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A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality

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  • Hai Yang

    (Department of Civil Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China)

  • S. C. Wong

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

Abstract

We consider a heterogeneous two-dimensional space where a given set of competitive facilities is located. Customers are assumed to be scattered continuously over the space, and each customer is assumed to choose a facility to minimize individual total cost of receiving service. The total cost consists of both the congested travel time to the facility and a cost associated with the congestion externality at the facility. Furthermore, customer demand at any location is assumed to be a function of the total cost of receiving service. Given these assumptions, it is of interest to estimate the market areas and market shares captured by each competitive facility. This problem is formulated here as a calculus of variations problem, and its optimality conditions are shown to be equivalent to the spatial customer choice equilibrium conditions with elastic demand and market externality. The model is solved by an efficient finite element method and illustrated with a numerical example.

Suggested Citation

  • Hai Yang & S. C. Wong, 2000. "A Continuous Equilibrium Model for Estimating Market Areas of Competitive Facilities with Elastic Demand and Market Externality," Transportation Science, INFORMS, vol. 34(2), pages 216-227, May.
    • Handle: RePEc:inm:ortrsc:v:34:y:2000:i:2:p:216-227
    DOI: 10.1287/trsc.34.2.216.12307
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    References listed on IDEAS

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    Cited by:

    1. Yan-Qun Jiang & S.C. Wong & Peng Zhang & Keechoo Choi, 2017. "Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City," Transportation Science, INFORMS, vol. 51(3), pages 931-945, August.
    2. 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.
    3. 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.
    4. Wong, Wai & Wong, S.C., 2015. "Systematic bias in transport model calibration arising from the variability of linear data projection," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 1-18.
    5. Wong, Wai & Wong, S.C., 2016. "Biased standard error estimations in transport model calibration due to heteroscedasticity arising from the variability of linear data projection," Transportation Research Part B: Methodological, Elsevier, vol. 88(C), pages 72-92.
    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. 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.
    8. Long, Jiancheng & Szeto, W.Y. & Du, Jie & Wong, R.C.P., 2017. "A dynamic taxi traffic assignment model: A two-level continuum transportation system approach," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 222-254.
    9. 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.
    10. Xu, Min & Meng, Qiang, 2020. "Optimal deployment of charging stations considering path deviation and nonlinear elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 135(C), pages 120-142.

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