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Optimal 2-Facility Network Districting in the Presence of Queuing

Author

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  • Oded Berman

    (University of Calgary, Calgary, Alberta, Canada)

  • Richard C. Larson

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

This paper considers a districting problem for a demand-responsive service system in which queuing is allowed. Customers, located at the nodes of a transportation network, call in a Poisson manner, asking for on-scene service by a mobile service unit. Two such units service the entire network, with unit i ( i = 1, 2) responsible for all nodes N i in its unique “service territory.” In response to a call from within N ı , unit i , if available, is dispatched immediately to the customer; if the unit is busy with a previous customer, the call is dispatched in a FIFO manner. Each service territory, with its response unit, behaves as an independently operating M / G /1 queuing system. The problem addressed in this paper is determination of the optimal service territories, given fixed home locations for each of the service units, so as to minimize the average response time (queuing delay plus travel time) to a random customer. Exact results are obtained for limiting values of demand rate, and efficient heuristics are presented for arbitrary demand rates.

Suggested Citation

  • Oded Berman & Richard C. Larson, 1985. "Optimal 2-Facility Network Districting in the Presence of Queuing," Transportation Science, INFORMS, vol. 19(3), pages 261-277, August.
    • Handle: RePEc:inm:ortrsc:v:19:y:1985:i:3:p:261-277
    DOI: 10.1287/trsc.19.3.261
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    Citations

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    Cited by:

    1. Prahalad Venkateshan & Kamlesh Mathur, 2015. "A Heuristic for the Multisource Weber Problem with Service Level Constraints," Transportation Science, INFORMS, vol. 49(3), pages 472-483, August.
    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. Drexl, Andreas & Klose, Andreas, 2001. "Facility location models for distribution system design," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 546, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    4. Oded Berman & Zvi Drezner & Arie Tamir & George Wesolowsky, 2009. "Optimal location with equitable loads," Annals of Operations Research, Springer, vol. 167(1), pages 307-325, March.
    5. Pouraliakbari-Mamaghani, Mahsa & Saif, Ahmed & Kamal, Noreen, 2023. "Reliable design of a congested disaster relief network: A two-stage stochastic-robust optimization approach," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    6. Mahsa Pouraliakbari-Mamaghani & Ali Ghodratnama & Seyed Hamid Reza Pasandideh & Ahmed Saif, 2022. "A robust possibilistic programming approach for blood supply chain network design in disaster relief considering congestion," Operational Research, Springer, vol. 22(3), pages 1987-2032, July.
    7. Sourirajan, Karthik & Ozsen, Leyla & Uzsoy, Reha, 2009. "A genetic algorithm for a single product network design model with lead time and safety stock considerations," European Journal of Operational Research, Elsevier, vol. 197(2), pages 599-608, September.
    8. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    9. 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.
    10. Warsing, Donald P. & Souza, Gilvan C. & Greis, Noel P., 2001. "Determining the value of dedicated multimodal cargo facilities in a multi-region distribution network," European Journal of Operational Research, Elsevier, vol. 133(1), pages 81-93, August.

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