IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v53y2019i6p1656-1672.html
   My bibliography  Save this article

The Covering Path Problem on a Grid

Author

Listed:
  • Liwei Zeng

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Sunil Chopra

    (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

  • Karen Smilowitz

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

This paper introduces the covering path problem on a grid (CPPG) that finds the cost-minimizing path connecting a subset of points in a grid such that each point that needs to be covered is within a predetermined distance of a point from the chosen subset. We leverage the geometric properties of the grid graph, which captures the road network structure in many transportation problems, including our motivating setting of school bus routing. As defined in this paper, the CPPG is a biobjective optimization problem comprising one cost term related to path length and one cost term related to stop count. We develop a trade-off constraint, which quantifies the trade-off between path length and stop count and provides a lower bound for the biobjective optimization problem. We introduce simple construction techniques to provide feasible paths that match the lower bound within a constant factor. Importantly, this solution approach uses transformations of the general CPPG to either a discrete CPPG or continuous CPPG based on the value of the coverage radius. For both the discrete and continuous versions, we provide fast constant-factor approximations, thus solving the general CPPG.

Suggested Citation

  • Liwei Zeng & Sunil Chopra & Karen Smilowitz, 2019. "The Covering Path Problem on a Grid," Transportation Science, INFORMS, vol. 53(6), pages 1656-1672, November.
  • Handle: RePEc:inm:ortrsc:v:53:y:2019:i:6:p:1656-1672
    DOI: 10.1287/trsc.2019.0901
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2019.0901
    Download Restriction: no

