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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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    1. Yang, Hai & Yagar, Sam & Iida, Yasunori, 1994. "Traffic assignment in a congested discrete/ continuous transportation system," Transportation Research Part B: Methodological, Elsevier, vol. 28(2), pages 161-174, April.
    2. Drezner, Zvi & Wesolowsky, George O., 1996. "Location-allocation on a line with demand-dependent costs," European Journal of Operational Research, Elsevier, vol. 90(3), pages 444-450, May.
    3. Jossef Perl & Peng-Kuan Ho, 1990. "Public Facilities Location under Elastic Demand," Transportation Science, INFORMS, vol. 24(2), pages 117-136, May.
    4. Tammy Drezner & Zvi Drezner, 1997. "Replacing continuous demand with discrete demand in a competitive location model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 81-95, February.
    5. Eiselt, H. A. & Laporte, G., 1989. "Competitive spatial models," European Journal of Operational Research, Elsevier, vol. 39(3), pages 231-242, April.
    6. Hai Yang, 1996. "A spatial price equilibrium model with congestion effects," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 30(4), pages 359-371.
    7. Kohlberg, Elon, 1983. "Equilibrium store locations when consumers minimize travel time plus waiting time," Economics Letters, Elsevier, vol. 11(3), pages 211-216.
    8. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
    9. Dafermos, Stella C., 1980. "Continuum modelling of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 295-301, September.
    10. Hau Leung Lee & Morris A. Cohen, 1985. "Equilibrium Analysis of Disaggregate Facility Choice Systems Subject to Congestion-Elastic Demand," Operations Research, INFORMS, vol. 33(2), pages 293-311, April.
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    Cited by:

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    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. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    9. 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.
    10. She, Ruifeng & Ouyang, Yanfeng, 2024. "Hybrid truck–drone delivery under aerial traffic congestion," Transportation Research Part B: Methodological, Elsevier, vol. 185(C).
    11. 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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