We study a polytope which arises from a mixed integer programming formulation of the quadratic semi-assignment problem. We introduce an isomorphic projection and transform the polytope to a tractable full-dimensional polytope. As a result, some basic polyhedral properties, such as the dimension, the affine hull, and the trivial facets, are obtained. Further, we present valid inequalities called cut- and clique-inequalities and give complete characterizations for them to be facet-defining. We also discuss a simultaneous lifting of the clique-type facets. Finally, we show an application of the quadratic semi-assignment problem to hub location problems with some computational experiences. © 2008 Elsevier B.V. All rights reserved.
Saito, H., Fujie, T., Matsui, T., & Matuura, S. (2009). A study of the quadratic semi-assignment polytope. Discrete Optimization, 6(1), 37–50. https://doi.org/10.1016/j.disopt.2008.08.003