Lower bounds for large traveling umpire instances: New valid inequalities and a branch-and-cut algorithm

Lucas De Oliveira, Cid C. De Souza, Tallys Yunes

Research output: Contribution to journalArticle

1 Scopus citations


Given a double round-robin tournament, the Traveling Umpire Problem (TUP) seeks to assign umpires to the games of the tournament while minimizing the total distance traveled by the umpires. The assignment must satisfy constraints that prevent umpires from seeing teams and venues too often, while making sure all games have umpires in every round, and all umpires visit all venues. We propose a new integer programming model for the TUP that generalizes the two best existing models, introduce new families of strong valid inequalities, and implement a branch-and-cut algorithm to solve instances from the TUP benchmark. When compared against published state-of-the-art methods, our algorithm significantly improves all best known lower bounds for large TUP instances (with 20 or more teams).

Original languageEnglish (US)
Pages (from-to)147-159
Number of pages13
JournalComputers and Operations Research
StatePublished - Aug 1 2016



  • Branch-and-cut
  • Integer programming
  • OR in sports
  • Sports scheduling
  • Traveling umpire problem

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research

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