# A local search approximation algorithm for the uniform capacitated *k*-facility location problem

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## Abstract

In the uniform capacitated *k*-facility location problem (UC-*k*-FLP), we are given a set of facilities and a set of clients. Every client has a demand. Every facility have an opening cost and an uniform capacity. For each client–facility pair, there is an unit service cost to serve the client with unit demand by the facility. The total demands served by a facility cannot exceed the uniform capacity. We want to open at most *k* facilities to serve all the demands of the clients without violating the capacity constraint such that the total opening and serving cost is minimized. The main contribution of this work is to present the first combinatorial bi-criteria approximation algorithm for the UC-*k*-FLP by violating the cardinality constraint.

### Keywords

*k*-Facility location Uniform capacitated Approximation algorithm Local search

## Notes

### Acknowledgements

The second author is supported by Natural Science Foundation of China (No. 11531014). The third author is supported by Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106. The fourth author is supported by Higher Educational Science and Technology Program of Shandong Province (No. J15LN22).

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