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Local search algorithm for universal facility location problem with linear penalties

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Abstract

The universal facility location problem generalizes several classical facility location problems, such as the uncapacitated facility location problem and the capacitated location problem (both hard and soft capacities). In the universal facility location problem, we are given a set of demand points and a set of facilities. We wish to assign the demands to facilities such that the total service as well as facility cost is minimized. The service cost is proportional to the distance that each unit of the demand has to travel to its assigned facility. The open cost of facility i depends on the amount z of demand assigned to i and is given by a cost function \(f_i(z)\). In this work, we extend the universal facility location problem to include linear penalties, where we pay certain penalty cost whenever we refuse serving some demand points. As our main contribution, we present a (\(7.88+\epsilon \))-approximation local search algorithm for this problem.

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Acknowledgments

The authors thank the anonymous reviewers for their helpful comments. The research of the first author is supported by Collaborative Innovation Center on Beijing Society-building and Social Governance. The second author is supported by NSFC (Nos.11371001 and 11531014). The third author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106. The fourth author’s research is supported by NSFC (No. 11501412).

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Authors and Affiliations

  1. Department of Information and Operations Research, College of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Yicheng Xu & Dachuan Xu

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  3. College of Science, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

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  1. Yicheng Xu
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Chenchen Wu
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Corresponding author

Correspondence to Dachuan Xu.

Additional information

This paper has been presented on the 2015 World Congress on Global Optimization.

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Xu, Y., Xu, D., Du, D. et al. Local search algorithm for universal facility location problem with linear penalties. J Glob Optim 67, 367–378 (2017). https://doi.org/10.1007/s10898-015-0394-0

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