Optimizing Sports Scheduling: Mathematical and Constraint Programming to Minimize Traveled Distance with Benchmark From The Norwegian Professional Volleyball League

Abstract

In this thesis, we present models to schedule round-robin tournaments. Based on attributes of the 2017/2018 schedule for the Norwegian top volleyball league, the Mizuno League, the models aim to (1) distribute the number of breaks more evenly among the teams in the league, (2) introduce a maximum number of consecutive home or away matches, (3) more evenly distribute the number of matches per round (4) reduce the total number of rounds from 15 to 14 (5) create a fairer and over-all better schedule and (6) minimize travel distance, and thereby costs. The thesis describes five models to tackle the aims above: • Model 1: A linear integer programming model to schedule a single roundrobin. • Model 2: A linear integer programming model to minimize breaks in a single round-robin tournament. • Model 3: A constraint programming model to minimize breaks in a double round-robin tournament. • Model 4: A linear integer programming model to minimize travel distance with predefined timetables in a double round-robin tournament. • Model 5: A constraint programming model to minimize travel distance in a double round-robin tournament. All models attempt to schedule a seasonal tournament based on the constraints and objective of the top Norwegian volleyball league, The Mizuno League. The Models are tested and benchmarked on the number of breaks and travel distance from the schedule of 2017/2018 season of the Mizuno League. Model 2 to 5 all reduced the number of breaks compared to the Mizuno League. Model 5, a constraint programming model proved to reduce travel distance by 10% to 29%. Because of tight budgets, the most suitable model to schedule the Mizuno League is Model 5. Efforts have been taken in section 6 to alter the schedule from Model 5 to best fit the practical requirements of the Mizuno League. Finally, we re-solve Model 5 where we change the objective of minimizing travel distance to minimize travel cost.