# A bi-objective approach to discrete cost-bottleneck location problems

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## Abstract

This paper considers a family of bi-objective discrete facility location problems with a cost objective and a bottleneck objective. A special case is, for instance, a bi-objective version of the (vertex) *p*-centdian problem. We show that bi-objective facility location problems of this type can be solved efficiently by means of an \(\varepsilon \)-constraint method that solves at most \((n-1)\cdot m\) minisum problems, where *n* is the number of customer points and *m* the number of potential facility sites. Additionally, we compare the approach to a lexicographic \(\varepsilon \)-constrained method that only returns efficient solutions and to a two-phase method relying on the perpendicular search method. We report extensive computational results obtained from several classes of facility location problems. The proposed algorithm compares very favorably to both the lexicographic \(\varepsilon \)-constrained method and to the two phase method.

## Keywords

Discrete facility location Bi-objective optimization \(\varepsilon \)-Constrained method Lexicographic optimization## Notes

### Acknowledgements

The authors would like to thank Professor Kim Allan Andersen for insightful comments and suggestions. This work was supported by a grant from Købmand Ferdinand Sallings Mindefond.

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