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The Multiperiod Location-Allocation Problem with Relocation of Facilities


  • George O. Wesolowsky

    (McMaster University)

  • William G. Truscott

    (McMaster University)


A dynamic or multiperiod location-allocation formulation is developed from the static problem of locating G facilities among M possible sites to serve N demand points. This dynamic model provides a tool for analyzing tradeoffs among present values of static distribution costs in each period and costs of relocating facilities. The objective is to specify the plan for facility locations and relocations and for attendant allocations of demands which minimize these costs. Two methods of solution are presented. First, a mixed-integer programming approach is used to solve sample problems. From computational results reported for structurally-similar problems, it seems that efficient general purpose codes for this method would be capable of solving problems with at least 5 periods, 5 potential sites, and 15 demand points. The second method, dynamic programming, is capable of increasing the size of problems that are computationally feasible. The dynamic programming approach is quite attractive when the relative values of G and M restrict the state space to a manageable size and constraints on the extent of location changes in each period limit the number of alternate decisions. Possible extensions of the model and solution procedures are discussed.

Suggested Citation

  • George O. Wesolowsky & William G. Truscott, 1975. "The Multiperiod Location-Allocation Problem with Relocation of Facilities," Management Science, INFORMS, vol. 22(1), pages 57-65, September.
  • Handle: RePEc:inm:ormnsc:v:22:y:1975:i:1:p:57-65

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    1. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    2. Badri, Masood A., 1999. "Combining the analytic hierarchy process and goal programming for global facility location-allocation problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 237-248, September.
    3. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    4. repec:spr:infosf:v:3:y:2001:i:4:d:10.1023_a:1012872704057 is not listed on IDEAS
    5. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    6. Güden, Hüseyin & Süral, Haldun, 2014. "Locating mobile facilities in railway construction management," Omega, Elsevier, vol. 45(C), pages 71-79.
    7. Vatsa, Amit Kumar, 2014. "Multi-Period Facility Location Problem with an Uncertain Number of Servers," IIMA Working Papers WP2014-02-06, Indian Institute of Management Ahmedabad, Research and Publication Department.
    8. Current, John & Ratick, Samuel & ReVelle, Charles, 1998. "Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach," European Journal of Operational Research, Elsevier, vol. 110(3), pages 597-609, November.
    9. Guerriero, Francesca & Miglionico, Giovanna & Olivito, Filomena, 2016. "Location and reorganization problems: The Calabrian health care system case," European Journal of Operational Research, Elsevier, vol. 250(3), pages 939-954.
    10. Ai, Yun-fei & Lu, Jing & Zhang, Li-li, 2015. "The optimization model for the location of maritime emergency supplies reserve bases and the configuration of salvage vessels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 83(C), pages 170-188.
    11. Vladimir Marianov & Daniel Serra, 2009. "Median problems in networks," Economics Working Papers 1151, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Lei, Chao & Lin, Wei-Hua & Miao, Lixin, 2014. "A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 699-710.
    13. Vatsa, Amit Kumar & Ghosh, Diptesh, 2014. "Tabu Search for Multi-Period Facility Location: Uncapacitated Problem with an Uncertain Number of Servers," IIMA Working Papers WP2014-11-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    14. Yongxi Huang & Yueyue Fan & Nils Johnson, 2010. "Multistage System Planning for Hydrogen Production and Distribution," Networks and Spatial Economics, Springer, vol. 10(4), pages 455-472, December.
    15. Sonmez, Ayse Durukan & Lim, Gino J., 2012. "A decomposition approach for facility location and relocation problem with uncertain number of future facilities," European Journal of Operational Research, Elsevier, vol. 218(2), pages 327-338.
    16. Yao, Zhishuang & Lee, Loo Hay & Jaruphongsa, Wikrom & Tan, Vicky & Hui, Chen Fei, 2010. "Multi-source facility location-allocation and inventory problem," European Journal of Operational Research, Elsevier, vol. 207(2), pages 750-762, December.

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