Abstract
In a general k-level uncapacitated facility location problem (k-GLUFLP), we are given a set of demand points, denoted by D, where clients are located. Facilities have to be located at a given set of potential sites, which is denoted by F in order to serve the clients. Each client needs to be served by a chain of k different facilities. The problem is to determine some sites of F to be set up and to find an assignment of each client to a chain of k facilities so that the sum of the setup costs and the shipping costs is minimized. In this paper, for a fixed k, an approximation algorithm within a factor of 3 of the optimum cost is presented for k-GLUFLP under the assumption that the shipping costs satisfy the properties of metric space. In addition, when no fixed cost is charged for setting up the facilities and k=2, we show that the problem is strong NP-complete and the constant approximation factor is further sharpen to be 3/2 by a simple algorithm. Furthermore, it is shown that this ratio analysis is tight.
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Acknowledgements
This work was supported in part by the Chinese National Natural Science Foundation Grant (No.10771060 and 60872039).
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Li, R., Huang, HC. & Huang, J. Heuristic algorithms for general k-level facility location problems. J Oper Res Soc 64, 106–113 (2013). https://doi.org/10.1057/jors.2012.31
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DOI: https://doi.org/10.1057/jors.2012.31