IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v61y2010i6d10.1057_jors.2009.12.html
   My bibliography  Save this article

Location of single-server immobile facilities subject to a loss constraint

Author

Listed:
  • B Boffey

    (University of Liverpool
    Staffordshire University)

  • R D Galvão

    (COPPE/Federal University of Rio de Janeiro)

  • V Marianov

    (Pontificia Universidad Católica de Chile)

Abstract

Waiting may be unacceptable, even a short time, at a facility providing a service involving medical or other emergencies. Hence, it is appropriate to locate such facilities so that the rate at which users are lost is limited. Each facility will here be modelled as an M/E r /m/N queueing system subject to a loss restriction constraint and the single-server case (m=1) will be treated in detail. Introduction of the Erlang distribution for service times allows a better fit of the model to actual values of both mean and variance than do currently available models that use an exponential distribution. Location of facilities will be such that the average travel time to a facility is minimized. It is shown how a deterministic constraint, equivalent to the loss constraint, can be generated resulting in an integer linear program, and values of a parameter ρ c which facilitates this linearization are tabulated for various values of r, N and service level demanded. Numerical experiments are performed including an application loosely related to the location of neonatal clinics in the Municipality of Rio de Janeiro. Finally, there is a discussion of how further improved modelling of the service time distribution might be effected.

Suggested Citation

  • B Boffey & R D Galvão & V Marianov, 2010. "Location of single-server immobile facilities subject to a loss constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(6), pages 987-999, June.
    • Handle: RePEc:pal:jorsoc:v:61:y:2010:i:6:d:10.1057_jors.2009.12
    DOI: 10.1057/jors.2009.12
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/jors.2009.12
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/jors.2009.12?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. Marianov, Vladimir & Serra, Daniel, 2001. "Hierarchical location-allocation models for congested systems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 195-208, November.
    2. Vladimir Marianov & Daniel Serra, 1994. "Probabilistic maximal covering location models for congested systems," Economics Working Papers 70, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Vladimir Marianov, 2003. "Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential," Annals of Operations Research, Springer, vol. 123(1), pages 125-141, October.
    4. Vladimir Marianov & Daniel Serra, 2000. "Location models for airline hubs behaving as M/D/c queues," Economics Working Papers 453, Department of Economics and Business, Universitat Pompeu Fabra.
    5. B Boffey & D Yates & R D Galvão, 2003. "An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 21-31, January.
    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. Yang, Woosuk, 2018. "A user-choice model for locating congested fast charging stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 110(C), pages 189-213.

    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. V Marianov & T B Boffey & R D Galvão, 2009. "Optimal location of multi-server congestible facilities operating as M/E r /m/N queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(5), pages 674-684, May.
    2. Boffey, Brian & Galvao, Roberto & Espejo, Luis, 2007. "A review of congestion models in the location of facilities with immobile servers," European Journal of Operational Research, Elsevier, vol. 178(3), pages 643-662, May.
    3. Daniel Serra & Francisco Silva, 2002. "Locating emergency services with priority rules: The priority queuing covering location problem," Economics Working Papers 642, Department of Economics and Business, Universitat Pompeu Fabra, revised May 2008.
    4. 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.
    5. Teodora Dan & Patrice Marcotte, 2019. "Competitive Facility Location with Selfish Users and Queues," Operations Research, INFORMS, vol. 67(2), pages 479-497, March.
    6. Galvao, Roberto D. & Acosta Espejo, Luis Gonzalo & Boffey, Brian & Yates, Derek, 2006. "Load balancing and capacity constraints in a hierarchical location model," European Journal of Operational Research, Elsevier, vol. 172(2), pages 631-646, July.
    7. O Berman & Z Drezner, 2007. "The multiple server location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 91-99, January.
    8. Marianov, Vladimir & Serra, Daniel, 2001. "Hierarchical location-allocation models for congested systems," European Journal of Operational Research, Elsevier, vol. 135(1), pages 195-208, November.
    9. P R Harper & S Phillips & J E Gallagher, 2005. "Geographical simulation modelling for the regional planning of oral and maxillofacial surgery across London," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(2), pages 134-143, February.
    10. Jayaswal, Sachin & Vidyarthi, Navneet, 2013. "Capacitated Multiple Allocation Hub Location with Service Level Constraints for Multiple Consignment Classes," IIMA Working Papers WP2013-11-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    11. Daniel Serra, 2003. "Location of multiple server common service centers or public facilities for minimizing general congestion and travel cost functions," Economics Working Papers 658, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Mohammad Yavari & Mohammad Mousavi-Saleh, 2021. "Restructuring hierarchical capacitated facility location problem with extended coverage radius under uncertainty," Operational Research, Springer, vol. 21(1), pages 91-138, March.
    13. Francisco Silva & Daniel Serra, 2007. "Incorporating Waiting Time in Competitive Location Models," Networks and Spatial Economics, Springer, vol. 7(1), pages 63-76, March.
    14. Caccavale, Maria Virginia & Iovanella, Antonio & Lancia, Carlo & Lulli, Guglielmo & Scoppola, Benedetto, 2014. "A model of inbound air traffic: The application to Heathrow airport," Journal of Air Transport Management, Elsevier, vol. 34(C), pages 116-122.
    15. Alumur, Sibel A. & Nickel, Stefan & Saldanha-da-Gama, Francisco, 2012. "Hub location under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 46(4), pages 529-543.
    16. Shariat-Mohaymany, Afshin & Babaei, Mohsen & Moadi, Saeed & Amiripour, Sayyed Mahdi, 2012. "Linear upper-bound unavailability set covering models for locating ambulances: Application to Tehran rural roads," European Journal of Operational Research, Elsevier, vol. 221(1), pages 263-272.
    17. Jayaswal, Sachin, 2014. "Emergency Medical Service System Design under Service Level Constraints for Heterogeneous Patients," IIMA Working Papers WP2014-11-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    18. Soo-Haeng Cho & Hoon Jang & Taesik Lee & John Turner, 2014. "Simultaneous Location of Trauma Centers and Helicopters for Emergency Medical Service Planning," Operations Research, INFORMS, vol. 62(4), pages 751-771, August.
    19. Vladimir Marianov & Daniel Serra, 2000. "Location models for airline hubs behaving as M/D/c queues," Economics Working Papers 453, Department of Economics and Business, Universitat Pompeu Fabra.
    20. Robert Cromley & Dean Hanink, 2008. "Population growth and the development of a central place system," Journal of Geographical Systems, Springer, vol. 10(4), pages 383-405, December.

    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:pal:jorsoc:v:61:y:2010:i:6:d:10.1057_jors.2009.12. 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.palgrave-journals.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.