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On Insensitivities in Urban Redistricting and Facility Location

Author

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  • Richard C. Larson

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Keith A. Stevenson

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

This paper considers one class of problems associated with urban service systems that dispatch vehicles from fixed facilities. Given the limited resources available, one important issue is the location of the facilities and the design of their response districts to minimize average response time in the face of spatially distributed demand patterns. Calculations with spatially homogeneous demands suggest that the mean travel time resulting from totally random distribution of facilities in the region served is reduced by only 25 per cent when the facilities are optimally distributed. This apparent insensitivity of mean travel time to facility location is pursued in detail by analyzing two classes of systems involving a pair of facilities. In the first case, a procedure is outlined for determining the optimal location of a second facility, given a position for the first facility, when no interfacility cooperation is allowed. In the second case, the same region is examined, but allowing a form of interfacility cooperation. These simple models suggest that, because of insensitivities, it may not be necessary to quantize geographical data finely and then to try laboriously to find the “optimal” solutions to redistricting and facility-location problems. Redistricting and facility location based on rather crude assumptions and an awareness of some of the heuristic properties illustrated by simple analytical models may yield mean travel times very near the minimum possible.

Suggested Citation

  • Richard C. Larson & Keith A. Stevenson, 1972. "On Insensitivities in Urban Redistricting and Facility Location," Operations Research, INFORMS, vol. 20(3), pages 595-612, June.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:3:p:595-612
    DOI: 10.1287/opre.20.3.595
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    Cited by:

    1. L Bach, 1981. "The Problem of Aggregation and Distance for Analyses of Accessibility and Access Opportunity in Location-Allocation Models," Environment and Planning A, , vol. 13(8), pages 955-978, August.
    2. Liu, Han & Hua, Cheng & Lei, Chao, 2021. "Planning for time-varying volunteer firefighter systems under probabilistic service disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    3. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    4. Fang Wei & Wenwen Xu & Chen Hua, 2022. "A Multi-Objective Optimization of Physical Activity Spaces," Land, MDPI, vol. 11(11), pages 1-17, November.
    5. Gregory Dobson & Euthemia Stavrulaki, 2007. "Simultaneous price, location, and capacity decisions on a line of time‐sensitive customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 1-10, February.
    6. 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.
    7. Richard Charles Larson, 2002. "Public Sector Operations Research: A Personal Journey," Operations Research, INFORMS, vol. 50(1), pages 135-145, February.
    8. Batta, Rajan & Lejeune, Miguel & Prasad, Srinivas, 2014. "Public facility location using dispersion, population, and equity criteria," European Journal of Operational Research, Elsevier, vol. 234(3), pages 819-829.
    9. Geroliminis, Nikolas & Karlaftis, Matthew G. & Skabardonis, Alexander, 2009. "A spatial queuing model for the emergency vehicle districting and location problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 798-811, August.
    10. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.

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