Lower bounds for the quadratic semi-assignment problem

This paper presents a class of lower bounds for the Quadratic Semi-Assignment Problem (QSAP). These bounds are based on recent results on polynomially solvable cases, in particular we will consider the QSAPs whose quadratic cost coefficients define a reducible graph. The idea is to decompose the problem into several subproblems, each defined on a reducible subgraph. A Lagrangean decomposition technique is used to improve the results. Several lower bounds are computationally compared on several types of test problems.