The facility location problem with maximum distance constraint
Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of L. The goal is to minimise the sum of the opening costs of the facilities....
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| Published in: | Information processing letters Vol. 184; p. 106447 |
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| Abstract | Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of L. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no (α,1)-approximation algorithm with α<3 exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the k-supplier problem. The difference between this algorithm and the previous one in [12] is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.
•Prove the FLP-MD is NP-hard and analyze the lower bound of the problem.•Provide an approximation algorithm with a ratio of (3,1) for the FLP-MD.•Propose a new algorithm with an approximation ratio of 3 for the k-supplier problem. |
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| AbstractList | Motivated by practical problems, we investigate the facility location problem with maximum distance constraint, which requires that the distance from each customer to open facilities must not exceed a given threshold value of L. The goal is to minimise the sum of the opening costs of the facilities. We show that this problem is NP-hard and analyse its lower bound. As no (α,1)-approximation algorithm with α<3 exists, we provide a (3,1)-approximation algorithm that violates the maximum distance constraint. Based on this algorithm, we propose a 3-approximation algorithm for the k-supplier problem. The difference between this algorithm and the previous one in [12] is that the proposed algorithm avoids the construction of many bottleneck graphs, making the proposed algorithm less demanding in terms of memory and more suitable for large-scale problems.
•Prove the FLP-MD is NP-hard and analyze the lower bound of the problem.•Provide an approximation algorithm with a ratio of (3,1) for the FLP-MD.•Propose a new algorithm with an approximation ratio of 3 for the k-supplier problem. |
| ArticleNumber | 106447 |
| Author | Li, Xiaowei Lu, Xiwen |
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| Cites_doi | 10.1137/151002320 10.1016/j.ic.2012.01.007 10.1007/s11590-021-01701-8 10.1137/S0097539703405754 10.1007/s10878-020-00538-8 10.1145/5925.5933 10.1016/S1571-0653(05)80067-8 10.1007/s10255-017-0714-x 10.1007/s00453-011-9526-1 10.1137/S0097539703435716 10.1016/j.camwa.2008.10.004 10.1006/jagm.1998.0993 10.1007/s10107-005-0673-5 10.1007/s00453-014-9911-7 10.1016/j.tcs.2020.05.022 10.1007/s10107-004-0524-9 10.1287/moor.1040.0125 10.1016/S0020-0190(99)00144-1 10.1007/s10878-007-9127-8 10.1145/375827.375845 10.1137/S0097539702416402 |
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