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A combined distribution and assignment model for continuous facility location problem

Author

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  • S. C. Wong

    (Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China)

  • S. H. Sun

    (Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China)

Abstract

Consider a general, heterogeneous geographical space with a set of competitive facilities, where the customers' demand locations from each of the facilities are continuously dispersed over the area. The total demand generated from a particular location in the space is fixed, but the demands from this location to the set of competitive facilities are subject to a distribution function with respect to the relative transportation costs to these facilities. Furthermore, we take into account congested transportation cost in characterizing customer choices. Congestion effect is explicitly built into our model by using a flow-dependent and location-dependent transportation cost function. The routing behavior of customers over the space and the user equilibrium choices of facilities are modeled by constructing a spatial user equilibrium flow pattern. The problem is formulated as a combined distribution and assignment model. An iterative algorithm between the distribution function for the choice of facilities and a mixed finite element method for route choices is proposed to solve the resulting continuous facility location problem. A numerical example is given to demonstrate the effectiveness of the proposed methodology.

Suggested Citation

  • S. C. Wong & S. H. Sun, 2001. "A combined distribution and assignment model for continuous facility location problem," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(2), pages 267-281.
    • Handle: RePEc:spr:anresc:v:35:y:2001:i:2:p:267-281
    Note: Received: May 1999/Accepted: May 2000
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    Citations

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    Cited by:

    1. Ho, H.W. & Wong, S.C. & Yang, Hai & Loo, Becky P.Y., 2005. "Cordon-based congestion pricing in a continuum traffic equilibrium system," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 813-834.
    2. Karakaya, Emrah, 2016. "Finite Element Method for forecasting the diffusion of photovoltaic systems: Why and how?," Applied Energy, Elsevier, vol. 163(C), pages 464-475.
    3. Huang, Ling & Wong, S.C. & Zhang, Mengping & Shu, Chi-Wang & Lam, William H.K., 2009. "Revisiting Hughes' dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 127-141, January.
    4. Ho, H.W. & Wong, S.C. & Loo, Becky P.Y., 2006. "Combined distribution and assignment model for a continuum traffic equilibrium problem with multiple user classes," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 633-650, September.
    5. Ouyang, Yanfeng & Wang, Zhaodong & Yang, Hai, 2015. "Facility location design under continuous traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 18-33.
    6. Wang, Zhaodong & Xie, Siyang & Ouyang, Yanfeng, 2022. "Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 123-140.
    7. Craparo, Emily M. & Fügenschuh, Armin & Hof, Christoph & Karatas, Mumtaz, 2019. "Optimizing source and receiver placement in multistatic sonar networks to monitor fixed targets," European Journal of Operational Research, Elsevier, vol. 272(3), pages 816-831.
    8. Karakaya, Emrah, 2014. "Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems," INDEK Working Paper Series 2014/6, Royal Institute of Technology, Department of Industrial Economics and Management.

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