We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x 1000. We use heuristics that produce a feasible integer solution and use a Lagrangian relaxation to obtain a lower bound on the optimal value. In particular, we present new heuristics whose gap from optimality was generally below 1%. The heuristics combine the volume algorithm and randomized rounding. For the uncapacitated facility location problem, our computational experiments show that our heuristic compares favorably against DUALOC.
IBM Research Report RC21606, 1999