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Non-linear Integer Programming Model and Algorithms for Connected p-facility Location Problem

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  • Zhu Jianming

    (College of Engineering and Information Technology, University of Chinese Academy of Sciences, Beijing100049, China)

Abstract

In this paper, a new location analysis method is presented. Given a connected graph G = (V, E)with nonnegative edge cost ce for each edge e ∊ E, dij is the cost of the shortest path between vertices i and j in the graph. The Connected p-facility Location Problem (CpLP) is to choose p vertices from V so as to minimize the total cost of shortest path of pair-wise of these p vertices. This problem is proved to be NP-hard and non-linear integer programming is formulated. Then, two algorithms are designed for solving the CpLP. One is a heuristic algorithm based on classical maximum clique approach, while the second one is genetic algorithm. Finally, computational results show the comparison between these two algorithms.

Suggested Citation

  • Zhu Jianming, 2014. "Non-linear Integer Programming Model and Algorithms for Connected p-facility Location Problem," Journal of Systems Science and Information, De Gruyter, vol. 2(5), pages 451-460, October.
    • Handle: RePEc:bpj:jossai:v:2:y:2014:i:5:p:451-460:n:6
    DOI: 10.1515/JSSI-2014-0451
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    1. Nagy, Gabor & Salhi, Said, 2007. "Location-routing: Issues, models and methods," European Journal of Operational Research, Elsevier, vol. 177(2), pages 649-672, March.
    2. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
    3. Leon Cooper, 1963. "Location-Allocation Problems," Operations Research, INFORMS, vol. 11(3), pages 331-343, June.
    4. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    5. E. C. Sewell, 1998. "A Branch and Bound Algorithm for the Stability Number of a Sparse Graph," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 438-447, November.
    6. Saïd Salhi & Gábor Nagy, 2009. "Local improvement in planar facility location using vehicle routing," Annals of Operations Research, Springer, vol. 167(1), pages 287-296, March.
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