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The maximum covering problem with travel time uncertainty

Author

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  • Oded Berman
  • Iman Hajizadeh
  • Dmitry Krass

Abstract

Both public and private facilities often have to provide adequate service under a variety of conditions. In particular travel times, that determine customer access, change due to changing traffic patterns throughout the day, as well as a result of special events ranging from traffic accidents to natural disasters. This article studies the maximum covering location problem on a network with travel time uncertainty represented by different travel time scenarios. Three model types—expected covering, robust covering, and expected p-robust covering—are studied; each one is appropriate for different types of facilities operating under different conditions. Exact and approximate algorithms are developed. The models are applied to the analysis of the location of fire stations in the city of Toronto. Using real traffic data it is shown that the current system design is quite far from optimality. The best locations for the four new fire stations that the city of Toronto is planning to add to the system are determined and alternative improvement plans are discussed.

Suggested Citation

  • Oded Berman & Iman Hajizadeh & Dmitry Krass, 2013. "The maximum covering problem with travel time uncertainty," IISE Transactions, Taylor & Francis Journals, vol. 45(1), pages 81-96.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:1:p:81-96
    DOI: 10.1080/0740817X.2012.689121
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    Citations

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    Cited by:

    1. Zhizhu Lai & Qun Yue & Zheng Wang & Dongmei Ge & Yulong Chen & Zhihong Zhou, 2022. "The min-p robust optimization approach for facility location problem under uncertainty," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1134-1160, September.
    2. Bakker, Hannah & Diehlmann, Florian & Wiens, Marcus & Nickel, Stefan & Schultmann, Frank, 2023. "School or parking lot? Selecting locations for points of distribution in urban disasters," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    3. Hamed Kazemipoor & Mohammad Ebrahim Sadeghi & Agnieszka Szmelter-Jarosz & Mohadese Aghabozorgi, 2022. "Providing a model for the issue of multi-period ambulance location," Papers 2206.11811, arXiv.org.
    4. Berman, Oded & Hajizadeh, Iman & Krass, Dmitry & Rahimi-Vahed, Alireza, 2018. "Reconfiguring a set of coverage-providing facilities under travel time uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 62(C), pages 1-12.
    5. Zhang, Sizhe & Cardin, Michel-Alexandre, 2017. "Flexibility and real options analysis in emergency medical services systems using decision rules and multi-stage stochastic programming," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 120-140.
    6. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    7. Wang, Wei & Wang, Shuaian & Zhen, Lu & Qu, Xiaobo, 2022. "EMS location-allocation problem under uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    8. Farahani, Reza Zanjirani & Fallah, Samira & Ruiz, Rubén & Hosseini, Sara & Asgari, Nasrin, 2019. "OR models in urban service facility location: A critical review of applications and future developments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 1-27.
    9. Chao-Hsien Yeh & Yi-Ru Chen, 2020. "Location model analysis of flood relief facilities: a case study of the Fazih River floodplain, Taiwan," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(1), pages 317-327, August.
    10. Fang Zong & Meng Zeng & Yang Cao & Yixuan Liu, 2021. "Local Dynamic Path Planning for an Ambulance Based on Driving Risk and Attraction Field," Sustainability, MDPI, vol. 13(6), pages 1-13, March.

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