In the paper "Computing lower
bounds for the quadratic assignment problem with an interior point
algorithm for linear programming,"
(Resende, Ramakrishnan,
and Drezner, O.R. 43 (781-791) 1995), we computed an LP-based lower
bound for the QAP using a interior point algorithm on numerous
problems from the QAPLIB. These linear programs are very difficult
for direct factorization based LP solvers.
I distribute MPS files of several of the LPs considered in the paper: