IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v22y2014i1p144-169.html
   My bibliography  Save this article

Comparative error bound theory for three location models: continuous demand versus discrete demand

Author

Listed:
  • Richard Francis
  • Timothy Lowe

Abstract

We develop a unified error bound theory to compare a given p-median, p-center or covering location model with continuously distributed demand points in R n to a corresponding given original model of the same type having a finite collection of demand points in R n . We give ways to construct either a continuous or finite demand point model from the other model and also control the error bound. Our work uses Voronoi tilings extensively, and is related to earlier error bound theory for aggregating finitely many demand points. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:1:p:144-169
    DOI: 10.1007/s11750-011-0244-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-011-0244-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-011-0244-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Hodgson & Jared Hewko, 2003. "Aggregation and Surrogation Error in the p-Median Model," Annals of Operations Research, Springer, vol. 123(1), pages 53-66, October.
    2. Yanfeng Ouyang & Carlos F. Daganzo, 2006. "Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design," Transportation Science, INFORMS, vol. 40(1), pages 89-98, February.
    3. Erdemir, Elif Tokar & Batta, Rajan & Spielman, Seth & Rogerson, Peter A. & Blatt, Alan & Flanigan, Marie, 2008. "Location coverage models with demand originating from nodes and paths: Application to cellular network design," European Journal of Operational Research, Elsevier, vol. 190(3), pages 610-632, November.
    4. Tingting Cui & Yanfeng Ouyang & Zuo-Jun Max Shen, 2010. "Reliable Facility Location Design Under the Risk of Disruptions," Operations Research, INFORMS, vol. 58(4-part-1), pages 998-1011, August.
    5. Naveen Donthu & Roland T. Rust, 1989. "Note—Estimating Geographic Customer Densities Using Kernel Density Estimation," Marketing Science, INFORMS, vol. 8(2), pages 191-203.
    6. Arthur M. Geoffrion, 1976. "The Purpose of Mathematical Programming is Insight, Not Numbers," Interfaces, INFORMS, vol. 7(1), pages 81-92, November.
    7. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    8. Evan L. Porteus & Jonathan S. Yormark, 1972. "More on Min-Max Allocation," Management Science, INFORMS, vol. 18(9), pages 502-507, May.
    9. 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.
    10. B. C. Tansel & R. L. Francis & T. J. Lowe & M. L. Chen, 1982. "Duality and Distance Constraints for the Nonlinear p -Center Problem and Covering Problem on a Tree Network," Operations Research, INFORMS, vol. 30(4), pages 725-744, August.
    11. Cui, Tingting & Ouyang, Yanfeng & Shen, Zuo-Jun Max J, 2010. "Reliable Facility Location Design under the Risk of Disruptions," University of California Transportation Center, Working Papers qt5sh2c7pw, University of California Transportation Center.
    12. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    13. Okabe, Atsuyuki & Suzuki, Atsuo, 1997. "Locational optimization problems solved through Voronoi diagrams," European Journal of Operational Research, Elsevier, vol. 98(3), pages 445-456, May.
    14. Gabriel Y. Handler, 1985. "Medi-Centers of a Tree," Transportation Science, INFORMS, vol. 19(3), pages 246-260, August.
    15. Frank Plastria, 2001. "On the choice of aggregation points for continuousp-median problems: A case for the gravity centre," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 217-242, December.
    16. Jonathan Halpern, 1978. "Finding Minimal Center-Median Convex Combination (Cent-Dian) of a Graph," Management Science, INFORMS, vol. 24(5), pages 535-544, January.
    17. Suzuki, Atsuo & Drezner, Zvi, 2009. "The minimum equitable radius location problem with continuous demand," European Journal of Operational Research, Elsevier, vol. 195(1), pages 17-30, May.
    18. David F. Rogers & Robert D. Plante & Richard T. Wong & James R. Evans, 1991. "Aggregation and Disaggregation Techniques and Methodology in Optimization," Operations Research, INFORMS, vol. 39(4), pages 553-582, August.
    19. S. L. Hakimi, 1965. "Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems," Operations Research, INFORMS, vol. 13(3), pages 462-475, June.
    20. Stephen Jacobsen, 1971. "On Marginal Allocation in Single Constraint Min-Max Problems," Management Science, INFORMS, vol. 17(11), pages 780-783, July.
    21. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, 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. Ran Wei, 2016. "Coverage Location Models," International Regional Science Review, , vol. 39(1), pages 48-76, January.
    2. Juana L. Redondo & Alfredo Marín & Pilar M. Ortigosa, 2016. "A parallelized Lagrangean relaxation approach for the discrete ordered median problem," Annals of Operations Research, Springer, vol. 246(1), pages 253-272, November.

