A study of the quadratic semi-assignment polytope

Authors:
Hiroo Saito;Tetsuya Fujie;Tomomi Matsui;Shiro Matuura
Affiliations:
Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;School of Business Administration, University of Hyogo, Kobe 651-2197, Japan;Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Venue:
Discrete Optimization
Year:
2009

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Abstract

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.