IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v28y2014i4d10.1007_s10878-012-9580-x.html
   My bibliography  Save this article

Local search algorithms for multiple-depot vehicle routing and for multiple traveling salesman problems with proved performance guarantees

Author

Listed:
  • Asaf Levin

    (Technion–Israel Institute of Technology)

  • Uri Yovel

    (Technion–Israel Institute of Technology)

Abstract

We consider two related problems: the multiple-depot vehicle routing problem (MDVRP) and the Multiple traveling salesman problem (mTSP). In both of them, given is the complete graph on n vertices $$G = (V,E)$$ with nonnegative edge lengths that form a metric on V. Also given is a positive integer k. In typical applications, V represents locations of customers and k represents the number of available vehicles. In MDVPR, we are also given a set of k depots $$\{O_1,\ldots ,O_k\} \subseteq V$$ , and the goal is to find a minimum-length cycle cover of G of size k, that is, a collection of k (possibly empty) cycles such that each $$v \in V$$ is in exactly one cycle, and each cycle in the cover contains exactly one depot. In mTSP, no depots are given, so the goal is to find (any) minimum-length cycle cover of G of size k. We present local search algorithms for both problems, and we prove that their approximation ratio is 2.

Suggested Citation

  • Asaf Levin & Uri Yovel, 2014. "Local search algorithms for multiple-depot vehicle routing and for multiple traveling salesman problems with proved performance guarantees," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 726-747, November.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9580-x
    DOI: 10.1007/s10878-012-9580-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9580-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-012-9580-x?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. Orlin, James & Punnen, Abraham & Schulz, Andreas, 2004. "Approximate Local Search in Combinatorial Optimization," Working papers 4325-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    3. Chung-Lun Li & David Simchi-Levi, 1990. "Worst-Case Analysis of Heuristics for Multidepot Capacitated Vehicle Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 64-73, February.
    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. Tobias Harks & Felix G König & Jannik Matuschke, 2013. "Approximation Algorithms for Capacitated Location Routing," Transportation Science, INFORMS, vol. 47(1), pages 3-22, February.
    2. Carrasco Heine, Oscar F. & Demleitner, Antonia & Matuschke, Jannik, 2023. "Bifactor approximation for location routing with vehicle and facility capacities," European Journal of Operational Research, Elsevier, vol. 304(2), pages 429-442.
    3. Ben Hermans & Roel Leus & Jannik Matuschke, 2022. "Exact and Approximation Algorithms for the Expanding Search Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 281-296, January.
    4. Yuan, Shuai & Skinner, Bradley & Huang, Shoudong & Liu, Dikai, 2013. "A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 228(1), pages 72-82.
    5. Rajeev Kumar, 2022. "A Gig Worker-Centric Approach for Efficient Picking and Delivery of Electric Scooters," International Journal of Business Analytics (IJBAN), IGI Global, vol. 9(1), pages 1-14, January.
    6. 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.
    7. Sebastian Twaróg & Krzysztof Szwarc & Martyna Wronka-Pośpiech & Małgorzata Dobrowolska & Anna Urbanek, 2021. "Multiple probabilistic traveling salesman problem in the coordination of drug transportation—In the context of sustainability goals and Industry 4.0," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-19, March.
    8. Semih Yalçındağ & Andrea Matta & Evren Şahin & J. George Shanthikumar, 2016. "The patient assignment problem in home health care: using a data-driven method to estimate the travel times of care givers," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 304-335, June.
    9. CASTRO, Marco & SÖRENSEN, Kenneth & VANSTEENWEGEN, Pieter & GOOS, Peter, 2012. "A simple GRASP+VND for the travelling salesperson problem with hotel selection," Working Papers 2012024, University of Antwerp, Faculty of Business and Economics.
    10. Hartmann, Sönke, 2013. "Scheduling reefer mechanics at container terminals," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 17-27.
    11. Cemalettin Öztürk & F. Zeynep Sargut & M. Arslan Örnek & Deniz Türsel Eliiyi, 2017. "Optimisation and heuristic approaches for assigning inbound containers to outbound carriers," Maritime Policy & Management, Taylor & Francis Journals, vol. 44(7), pages 825-836, October.
    12. Andrzej Grzybowski, 2009. "A Note On A Single Vehicle And One Destination Routing Problem And Its Game-Theoretic Models," Advanced Logistic systems, University of Miskolc, Department of Material Handling and Logistics, vol. 3(1), pages 71-76, December.
    13. T Öncan & S N Kabadi & K P K Nair & A P Punnen, 2008. "VLSN search algorithms for partitioning problems using matching neighbourhoods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(3), pages 388-398, March.
    14. Emde, Simon & Tahirov, Nail & Gendreau, Michel & Glock, Christoph H., 2021. "Routing automated lane-guided transport vehicles in a warehouse handling returns," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1085-1098.
    15. Du, Mingyang & Cheng, Lin & Li, Xuefeng & Tang, Fang, 2020. "Static rebalancing optimization with considering the collection of malfunctioning bikes in free-floating bike sharing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    16. Martin Gairing & Rahul Savani, 2019. "Computing Stable Outcomes in Symmetric Additively Separable Hedonic Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1101-1121, August.
    17. Mujawar, Sachin & Huang, Simin & Nagi, Rakesh, 2012. "Scheduling to minimize stringer utilization for continuous annealing operations," Omega, Elsevier, vol. 40(4), pages 437-444.
    18. Nourinejad, Mehdi & Zhu, Sirui & Bahrami, Sina & Roorda, Matthew J., 2015. "Vehicle relocation and staff rebalancing in one-way carsharing systems," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 81(C), pages 98-113.
    19. F. Angel-Bello & Y. Cardona-Valdés & A. Álvarez, 2019. "Mixed integer formulations for the multiple minimum latency problem," Operational Research, Springer, vol. 19(2), pages 369-398, June.
    20. Haluk Yapicioglu, 2018. "Multiperiod Multi Traveling Salesmen Problem Considering Time Window Constraints with an Application to a Real World Case," Networks and Spatial Economics, Springer, vol. 18(4), pages 773-801, December.

    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:spr:jcomop:v:28:y:2014:i:4:d:10.1007_s10878-012-9580-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.