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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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