IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v34y2000i2p216-227.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/trsc.34.2.216.12307
    Download Restriction: no
    File URL: https://libkey.io/10.1287/trsc.34.2.216.12307?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Kohlberg, Elon, 1983. "Equilibrium store locations when consumers minimize travel time plus waiting time," Economics Letters, Elsevier, vol. 11(3), pages 211-216.
    5. Dafermos, Stella C., 1980. "Continuum modelling of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 295-301, September.
    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. Jossef Perl & Peng-Kuan Ho, 1990. "Public Facilities Location under Elastic Demand," Transportation Science, INFORMS, vol. 24(2), pages 117-136, May.
    8. Eiselt, H. A. & Laporte, G., 1989. "Competitive spatial models," European Journal of Operational Research, Elsevier, vol. 39(3), pages 231-242, April.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marianov, Vladimir & Rí­os, Miguel & Icaza, Manuel José, 2008. "Facility location for market capture when users rank facilities by shorter travel and waiting times," European Journal of Operational Research, Elsevier, vol. 191(1), pages 32-44, November.
    2. Haase, Knut & Hoppe, Mirko, 2008. "Standortplanung unter Wettbewerb - Teil 1: Grundlagen," Discussion Papers 2/2008, Technische Universität Dresden, "Friedrich List" Faculty of Transport and Traffic Sciences, Institute of Transport and Economics.
    3. Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
    4. Daniel Serra & Charles Revelle, 1997. "Competitive location and pricing on networks," Economics Working Papers 219, Department of Economics and Business, Universitat Pompeu Fabra.
    5. 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.
    6. H. A. Eiselt & Vladimir Marianov, 2020. "Stability of utility functions and apportionment rules in location models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 772-792, October.
    7. 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.
    8. Roboredo, Marcos Costa & Pessoa, Artur Alves, 2013. "A branch-and-cut algorithm for the discrete (r∣p)-centroid problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 101-109.
    9. Vladimir Marianov & H. A. Eiselt, 2016. "On agglomeration in competitive location models," Annals of Operations Research, Springer, vol. 246(1), pages 31-55, November.
    10. 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.
    11. Wong, S. C., 1998. "Multi-commodity traffic assignment by continuum approximation of network flow with variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 567-581, November.
    12. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    13. Daniel Serra & Charles Revelle, 1994. "Competitive location in discrete space," Economics Working Papers 96, Department of Economics and Business, Universitat Pompeu Fabra.
    14. Christian Ahlin & Peter Ahlin, 2006. "Hotelling Was Right About Snob/Congestion Goods (Asymptotically)," Vanderbilt University Department of Economics Working Papers 0621, Vanderbilt University Department of Economics.
    15. Wenxuan Shan & Qianqian Yan & Chao Chen & Mengjie Zhang & Baozhen Yao & Xuemei Fu, 2019. "Optimization of competitive facility location for chain stores," Annals of Operations Research, Springer, vol. 273(1), pages 187-205, February.
    16. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
    17. Clara Campos Rodríguez & Dolores Santos Peñate & José Moreno Pérez, 2010. "An exact procedure and LP formulations for the leader—follower location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 97-121, July.
    18. Plastria, Frank, 2001. "Static competitive facility location: An overview of optimisation approaches," European Journal of Operational Research, Elsevier, vol. 129(3), pages 461-470, March.
    19. Rhim, Hosun & Ho, Teck H. & Karmarkar, Uday S., 2003. "Competitive location, production, and market selection," European Journal of Operational Research, Elsevier, vol. 149(1), pages 211-228, August.
    20. Rafael Suárez‐Vega & Dolores R. Santos‐Peñate & Pablo Dorta‐González, 2004. "Competitive Multifacility Location on Networks: the (r∣Xp)‐Medianoid Problem," Journal of Regional Science, Wiley Blackwell, vol. 44(3), pages 569-588, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:34:y:2000:i:2:p:216-227. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.