# A Multi-Exchange Local Search Algorithm for the Capacitated Facility Location Problem

We present a multi-exchange local search algorithm for approximating the capacitated facility location problem (CFLP), where a new local improvement operation is introduced that possibly exchanges multiple facilities simultaneously. We give a tight analysis for our algorithm and show that the performance guarantee of the algorithm is between $3+2\sqrt{2}-\epsilon$ and $3+2\sqrt{2}+\epsilon$ for any given constant $\epsilon>0$. Previously known best approximation ratio for the CFLP is $7.88$, due to Mahdian and P\'{a}l (2003), based on the operations proposed by P\'{a}l, Tardos and Wexler (2001). Our upper bound $3+2\sqrt{2}+\epsilon$ also matches the best known ratio, obtained by Chudak and Williamson (1999), for the CFLP with uniform capacities. In order to obtain the tight bound of our new algorithm, we make interesting use of techniques from the area of parallel machine scheduling.

## Citation

Working paper, Oct. 2003, Department of Management Science and Engineering, Stanford University, CA, 94305