IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v270y2018i2p419-429.html
   My bibliography  Save this article

Fixed-parameter algorithms for rectilinear Steiner tree and rectilinear traveling salesman problem in the plane

Author

Listed:
  • Cambazard, Hadrien
  • Catusse, Nicolas

Abstract

Given a set P of n points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance considered between two points is the l1 distance. In this paper, a fixed-parameter algorithm for the Rectilinear TSP is presented and relies on techniques for solving TSP on bounded-treewidth graphs. It proves that the problem can be solved in O(nh7h) where h ≤ n denotes the number of horizontal lines containing the points of P. The same technique can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of P providing a O(nh5h) time complexity. Both bounds improve over the best time bounds known for these problems.

Suggested Citation

  • Cambazard, Hadrien & Catusse, Nicolas, 2018. "Fixed-parameter algorithms for rectilinear Steiner tree and rectilinear traveling salesman problem in the plane," European Journal of Operational Research, Elsevier, vol. 270(2), pages 419-429.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:419-429
    DOI: 10.1016/j.ejor.2018.03.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718302716
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.03.042?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. Donald Ratliff & Arnon S. Rosenthal, 1983. "Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem," Operations Research, INFORMS, vol. 31(3), pages 507-521, June.
    2. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    3. Roodbergen, Kees Jan & de Koster, Rene, 2001. "Routing order pickers in a warehouse with a middle aisle," European Journal of Operational Research, Elsevier, vol. 133(1), pages 32-43, August.
    4. Valle, Cristiano Arbex & Beasley, John E. & da Cunha, Alexandre Salles, 2017. "Optimally solving the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 817-834.
    5. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Saylam, Serhat & Çelik, Melih & Süral, Haldun, 2024. "Arc routing based compact formulations for picker routing in single and two block parallel aisle warehouses," European Journal of Operational Research, Elsevier, vol. 313(1), pages 225-240.
    2. Neves-Moreira, Fábio & Amorim, Pedro, 2024. "Learning efficient in-store picking strategies to reduce customer encounters in omnichannel retail," International Journal of Production Economics, Elsevier, vol. 267(C).
    3. Bock, Stefan, 2024. "Vehicle routing for connected service areas - a versatile approach covering single, hierarchical, and bi-criteria objectives," European Journal of Operational Research, Elsevier, vol. 313(3), pages 905-925.
    4. Briant, Olivier & Cambazard, Hadrien & Cattaruzza, Diego & Catusse, Nicolas & Ladier, Anne-Laure & Ogier, Maxime, 2020. "An efficient and general approach for the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 285(2), pages 497-512.
    5. Dmitry Kruchinin & Vladimir Kruchinin & Yuriy Shablya, 2021. "Method for Obtaining Coefficients of Powers of Bivariate Generating Functions," Mathematics, MDPI, vol. 9(4), pages 1-17, February.
    6. Rajabighamchi, Farzaneh & van Hoesel, Stan & Defryn, Christof, 2023. "The order picking problem under a scattered storage policy," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Mustapha Haouassi & Yannick Kergosien & Jorge E. Mendoza & Louis-Martin Rousseau, 2022. "The integrated orderline batching, batch scheduling, and picker routing problem with multiple pickers: the benefits of splitting customer orders," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 614-645, September.
    8. Maximilian Schiffer & Nils Boysen & Patrick S. Klein & Gilbert Laporte & Marco Pavone, 2022. "Optimal Picking Policies in E-Commerce Warehouses," Management Science, INFORMS, vol. 68(10), pages 7497-7517, October.
    9. AERTS, Babiche & CORNELISSENS, Trijntje & SÖRENSEN, Kenneth, 2020. "Solving the joint order batching and picker routing problem, as a clustered vehicle routing problem," Working Papers 2020003, University of Antwerp, Faculty of Business and Economics.
    10. Rajabighamchi, Farzaneh & van Hoesel, Stan & Defryn, Christof, 2023. "Graph reduction for the planar Travelling Salesman Problem," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Diefenbach, Heiko & Grosse, Eric H. & Glock, Christoph H., 2024. "Human-and-cost-centric storage assignment optimization in picker-to-parts warehouses," European Journal of Operational Research, Elsevier, vol. 315(3), pages 1049-1068.
    12. Boysen, Nils & de Koster, René & Füßler, David, 2021. "The forgotten sons: Warehousing systems for brick-and-mortar retail chains," European Journal of Operational Research, Elsevier, vol. 288(2), pages 361-381.

