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Scheduling School Buses

Author

Listed:
  • Arthur J. Swersey

    (School of Management, Yale University, Box 1A, New Haven, Connecticut 06520)

  • Wilson Ballard

    (American Graduate School of International Management, Phoenix, Arizona 85306)

Abstract

In the scheduling situation considered here, we are given a set of routes, each associated with a particular school. A single bus is assigned to each route, picking up the students and arriving at their school within a specified time window. The scheduling problem is to find the fewest buses needed to cover all the routes while meeting the time window specifications. We present two integer programming formulations of the scheduling problem and apply them to actual data from New Haven, Connecticut for two different years, as well as to 30 randomly generated problems. Linear programming relaxations of these integer programs were found to produce integer solutions more than 75 percent of the time. In the remaining cases, we found that the few fractional values can be adjusted to integer values without increasing the number of buses needed. Our method reduces the number of buses needed by about 25 percent compared to the manual solutions developed by the New Haven school bus scheduler.

Suggested Citation

  • Arthur J. Swersey & Wilson Ballard, 1984. "Scheduling School Buses," Management Science, INFORMS, vol. 30(7), pages 844-853, July.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:7:p:844-853
    DOI: 10.1287/mnsc.30.7.844
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    Citations

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    Cited by:

    1. Wang, Xiubin & Regan, Amelia C., 2002. "Local truckload pickup and delivery with hard time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 36(2), pages 97-112, February.
    2. M. Spada & M. Bierlaire & Th. M. Liebling, 2005. "Decision-Aiding Methodology for the School Bus Routing and Scheduling Problem," Transportation Science, INFORMS, vol. 39(4), pages 477-490, November.
    3. Byungjun Ju & Minsu Kim & Ilkyeong Moon, 2021. "Vehicle Routing Problem Considering Reconnaissance and Transportation," Sustainability, MDPI, vol. 13(6), pages 1-19, March.
    4. Park, Junhyuk & Kim, Byung-In, 2010. "The school bus routing problem: A review," European Journal of Operational Research, Elsevier, vol. 202(2), pages 311-319, April.
    5. Kim, Byung-In & Kim, Seongbae & Park, Junhyuk, 2012. "A school bus scheduling problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 577-585.
    6. Zolfagharinia, Hossein & Haughton, Michael, 2018. "The importance of considering non-linear layover and delay costs for local truckers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 109(C), pages 331-355.
    7. Guoqiang Shen & Zhangye Wang & Long Zhou & Yu Liu & Xiaoyi Yan, 2020. "Home-Based Locational Accessibility to Essential Urban Services: The Case of Wake County, North Carolina, USA," Sustainability, MDPI, vol. 12(21), pages 1-21, November.
    8. Banerjee, Dipayan & Smilowitz, Karen, 2019. "Incorporating equity into the school bus scheduling problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 228-246.
    9. Dasdemir, Erdi & Testik, Murat Caner & Öztürk, Diclehan Tezcaner & Şakar, Ceren Tuncer & Güleryüz, Güldal & Testik, Özlem Müge, 2022. "A multi-objective open vehicle routing problem with overbooking: Exact and heuristic solution approaches for an employee transportation problem," Omega, Elsevier, vol. 108(C).
    10. Zolfagharinia, Hossein & Haughton, Michael A., 2017. "Operational flexibility in the truckload trucking industry," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 437-460.
    11. Kuo, Yong-Hong & Leung, Janny M.Y. & Yan, Yimo, 2023. "Public transport for smart cities: Recent innovations and future challenges," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1001-1026.

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