Hiroo Saito, Tetsuya Fujie, Tomomi Matsui, Shiro Matuura
DISCRETE OPTIMIZATION, 6(1) 37-50, Feb, 2009 Peer-reviewed
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 semiassignment problem to hub location problems with some computational experiences. (C) 2008 Elsevier B.V. All rights reserved.