    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. Briant, Olivier & Cambazard, Hadrien & Cattaruzza, Diego & Catusse, Nicolas & Ladier, Anne-Laure & Ogier, Maxime, 2020. "An efficient and general approach for the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 285(2), pages 497-512.
    2. Sebastian Henn & André Scholz & Meike Stuhlmann & Gerhard Wäscher, 2015. "A New Mathematical Programming Formulation for the Single-Picker Routing Problem in a Single-Block Layout," FEMM Working Papers 150005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    3. Ardjmand, Ehsan & Shakeri, Heman & Singh, Manjeet & Sanei Bajgiran, Omid, 2018. "Minimizing order picking makespan with multiple pickers in a wave picking warehouse," International Journal of Production Economics, Elsevier, vol. 206(C), pages 169-183.
    4. Lu, Wenrong & McFarlane, Duncan & Giannikas, Vaggelis & Zhang, Quan, 2016. "An algorithm for dynamic order-picking in warehouse operations," European Journal of Operational Research, Elsevier, vol. 248(1), pages 107-122.
    5. Dominik Goeke & Michael Schneider, 2021. "Modeling Single-Picker Routing Problems in Classical and Modern Warehouses," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 436-451, May.
    6. Arbex Valle, Cristiano & Beasley, John E, 2020. "Order batching using an approximation for the distance travelled by pickers," European Journal of Operational Research, Elsevier, vol. 284(2), pages 460-484.
    7. Neves-Moreira, Fábio & Amorim, Pedro, 2024. "Learning efficient in-store picking strategies to reduce customer encounters in omnichannel retail," International Journal of Production Economics, Elsevier, vol. 267(C).
    8. André Scholz, 2016. "An Exact Solution Approach to the Single-Picker Routing Problem in Warehouses with an Arbitrary Block Layout," FEMM Working Papers 160006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    9. Scholz, André & Henn, Sebastian & Stuhlmann, Meike & Wäscher, Gerhard, 2016. "A new mathematical programming formulation for the Single-Picker Routing Problem," European Journal of Operational Research, Elsevier, vol. 253(1), pages 68-84.
    10. Çelik, Melih & Archetti, Claudia & Süral, Haldun, 2022. "Inventory routing in a warehouse: The storage replenishment routing problem," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1117-1132.
    11. Valle, Cristiano Arbex & Beasley, John E. & da Cunha, Alexandre Salles, 2017. "Optimally solving the joint order batching and picker routing problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 817-834.
    12. Scholz, André & Schubert, Daniel & Wäscher, Gerhard, 2017. "Order picking with multiple pickers and due dates – Simultaneous solution of Order Batching, Batch Assignment and Sequencing, and Picker Routing Problems," European Journal of Operational Research, Elsevier, vol. 263(2), pages 461-478.
    13. Yann Ruberg & André Scholz, 2016. "A Mathematical Programming Formulation for the Single-Picker Routing Problem in a Multi-Block Layout," FEMM Working Papers 160002, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    14. Mustapha Haouassi & Yannick Kergosien & Jorge E. Mendoza & Louis-Martin Rousseau, 2022. "The integrated orderline batching, batch scheduling, and picker routing problem with multiple pickers: the benefits of splitting customer orders," Flexible Services and Manufacturing Journal, Springer, vol. 34(3), pages 614-645, September.
    15. Saylam, Serhat & Çelik, Melih & Süral, Haldun, 2024. "Arc routing based compact formulations for picker routing in single and two block parallel aisle warehouses," European Journal of Operational Research, Elsevier, vol. 313(1), pages 225-240.
    16. Su, Yixuan & Zhu, Xi & Yuan, Jinlong & Teo, Kok Lay & Li, Meixia & Li, Chunfa, 2023. "An extensible multi-block layout warehouse routing optimization model," European Journal of Operational Research, Elsevier, vol. 305(1), pages 222-239.
    17. André Scholz & Daniel Schubert & Gerhard Wäscher, 2016. "Order picking with multiple pickers and due dates – Simultaneous solution of order batching, batch assignment and sequencing, and picker routing problems," FEMM Working Papers 160005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    18. Atashi Khoei, Arsham & Süral, Haldun & Tural, Mustafa Kemal, 2023. "Energy minimizing order picker forklift routing problem," European Journal of Operational Research, Elsevier, vol. 307(2), pages 604-626.
    19. AERTS, Babiche & CORNELISSENS, Trijntje & SÖRENSEN, Kenneth, 2020. "Solving the joint order batching and picker routing problem, as a clustered vehicle routing problem," Working Papers 2020003, University of Antwerp, Faculty of Business and Economics.
    20. Yu, M. & de Koster, M.B.M., 2007. "Performance Approximation and Design of Pick-and-Pass Order Picking Systems," ERIM Report Series Research in Management ERS-2007-082-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

    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:eee:ejores:v:270:y:2018:i:2:p:419-429. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.