Two-stage optimization of scheduling and referee assignment in football competitions based on fairness criteria

Articles in Press

Document Type : Research Note

Authors

1 Industrial Engineering Department, Sharif, University of Technology

2 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

10.24200/j65.2025.67488.2446

Abstract

In this study, a two-stage mathematical model is proposed for scheduling football league competitions with the primary goal of organizing matches in a fair and orderly manner. In the first stage, the sequence of matches, the assignment of home and away teams, and the allocation of referees are determined by considering various constraints to ensure justice in the competition. These constraints include alternating home and away match for each team, preventing a weak team from playing against two strong teams in consecutive weeks, and others aimed at promoting fairness. Subsequently, in the second stage, the exact scheduling of each match, specifying the day and time, is determined based on the outcomes of the first stage. The main innovation of this research is the stepwise decision-making process, which not only separates the determination of match sequence and exact timing but also incorporates practical constraints such as referee experience level, balancing the number of games officiated by each referee, and ensuring a minimum three-day interval between games for any team. Using the proposed model, it is possible to develop an optimal schedule for up to 6 teams and 8 referees over a 10-week period, and to conduct comprehensive analysis of the results. The results of the sensitivity analysis on the number of strong and weak referees indicate that when the number of both groups is equal, the smallest deviation from fairness-oriented criteria is observed. As the disparity between the sizes of these two groups increases (assuming the total number of referees remains constant), the deviation also increases. Overall, this model offers a practical and effective solution for fair scheduling and referee assignment in football leagues by integrating real-world requirements and fairness criteria into a comprehensive optimization framework, which can be adapted to various league sizes and complexities to ensure balanced and equitable competition.

Keywords

Main Subjects

Sharif Journal of Industrial Engineering & Management

Articles in Press, Accepted Manuscript
Available Online from 02 November 2025

Files

Share

How to cite

Statistics