    File URL: https://libkey.io/10.1287/trsc.2019.0901?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Selçuk Savaş & Rajan Batta & Rakesh Nagi, 2002. "Finite-Size Facility Placement in the Presence of Barriers to Rectilinear Travel," Operations Research, INFORMS, vol. 50(6), pages 1018-1031, December.
    2. Drexl, Michael & Schneider, Michael, 2015. "A survey of variants and extensions of the location-routing problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 283-308.
    3. Newton, Rita M. & Thomas, Warren H., 1969. "Design of school bus routes by computer," Socio-Economic Planning Sciences, Elsevier, vol. 3(1), pages 75-85, June.
    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. Lawrence D. Bodin & Lon Berman, 1979. "Routing and Scheduling of School Buses by Computer," Transportation Science, INFORMS, vol. 13(2), pages 113-129, May.
    6. Michel Gendreau & Gilbert Laporte & Frédéric Semet, 1997. "The Covering Tour Problem," Operations Research, INFORMS, vol. 45(4), pages 568-576, August.
    7. Prodhon, Caroline & Prins, Christian, 2014. "A survey of recent research on location-routing problems," European Journal of Operational Research, Elsevier, vol. 238(1), pages 1-17.
    8. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    9. Schittekat, Patrick & Kinable, Joris & Sörensen, Kenneth & Sevaux, Marc & Spieksma, Frits & Springael, Johan, 2013. "A metaheuristic for the school bus routing problem with bus stop selection," European Journal of Operational Research, Elsevier, vol. 229(2), pages 518-528.
    10. Maria Albareda-Sambola, 2015. "Location-Routing and Location-Arc Routing," Springer Books, in: Gilbert Laporte & Stefan Nickel & Francisco Saldanha da Gama (ed.), Location Science, edition 127, chapter 0, pages 399-418, Springer.
    11. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    12. Gavish, B. & Shlifer, E., 1979. "An approach for solving a class of transportation scheduling problems," European Journal of Operational Research, Elsevier, vol. 3(2), pages 122-134, March.
    13. Joaquín Pacheco & Rafael Caballero & Manuel Laguna & Julián Molina, 2013. "Bi-Objective Bus Routing: An Application to School Buses in Rural Areas," Transportation Science, INFORMS, vol. 47(3), pages 397-411, August.
    14. John R. Current & David A. Schilling, 1989. "The Covering Salesman Problem," Transportation Science, INFORMS, vol. 23(3), pages 208-213, August.
    15. Bowerman, Robert & Hall, Brent & Calamai, Paul, 1995. "A multi-objective optimization approach to urban school bus routing: Formulation and solution method," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 107-123, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ellegood, William A. & Solomon, Stanislaus & North, Jeremy & Campbell, James F., 2020. "School bus routing problem: Contemporary trends and research directions," Omega, Elsevier, vol. 95(C).
    2. Hernan Caceres & Rajan Batta & Qing He, 2017. "School Bus Routing with Stochastic Demand and Duration Constraints," Transportation Science, INFORMS, vol. 51(4), pages 1349-1364, November.
    3. Herminia I. Calvete & Carmen Galé & José A. Iranzo, 2022. "Approaching the Pareto Front in a Biobjective Bus Route Design Problem Dealing with Routing Cost and Individuals’ Walking Distance by Using a Novel Evolutionary Algorithm," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    4. Arslan, Okan, 2021. "The location-or-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 1-21.
    5. 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.
    6. Fischer, Vera & Pacheco Paneque, Meritxell & Legrain, Antoine & Bürgy, Reinhard, 2024. "A capacitated multi-vehicle covering tour problem on a road network and its application to waste collection," European Journal of Operational Research, Elsevier, vol. 315(1), pages 338-353.
    7. Fátima M. Souza Lima & Davi S. D. Pereira & Samuel V. Conceição & Ricardo S. Camargo, 2017. "A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads," 4OR, Springer, vol. 15(4), pages 359-386, December.
    8. 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.
    9. Veenstra, Marjolein & Roodbergen, Kees Jan & Coelho, Leandro C. & Zhu, Stuart X., 2018. "A simultaneous facility location and vehicle routing problem arising in health care logistics in the Netherlands," European Journal of Operational Research, Elsevier, vol. 268(2), pages 703-715.
    10. Olmez, Omer Berk & Gultekin, Ceren & Balcik, Burcu & Ekici, Ali & Özener, Okan Örsan, 2022. "A variable neighborhood search based matheuristic for a waste cooking oil collection network design problem," European Journal of Operational Research, Elsevier, vol. 302(1), pages 187-202.
    11. 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).
    12. Koç, Çağrı & Bektaş, Tolga & Jabali, Ola & Laporte, Gilbert, 2016. "The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm," European Journal of Operational Research, Elsevier, vol. 248(1), pages 33-51.
    13. Alessandro Hill & Roberto Baldacci & Edna Ayako Hoshino, 2019. "Capacitated ring arborescence problems with profits," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 357-389, June.
    14. Xiaopan Chen & Yunfeng Kong & Lanxue Dang & Yane Hou & Xinyue Ye, 2015. "Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-20, July.
    15. Herminia I. Calvete & Carmen Galé & José A. Iranzo & Paolo Toth, 2020. "A Partial Allocation Local Search Matheuristic for Solving the School Bus Routing Problem with Bus Stop Selection," Mathematics, MDPI, vol. 8(8), pages 1-20, July.
    16. Ellegood, William A. & Campbell, James F. & North, Jeremy, 2015. "Continuous approximation models for mixed load school bus routing," Transportation Research Part B: Methodological, Elsevier, vol. 77(C), pages 182-198.
    17. Agyeman, Stephen & Cheng, Lin, 2020. "Analysis of barriers to perceived service quality in Ghana: Students’ perspectives on bus mobility attributes," Transport Policy, Elsevier, vol. 99(C), pages 63-85.
    18. 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.
    19. Shichao Sun & Zhengyu Duan & Qi Xu, 2018. "School bus routing problem in the stochastic and time-dependent transportation network," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-17, August.
    20. Zang, Xiaoning & Jiang, Li & Liang, Changyong & Fang, Xiang, 2023. "Coordinated home and locker deliveries: An exact approach for the urban delivery problem with conflicting time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:53:y:2019:i:6:p:1656-1672. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.