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Facility location when demand is time dependent

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  • Zvi Drezner
  • G. O. Wesolowsky

Abstract

In this article we investigate the problem of locating a facility among a given set of demand points when the weights associated with each demand point change in time in a known way. It is assumed that the location of the facility can be changed one or more times during the time horizon. We need to find the time “breaks” when the location of the facility is to be changed, and the location of the facility during each time segment between breaks. We investigate the minisum Weber problem and also minimax facility location. For the former we show how to calculate the objective function for given time breaks and optimally solve the rectilinear distance problem with one time break and linear change of weights over time. Location of multiple time breaks is also discussed. For minimax location problems we devise two algorithms that solve the problem optimally for any number of time breaks and any distance metric. These algorithms are also applicable to network location problems.

Suggested Citation

  • Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:5:p:763-777
    DOI: 10.1002/1520-6750(199110)38:53.0.CO;2-A
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    References listed on IDEAS

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    1. Jack Elzinga & Donald Hearn & W. D. Randolph, 1976. "Minimax Multifacility Location with Euclidean Distances," Transportation Science, INFORMS, vol. 10(4), pages 321-336, November.
    2. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    3. 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.
    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. G. Y. Handler, 1973. "Minimax Location of a Facility in an Undirected Tree Graph," Transportation Science, INFORMS, vol. 7(3), pages 287-293, August.
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    Citations

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    Cited by:

    1. Reza Farahani & Zvi Drezner & Nasrin Asgari, 2009. "Single facility location and relocation problem with time dependent weights and discrete planning horizon," Annals of Operations Research, Springer, vol. 167(1), pages 353-368, March.
    2. Allman, Andrew & Zhang, Qi, 2020. "Dynamic location of modular manufacturing facilities with relocation of individual modules," European Journal of Operational Research, Elsevier, vol. 286(2), pages 494-507.
    3. Bhuvnesh Sharma & M. Ramkumar & Nachiappan Subramanian & Bharat Malhotra, 2019. "Dynamic temporary blood facility location-allocation during and post-disaster periods," Annals of Operations Research, Springer, vol. 283(1), pages 705-736, December.
    4. Clavijo López, Christian & Crama, Yves & Pironet, Thierry & Semet, Frédéric, 2024. "Multi-period distribution networks with purchase commitment contracts," European Journal of Operational Research, Elsevier, vol. 312(2), pages 556-572.
    5. George L. Vairaktarakis & Panagiotis Kouvelis, 1999. "Incorporation dynamic aspects and uncertainty in 1‐median location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 147-168, March.
    6. A Başar & B Çatay & T Ünlüyurt, 2011. "A multi-period double coverage approach for locating the emergency medical service stations in Istanbul," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 627-637, April.
    7. Tammy Drezner, 2009. "Location of retail facilities under conditions of uncertainty," Annals of Operations Research, Springer, vol. 167(1), pages 107-120, March.

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