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A Variational Inequality-Based Location-Allocation Algorithm for Locating Multiple Interactive Facilities

Author

Listed:
  • Yan Gu

    (Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Qinhuai District, Nanjing 210016, P. R. China2Key Laboratory of Mathematical Modelling and High Performance, Computing of Air Vehicles (NUAA), MIIT, 29 Yudao Street, Qinhuai District, Nanjing 210016, P. R. China)

  • Jianlin Jiang

    (Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Qinhuai District, Nanjing 210016, P. R. China3School of Information and Mathematics, Yangtze University, 1 Nanhuan Road, Jingzhou 434023, P. R. China)

  • Liyun Ling

    (Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Qinhuai District, Nanjing 210016, P. R. China)

  • Yibing Lv

    (School of Information and Mathematics, Yangtze University, 1 Nanhuan Road, Jingzhou 434023, P. R. China)

  • Su Zhang

    (Business School, Nankai University, 94 Weijin Road, Nankai District, Tianjin 300071, P. R. China)

Abstract

Multi-source Weber problem (MWP) is an important model in facility location, which has wide applications in various areas such as health service management, transportation system management, urban planning, etc. The location-allocation algorithm is a well-known method for solving MWP, which consists of a location phase and an allocation phase at each iteration. In this paper, we consider more general and practical case of MWP–the constrained multi-source location problem (CMSLP), i.e., the location of multiple facilities with considering interactive transportation between facilities, locational constraints on facilities and the gauge for measuring distances. A variational inequality approach is contributed to solving the location subproblem called the constrained multi-facility location problem (CMFLP) in location phase, which leads to an efficient projection-type method. Then a new location-allocation algorithm is developed for CMSLP. Global convergence of the projection-type method as well as local convergence of new location-allocation algorithm are proved. The efficiency of proposed methods is verified by some preliminary numerical results.

Suggested Citation

  • Yan Gu & Jianlin Jiang & Liyun Ling & Yibing Lv & Su Zhang, 2023. "A Variational Inequality-Based Location-Allocation Algorithm for Locating Multiple Interactive Facilities," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(01), pages 1-24, February.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:01:n:s0217595922400103
    DOI: 10.1142/S0217595922400103
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