Polyhedral results for assignment problems

This paper introduces an Integer Programming model for multidimensional assignment problems and examines the underlying polytopes. It also proposes a certain hierarchy among assignment polytopes. The dimension for classes of multidimensional assignment polytopes is established, unifying and generalising previous results. The framework introduced constitutes the first step towards a polyhedral characterisation for classes of assignment problems. The generic nature of this approach is illustrated by identifying a family of facets for a certain class of multidimensional assignment problems, namely “axial” problems.