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

TL;DR

This paper conducts a detailed polyhedral analysis of a cubic integer programming formulation for the unconstrained traveling tournament problem, introducing new facet-defining inequalities and assessing their impact on bounds.

Contribution

It provides the first polyhedral study of this problem's cubic formulation, including new inequalities and their effects on LP bounds.

Findings

Dimension of the integer hull established

New class of facet-defining inequalities introduced

Impact of inequalities on linear programming bounds evaluated

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.