Abstract
Facility location problem is a well established research area within Operations Research. Capacitated facility location problem is one of the most important variants, in which each facility has an upper bound on the demand, i.e., capacity. Moreover, the integrality gap of the natural linear program relaxation for the problem is infinite. Fortunately, the gap is finite when all opening costs for the facilities are the same. We consider a capacity facility location problem with penalties in which it is allowed some customers are not served by facilities and all opening costs are uniform. Based on LP-rounding framework, we propose a 5.732-approximation algorithm.
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We would like to thank the referees for their obvious diligence, thoughtful and insightful comments. These comments help us to make the paper better. The second author is supported by National Natural Science Foundation of China (No. 11971349).
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Supported by National Natural Science Foundation of China (No. 11971349). The previous version of the paper is accepted by The Fourteenth International Frontiers of Algorithmics Workshop (FAW 2020).
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Lv, W., Wu, C. An LP-rounding based algorithm for a capacitated uniform facility location problem with penalties. J Comb Optim 41, 888–904 (2021). https://doi.org/10.1007/s10878-021-00726-0
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DOI: https://doi.org/10.1007/s10878-021-00726-0