无约束旅游竞赛问题立方形式的多面体研究
A Polyhedral Study for the Cubic Formulation of the Unconstrained Traveling Tournament Problem
摘要：
研究了无约束旅行锦标赛问题，一个最小化团队旅行的运动竞赛问题。自20年前引入以来，大多数研究都致力于建模和重构方法。在本文中，我们进行了多面体的研究，三次整数规划制定建立的整数壳的尺寸，以及由模型不等式引起的面。此外，我们引入了一类新的不等式，并证明了它们是刻面定义的。最后，我们评估了这些不等式对线性规划界的影响。
英文摘要：
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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