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Multi-facility ordered median problems in directed networks

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Abstract

This paper uses a finite dominating set (FDS) to investigate the multi-facility ordered median problem (OMP) in a strongly connected directed network. The authors first prove that the multi-facility OMP has an FDS in the node set, which not only generalizes the FDS result provided by Kalcsics, et al. (2002), but also extends the FDS result from the single-facility case to the multiple case, filling an important gap. Then, based on this FDS result, the authors develop an exact algorithm to solve the problem. However, if the number of facilities is large, it is not practical to find the optimal solution, because the multi-facility OMP in directed networks is NP-hard. Hence, we present a constant-approximation algorithm for the p-median problem in directed networks. Finally, we pose an open problem for future research.

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Authors and Affiliations

  1. Faculty of Management and Administration, Macau University of Science and Technology, Macau, China

    Huajun Tang

  2. Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong, China

    T. C. Edwin Cheng & C. T. Ng

Authors
  1. Huajun Tang
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  2. T. C. Edwin Cheng
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  3. C. T. Ng
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Corresponding author

Correspondence to Huajun Tang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 70901050 and Macau Foundation under Grant No. 0144.

This paper was recommended for publication by Editor Jinhu LÜ.

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Tang, H., Cheng, T.C.E. & Ng, C.T. Multi-facility ordered median problems in directed networks. J Syst Sci Complex 24, 61–67 (2011). https://doi.org/10.1007/s11424-011-9327-2

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  • DOI: https://doi.org/10.1007/s11424-011-9327-2

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