Near-optimal solutions to large-scale facility location problems

Authors:
Francisco Barahona;FabiáN A. Chudak
Affiliations:
IBM, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA;IBM, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
Venue:
Discrete Optimization
Year:
2005

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Abstract

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 mxn=3000x3000; for the capacitated case the largest instances were 1000x1000. 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.