    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. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    2. 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.
    3. R. Francis & T. Lowe & M. Rayco & A. Tamir, 2009. "Aggregation error for location models: survey and analysis," Annals of Operations Research, Springer, vol. 167(1), pages 171-208, March.
    4. R. L. Francis & T. J. Lowe & Arie Tamir, 2000. "Aggregation Error Bounds for a Class of Location Models," Operations Research, INFORMS, vol. 48(2), pages 294-307, April.
    5. Li, Hongmei & Luo, Taibo & Xu, Yinfeng & Xu, Jiuping, 2018. "Minimax regret vertex centdian location problem in general dynamic networks," Omega, Elsevier, vol. 75(C), pages 87-96.
    6. Daoqin Tong & Alan T. Murray, 2009. "Maximising coverage of spatial demand for service," Papers in Regional Science, Wiley Blackwell, vol. 88(1), pages 85-97, March.
    7. Lei, Chao & Ouyang, Yanfeng, 2018. "Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 90-109.
    8. R.L. Francis & T.J. Lowe & M.B. Rayco & A. Tamir, 2003. "Exploiting self‐canceling demand point aggregation error for some planar rectilinear median location problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 614-637, September.
    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. Yun, Lifen & Qin, Yong & Fan, Hongqiang & Ji, Changxu & Li, Xiaopeng & Jia, Limin, 2015. "A reliability model for facility location design under imperfect information," Transportation Research Part B: Methodological, Elsevier, vol. 81(P2), pages 596-615.
    11. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    12. Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
    13. Sune Lauth Gadegaard & Andreas Klose & Lars Relund Nielsen, 2018. "A bi-objective approach to discrete cost-bottleneck location problems," Annals of Operations Research, Springer, vol. 267(1), pages 179-201, August.
    14. Xin Wang & Michael K. Lim & Yanfeng Ouyang, 2017. "A Continuum Approximation Approach to the Dynamic Facility Location Problem in a Growing Market," Transportation Science, INFORMS, vol. 51(1), pages 343-357, February.
    15. Michael K. Lim & Achal Bassamboo & Sunil Chopra & Mark S. Daskin, 2013. "Facility Location Decisions with Random Disruptions and Imperfect Estimation," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 239-249, May.
    16. O’Hanley, Jesse R. & Scaparra, M. Paola & García, Sergio, 2013. "Probability chains: A general linearization technique for modeling reliability in facility location and related problems," European Journal of Operational Research, Elsevier, vol. 230(1), pages 63-75.
    17. Mozhu Wang & Jianming Yao, 2023. "A reliable location design of unmanned vending machines based on customer satisfaction," Electronic Commerce Research, Springer, vol. 23(1), pages 541-575, March.
    18. Xinxin Yan & Hanping Hou & Jianliang Yang & Jiaqi Fang, 2021. "Site Selection and Layout of Material Reserve Based on Emergency Demand Graduation under Large-Scale Earthquake," Sustainability, MDPI, vol. 13(3), pages 1-15, January.
    19. Yun Bai & Xiaopeng Li & Fan Peng & Xin Wang & Yanfeng Ouyang, 2015. "Effects of Disruption Risks on Biorefinery Location Design," Energies, MDPI, vol. 8(2), pages 1-19, February.
    20. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.

    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:spr:topjnl:v:22:y:2014:i:1:p:144-169. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.