IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v149y2011i2d10.1007_s10957-010-9783-1.html
   My bibliography  Save this article

Siting and Sizing of Facilities under Probabilistic Demands

Author

Listed:
  • Luís M. Fernandes

    (Instituto Politécnico de Tomar and Instituto de Telecomunicações)

  • Joaquim J. Júdice

    (Universidade de Coimbra and Instituto de Telecomunicações)

  • Hanif D. Sherali

    (Virginia Polytechnic Institute & State University)

  • António P. Antunes

    (Universidade de Coimbra)

Abstract

In this paper a discrete location model for non-essential service facilities planning is described, which seeks the number, location, and size of facilities, that maximizes the total expected demand attracted by the facilities. It is assumed that the demand for service is sensitive to the distance from facilities and to their size. It is also assumed that facilities must satisfy a threshold level of demand (facilities are not economically viable below that level). A Mixed-Integer Nonlinear Programming (MINLP) model is proposed for this problem. A branch-and-bound algorithm is designed for solving this MINLP and its convergence to a global minimum is established. A finite procedure is also introduced to find a feasible solution for the MINLP that reduces the overall search in the binary tree generated by the branch-and-bound algorithm. Some numerical results using a GAMS/MINOS implementation of the algorithm are reported to illustrate its efficacy and efficiency in practice.

Suggested Citation

  • Luís M. Fernandes & Joaquim J. Júdice & Hanif D. Sherali & António P. Antunes, 2011. "Siting and Sizing of Facilities under Probabilistic Demands," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 420-440, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9783-1
    DOI: 10.1007/s10957-010-9783-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9783-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-010-9783-1?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. ReVelle, C. S. & Eiselt, H. A., 2005. "Location analysis: A synthesis and survey," European Journal of Operational Research, Elsevier, vol. 165(1), pages 1-19, August.
    2. Ennio Cascetta, 2009. "Transportation Systems Analysis," Springer Optimization and Its Applications, Springer, number 978-0-387-75857-2, December.
    3. Jossef Perl & Peng-Kuan Ho, 1990. "Public Facilities Location under Elastic Demand," Transportation Science, INFORMS, vol. 24(2), pages 117-136, May.
    4. Oded Berman & Dmitry Krass, 2002. "Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures," Annals of Operations Research, Springer, vol. 111(1), pages 197-225, March.
    5. Krarup, Jakob & Pruzan, Peter Mark, 1983. "The simple plant location problem: Survey and synthesis," European Journal of Operational Research, Elsevier, vol. 12(1), pages 36-57, January.
    6. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location and design problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 40-62, October.
    Full references (including those not matched with items on IDEAS)

    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. Luís M. Fernandes & Joaquim J. Júdice & Hanif D. Sherali & António P. Antunes, 2013. "Siting and Sizing of Facilities under Probabilistic Demands," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 284-304, July.
    2. Blas Pelegrín & Pascual Fernández & María Dolores García Pérez, 2016. "Profit maximization and reduction of the cannibalization effect in chain expansion," Annals of Operations Research, Springer, vol. 246(1), pages 57-75, November.
    3. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
    4. Junjie Wu & Jian Chen & Yili Ren, 2011. "GIS enabled service site selection: Environmental analysis and beyond," Information Systems Frontiers, Springer, vol. 13(3), pages 337-348, July.
    5. Lin, Yun Hui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Omnichannel facility location and fulfillment optimization," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 187-209.
    6. 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.
    7. Christian Burkart & Pamela C. Nolz & Walter J. Gutjahr, 2017. "Modelling beneficiaries’ choice in disaster relief logistics," Annals of Operations Research, Springer, vol. 256(1), pages 41-61, September.
    8. H Küçükaydın & N Aras & İ K Altınel, 2011. "A discrete competitive facility location model with variable attractiveness," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(9), pages 1726-1741, September.
    9. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2021. "Optimizing facility location and design," European Journal of Operational Research, Elsevier, vol. 289(1), pages 31-43.
    10. Kung, Ling-Chieh & Liao, Wei-Hung, 2018. "An approximation algorithm for a competitive facility location problem with network effects," European Journal of Operational Research, Elsevier, vol. 267(1), pages 176-186.
    11. Pelegrín, Blas & Fernández, Pascual & Dolores García Pérez, María & Cano Hernández, Saúl, 2012. "On the location of new facilities for chain expansion under delivered pricing," Omega, Elsevier, vol. 40(2), pages 149-158, April.
    12. H K Smith & G Laporte & P R Harper, 2009. "Locational analysis: highlights of growth to maturity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 140-148, May.
    13. Pelegrín, Mercedes, 2023. "New variants of the simple plant location problem and applications," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1094-1108.
    14. Zhang, Yue & Liang, Liping & Liu, Emma & Chen, Chong & Atkins, Derek, 2016. "Patient choice analysis and demand prediction for a health care diagnostics company," European Journal of Operational Research, Elsevier, vol. 251(1), pages 198-205.
    15. Gohram Baloch & Fatma Gzara, 2020. "Strategic Network Design for Parcel Delivery with Drones Under Competition," Transportation Science, INFORMS, vol. 54(1), pages 204-228, January.
    16. Rezapour, Shabnam & Farahani, Reza Zanjirani & Dullaert, Wout & De Borger, Bruno, 2014. "Designing a new supply chain for competition against an existing supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 124-140.
    17. Derya Celik Turkoglu & Mujde Erol Genevois, 2020. "A comparative survey of service facility location problems," Annals of Operations Research, Springer, vol. 292(1), pages 399-468, September.
    18. Dong-Guen Kim & Yeong-Dae Kim, 2013. "A Lagrangian heuristic algorithm for a public healthcare facility location problem," Annals of Operations Research, Springer, vol. 206(1), pages 221-240, July.
    19. Chandra Ade Irawan & Dylan Jones, 2019. "Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities," Annals of Operations Research, Springer, vol. 272(1), pages 41-67, January.
    20. Hammami, Ramzi & Frein, Yannick & Hadj-Alouane, Atidel B., 2009. "A strategic-tactical model for the supply chain design in the delocalization context: Mathematical formulation and a case study," International Journal of Production Economics, Elsevier, vol. 122(1), pages 351-365, November.

    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:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9783-1. 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.