This paper addresses the comprehensive problem of scheduling professional sports leagues by integrating three critical dimensions: match scheduling, time slot allocation, and referee assignment. We develop a general methodology applicable to round-robin tournaments that quantifies match attractiveness and competitiveness through simulation-based analysis of expected team performance. Using Poisson distribution and Monte Carlo simulation, we estimate match outcomes to derive attractiveness and competitiveness metrics based on competitive balance and relative team strength. These metrics are integrated into three sequential integer linear programming models. The first model generates the complete season fixture by determining home and away assignments while maximizing cumulative match attractiveness throughout the season. The second model strategically allocates matches to available time slots, balancing team exposure while managing prime time slot distribution. The third model assigns referees to matches while satisfying workload limits, mandatory rest periods, neutrality requirements, and conflict of interest constraints. We demonstrate the methodology's effectiveness through application to the 2024 season of the Liga Uruguaya de Basketball and, as a second case study, the 2024¿25 Italian Lega Basket Serie A. To validate the attractiveness-based approach, we compare schedules generated by maximizing match attractiveness against schedules created using random weights and against the schedules the leagues actually implemented. Statistical analysis demonstrates that the attractiveness-maximization objective produces significantly superior results in both overall calendar attractiveness (match scheduling model) and match exposure equity (time slot allocation model), increasing both by large margins over the implemented schedules. Our integrated approach represents a novel contribution by systematically combining simulation-based attractiveness quantification with optimization models, addressing a gap in existing research that typically treats these dimensions separately.
