Issue: 2027/Vol.37/No.1, Pages 1
REFEREE ASSIGNMENT PROBLEM WITH MULTIPLE LEAGUES IN NON-PROFESSIONAL FOOTBALL
Tankut Atan
, Burak Çavdaroğlu , Zühal Özcan
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: T. Atan, B. Çavdaroğlu, Z. Özcan. Referee assignment problem with multiple leagues in non-professional football. Operations Research and Decisions 2027: 37(1). DOI 10.37190/ord/236166
Abstract
This study introduces the Multi-League Referee Assignment Problem (MRAP), a practically motivated optimization problem arising in the scheduling of referees for non-professional football. MRAP accounts for multiple concurrent leagues with distinct scheduling constraints, qualification requirements, and fairness considerations. We formulate MRAP as an integer programming model and assess its performance through extensive numerical experiments on realistic synthetic data. The monolithic model becomes computationally infeasible for large instances. Therefore, we propose two heuristic approaches that decompose the problem temporally by weeks or structurally by leagues. These heuristics quickly produce high-quality solutions when referee availability is sufficient. Notably, shorter batches of weeks in temporal decomposition perform better, as longer batches create restrictive commitments. Sensitivity analyses further demonstrate the practical value of optimization-based decision support.
Keywords: OR in sports, round-robin tournaments, integer programming, heuristic methods, decision support
Received: 2 January 2026 Accepted: 8 September 2026
Published online: 8 September 2026