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A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem

Author

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  • G. O. Wesolowsky

    (McMaster University, Hamilton, Ontario)

  • R. F. Love

    (University of Wisconsin, Madison)

Abstract

This paper provides a method for approximating optimal location in a multi-facility Weber problem where rectangular distances apply. Optimality is achieved when the sum of weighted distances is minimized. Two upper bounds on the error incurred by using the approximation are developed. The formulation can be used in convex programming to solve some nonlinearly constrained problems.

Suggested Citation

  • G. O. Wesolowsky & R. F. Love, 1972. "A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem," Management Science, INFORMS, vol. 18(11), pages 656-663, July.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:11:p:656-663
    DOI: 10.1287/mnsc.18.11.656
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    Citations

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    Cited by:

    1. Carrizosa, E. & Munoz-Marquez, M. & Puerto, J., 1998. "The Weber problem with regional demand," European Journal of Operational Research, Elsevier, vol. 104(2), pages 358-365, January.
    2. Halit Üster & Robert F. Love, 2002. "Duality in constrained multi‐facility location models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(4), pages 410-421, June.
    3. He, Yuxin & Zhao, Yang & Luo, Qin & Tsui, Kwok-Leung, 2022. "Forecasting nationwide passenger flows at city-level via a spatiotemporal deep learning approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    4. Jing Yao & Alan T. Murray, 2014. "Serving regional demand in facility location," Papers in Regional Science, Wiley Blackwell, vol. 93(3), pages 643-662, August.
    5. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    6. Sándor P. Fekete & Joseph S. B. Mitchell & Karin Beurer, 2005. "On the Continuous Fermat-Weber Problem," Operations Research, INFORMS, vol. 53(1), pages 61-76, February.
    7. Venkateshan, Prahalad & Ballou, Ronald H. & Mathur, Kamlesh & Maruthasalam, Arulanantha P.P., 2017. "A Two-echelon joint continuous-discrete location model," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1028-1039.
    8. G Babich, 1978. "An Efficient Algorithm for Solving the Rectilinear Location-Allocation Problem," Environment and Planning A, , vol. 10(12), pages 1387-1395, December.

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