A polyhedral study for the cubic formulation of the unconstrained traveling tournament problem

Marije R. Siemann; Matthias Walter

doi:10.1016/j.disopt.2022.100741

A polyhedral study for the cubic formulation of the unconstrained traveling tournament problem

Marije R. Siemann^*
, Matthias Walter

^*Corresponding author for this work

Mathematics of Operations Research

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Abstract

We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull as well as of faces induced by model inequalities. Moreover, we introduce a new class of inequalities and show that they are facet-defining. Finally, we evaluate the impact of these inequalities on the linear programming bounds.

Original language	English
Article number	100741
Number of pages	33
Journal	Discrete optimization
Volume	46
DOIs	https://doi.org/10.1016/j.disopt.2022.100741
Publication status	Published - Nov 2022

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A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem
Siemann, M. & Walter, M., 18 Nov 2020, ArXiv.org, 29 p.
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abstract = "We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull as well as of faces induced by model inequalities. Moreover, we introduce a new class of inequalities and show that they are facet-defining. Finally, we evaluate the impact of these inequalities on the linear programming bounds.",

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AB - We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull as well as of faces induced by model inequalities. Moreover, we introduce a new class of inequalities and show that they are facet-defining. Finally, we evaluate the impact of these inequalities on the linear programming bounds.

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JO - Discrete optimization

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A polyhedral study for the cubic formulation of the unconstrained traveling tournament problem

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A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem

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