IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v116y2023ics0305048322002225.html
   My bibliography  Save this article

Approximations for many-visits multiple traveling salesman problems

Author

Listed:
  • Bérczi, Kristóf
  • Mnich, Matthias
  • Vincze, Roland

Abstract

A fundamental variant of the classical traveling salesman problem (TSP) is the so-called multiple TSP (mTSP), where a set of m salesmen jointly visit all cities from a set of n cities. The mTSP models many important real-life applications, in particular for vehicle routing problems. An extensive survey by Bektas (Omega34(3), 2006) lists a variety of heuristic and exact solution procedures for the mTSP that solve particular problem instances. In this work we consider a further generalization of mTSP, the many-visits mTSP, where each city v has a request r(v) of how many times it should be visited by the salesmen. This problem opens up new real-life applications such as aircraft sequencing, while at the same time it poses several computational challenges. We provide polynomial-time algorithms for several variants of the many-visits mTSP that compute constant-factor approximate solutions.

Suggested Citation

  • Bérczi, Kristóf & Mnich, Matthias & Vincze, Roland, 2023. "Approximations for many-visits multiple traveling salesman problems," Omega, Elsevier, vol. 116(C).
    • Handle: RePEc:eee:jomega:v:116:y:2023:i:c:s0305048322002225
    DOI: 10.1016/j.omega.2022.102816
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048322002225
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2022.102816?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. Michael Rothkopf, 1966. "Letter to the Editor—The Traveling Salesman Problem: On the Reduction of Certain Large Problems to Smaller Ones," Operations Research, INFORMS, vol. 14(3), pages 532-533, June.
    2. Li, Chongshou & Gong, Lijun & Luo, Zhixing & Lim, Andrew, 2019. "A branch-and-price-and-cut algorithm for a pickup and delivery problem in retailing," Omega, Elsevier, vol. 89(C), pages 71-91.
    3. Harilaos N. Psaraftis, 1980. "A Dynamic Programming Approach for Sequencing Groups of Identical Jobs," Operations Research, INFORMS, vol. 28(6), pages 1347-1359, December.
    4. Zhou Xu & Brian Rodrigues, 2015. "A 3/2-Approximation Algorithm for the Multiple TSP with a Fixed Number of Depots," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 636-645, November.
    5. Rathinam, Sivakumar & Sengupta, Raja, 2006. "Lower and Upper Bounds for a Symmetric Multiple Depot, Multiple Travelling Salesman Problem," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4z68041r, Institute of Transportation Studies, UC Berkeley.
    6. Davood Shiri & Vahid Akbari & F. Sibel Salman, 2020. "Online routing and scheduling of search-and-rescue teams," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(3), pages 755-784, September.
    7. Michael Khachay & Katherine Neznakhina, 2016. "Approximability of the minimum-weight k-size cycle cover problem," Journal of Global Optimization, Springer, vol. 66(1), pages 65-82, September.
    8. Xu, Zhou & Rodrigues, Brian, 2017. "An extension of the Christofides heuristic for the generalized multiple depot multiple traveling salesmen problem," European Journal of Operational Research, Elsevier, vol. 257(3), pages 735-745.
    9. Dell’Amico, Mauro & Montemanni, Roberto & Novellani, Stefano, 2021. "Algorithms based on branch and bound for the flying sidekick traveling salesman problem," Omega, Elsevier, vol. 104(C).
    10. Allahverdi, Ali & Ng, C.T. & Cheng, T.C.E. & Kovalyov, Mikhail Y., 2008. "A survey of scheduling problems with setup times or costs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 985-1032, June.
    11. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    12. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    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. N. Brauner & Y. Crama & A. Grigoriev & J. Klundert, 2005. "A Framework for the Complexity of High-Multiplicity Scheduling Problems," Journal of Combinatorial Optimization, Springer, vol. 9(3), pages 313-323, May.
    2. Wex, Felix & Schryen, Guido & Feuerriegel, Stefan & Neumann, Dirk, 2014. "Emergency response in natural disaster management: Allocation and scheduling of rescue units," European Journal of Operational Research, Elsevier, vol. 235(3), pages 697-708.
    3. Hartmann, Sönke, 2013. "Scheduling reefer mechanics at container terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 17-27.
    4. Mujawar, Sachin & Huang, Simin & Nagi, Rakesh, 2012. "Scheduling to minimize stringer utilization for continuous annealing operations," Omega, Elsevier, vol. 40(4), pages 437-444.
    5. Pohl, Maximilian & Kolisch, Rainer & Schiffer, Maximilian, 2021. "Runway scheduling during winter operations," Omega, Elsevier, vol. 102(C).
    6. Xiaofan Lai & Liang Xu & Zhou Xu & Yang Du, 2023. "An Approximation Algorithm for k -Depot Split Delivery Vehicle Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1179-1194, September.
    7. Samà, Marcella & D’Ariano, Andrea & D’Ariano, Paolo & Pacciarelli, Dario, 2017. "Scheduling models for optimal aircraft traffic control at busy airports: Tardiness, priorities, equity and violations considerations," Omega, Elsevier, vol. 67(C), pages 81-98.
    8. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    9. Geert De Maere & Jason A. D. Atkin & Edmund K. Burke, 2018. "Pruning Rules for Optimal Runway Sequencing," Transportation Science, INFORMS, vol. 52(4), pages 898-916, August.
    10. Senay Solak & Gustaf Solveling & John-Paul B. Clarke & Ellis L. Johnson, 2018. "Stochastic Runway Scheduling," Transportation Science, INFORMS, vol. 52(4), pages 917-940, August.
    11. Bendotti, Pascale & Fouilhoux, Pierre & Kedad-Sidhoum, Safia, 2018. "The Unit-capacity Constrained Permutation Problem," European Journal of Operational Research, Elsevier, vol. 268(2), pages 463-472.
    12. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.
    13. Javad Rezaeian & Reza Alizadeh Foroutan & Toraj Mojibi & Yacob Khojasteh, 2023. "Sensitivity Analysis of the Unrelated Parallel Machine Scheduling Problem with Rework Processes and Machine Eligibility Restrictions," SN Operations Research Forum, Springer, vol. 4(3), pages 1-24, September.
    14. Akbari, Vahid & Shiri, Davood & Sibel Salman, F., 2021. "An online optimization approach to post-disaster road restoration," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 1-25.
    15. Marko Ɖurasević & Domagoj Jakobović, 2019. "Creating dispatching rules by simple ensemble combination," Journal of Heuristics, Springer, vol. 25(6), pages 959-1013, December.
    16. Ahmed Ghoniem & Hanif D. Sherali & Hojong Baik, 2014. "Enhanced Models for a Mixed Arrival-Departure Aircraft Sequencing Problem," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 514-530, August.
    17. Dongni Li & Xianwen Meng & Miao Li & Yunna Tian, 2016. "An ACO-based intercell scheduling approach for job shop cells with multiple single processing machines and one batch processing machine," Journal of Intelligent Manufacturing, Springer, vol. 27(2), pages 283-296, April.
    18. A R Brentnall & R C H Cheng, 2009. "Some effects of aircraft arrival sequence algorithms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 962-972, July.
    19. Byung-Cheon Choi & Myoung-Ju Park, 2015. "A Batch Scheduling Problem with Two Agents," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-19, December.
    20. Bozorgirad, Mir Abbas & Logendran, Rasaratnam, 2013. "Bi-criteria group scheduling in hybrid flowshops," International Journal of Production Economics, Elsevier, vol. 145(2), pages 599-612.

    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:jomega:v:116:y:2023:i:c:s0305048322002225. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.