Abstract
We consider the k-level facility location problem with soft capacities (k-LFLPSC). In the k-LFLPSC, each facility i has a soft capacity u i along with an initial opening cost f i ≥ 0, i.e., the capacity of facility i is an integer multiple of u i incurring a cost equals to the corresponding multiple of f i . We firstly propose a new bifactor (ln(1/β)/(1 −β),1+2/(1 −β))-approximation algorithm for the k-level facility location problem (k-LFLP), where β ∈ (0, 1) is a fixed constant. Then, we give a reduction from the k-LFLPSC to the k-LFLP. The reduction together with the above bifactor approximation algorithm for the k-LFLP imply a 5.5053-approximation algorithm for the k-LFLPSC which improves the previous 6-approximation.
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The authors would like to thank the two anonymous reviewers for their insightful comments to improve the presentation of the paper.
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This work was supported in part by Natural Science Foundation of China under Grant No. 11501412. The second author’s research is supported by Natural Science Foundation of China under Grant No. 11531014.
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Wu, Cc., Xu, Dc. An improved approximation algorithm for the k-level facility location problem with soft capacities. Acta Math. Appl. Sin. Engl. Ser. 33, 1015–1024 (2017). https://doi.org/10.1007/s10255-017-0714-x
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DOI: https://doi.org/10.1007/s10255-017-0714-x