”
Margrét Rán, who has coached girls in Grótta’s youth football for the past seven years, is very familiar with the difficulties of organising training. “I’ve played football myself for many years, so I know how complicated it can be to schedule practices and make the best use of facilities. It becomes especially tricky when athletes are active in two or three sports, and coaches are also studying or working alongside coaching, so they are only available at certain times,” she says.
The optimisation model can save significant time in scheduling
The project and testing are still ongoing, but the initial results are very promising. They show that the optimisation model can save significant time in scheduling practices and improve the use of sports facilities.
“This approach could have a major impact on how sports clubs organise themselves, and the hope is that the solution can be used more widely, improving efficiency nationwide and across clubs,” says Tómas. “The research could have a substantial impact on sports in Iceland by improving facility use and saving time and effort for organisers, ultimately giving more people the opportunity to train and allowing clubs to use their resources better.”
Bjartur, Jóhann Steinn, and Margrét Rán agree, noting that the research addresses a real challenge faced by many sports clubs and could therefore have broad implications. “By maximising the use of training facilities and preventing scheduling conflicts, the project supports strong sports programs and enables clubs to use their resources more efficiently, benefiting both athletes and organisers,” they emphasise.
Interest in further development
Bjartur, Jóhann Steinn, and Margrét all graduated with bachelor’s degrees in industrial engineering in June. Asked whether they are interested in continuing to develop the optimization model, both Bjartur and Jóhann Steinn said yes. “It would be exciting to keep developing the project if there’s interest and if it proves useful in practice,” they said. For now, though, their main goal is to deliver the best possible results by the end of the summer.
The future looks bright for the three of them. Margrét Rán and Jóhann Steinn both plan to pursue further studies. Jóhann Steinn will begin a master’s in industrial engineering at DTU (Technical University of Denmark) this autumn, and Margrét plans to move to Copenhagen early next year. “I’m also going to do a master’s at DTU, starting in the spring semester, most likely in industrial engineering,” she says.
Bjartur, who has worked for the engineering firm Cowi the past three summers, plans to add to his professional experience this winter. “I’ll be working at Alvotech starting in September, and I’m planning on starting a master’s in Europe in the autumn of 2026, either in industrial engineering or a technical field,” he explains.