Facets of the axial three-index assignment polytope

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun [21]. Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational relevance of the new inequalities by performing (limited) computational experiments.