IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v239y2014i1p80-88.html
   My bibliography  Save this article

Approximation algorithms for solving the constrained arc routing problem in mixed graphs

Author

Listed:
  • Ding, Honglin
  • Li, Jianping
  • Lih, Ko-Wei

Abstract

Given a mixed graph G with vertex set V, let E and A denote the sets of edges and arcs, respectively. We use Q+ and Z+ to denote the sets of positive rational numbers and positive integers, respectively. For any connected mixed graph G=(V,E∪A;w;l,u) with a length function w:E∪A→Q+ and two integer functions l,u:E∪A→Z+ satisfying l(e)⩽u(e) for each e∈E∪A, we are asked to determine a minimum length tour T traversing each e∈E∪A at least l(e) and at most u(e) times. This new constrained arc routing problem generalizes the mixed Chinese postman problem. Let n=|V| and m=|E∪A| denote the number of vertices and edges (including arcs), respectively. Using network flow techniques, we design a (1+1/l0)-approximation algorithm in time O(n2m3logn) to solve this constrained arc routing problem such that l(e)

Suggested Citation

  • Ding, Honglin & Li, Jianping & Lih, Ko-Wei, 2014. "Approximation algorithms for solving the constrained arc routing problem in mixed graphs," European Journal of Operational Research, Elsevier, vol. 239(1), pages 80-88.
    • Handle: RePEc:eee:ejores:v:239:y:2014:i:1:p:80-88
    DOI: 10.1016/j.ejor.2014.04.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714003816
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.04.039?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. Lysgaard, Jens & Wøhlk, Sanne, 2014. "A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 800-810.
    2. Ghiani, Gianpaolo & Improta, Gennaro, 2000. "An efficient transformation of the generalized vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 122(1), pages 11-17, April.
    3. Beullens, Patrick & Muyldermans, Luc & Cattrysse, Dirk & Van Oudheusden, Dirk, 2003. "A guided local search heuristic for the capacitated arc routing problem," European Journal of Operational Research, Elsevier, vol. 147(3), pages 629-643, June.
    4. Corberan, A. & Marti, R. & Sanchis, J. M., 2002. "A GRASP heuristic for the mixed Chinese postman problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 70-80, October.
    5. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
    6. Zachariadis, E.E. & Kiranoudis, C.T., 2011. "Local search for the undirected capacitated arc routing problem with profits," European Journal of Operational Research, Elsevier, vol. 210(2), pages 358-367, April.
    7. Goel, Asvin & Gruhn, Volker, 2008. "A General Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 191(3), pages 650-660, December.
    8. Mourao, Maria Candida & Amado, Ligia, 2005. "Heuristic method for a mixed capacitated arc routing problem: A refuse collection application," European Journal of Operational Research, Elsevier, vol. 160(1), pages 139-153, January.
    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. Hashemi Doulabi, Seyed Hossein & Seifi, Abbas, 2013. "Lower and upper bounds for location-arc routing problems with vehicle capacity constraints," European Journal of Operational Research, Elsevier, vol. 224(1), pages 189-208.
    2. Aderemi Oluyinka Adewumi & Olawale Joshua Adeleke, 2018. "A survey of recent advances in vehicle routing problems," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(1), pages 155-172, February.
    3. Tan, K.C. & Chew, Y.H. & Lee, L.H., 2006. "A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 855-885, August.
    4. Sze, Jeeu Fong & Salhi, Said & Wassan, Niaz, 2017. "The cumulative capacitated vehicle routing problem with min-sum and min-max objectives: An effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 162-184.
    5. Bode, Claudia & Irnich, Stefan, 2014. "The shortest-path problem with resource constraints with (k,2)-loop elimination and its application to the capacitated arc-routing problem," European Journal of Operational Research, Elsevier, vol. 238(2), pages 415-426.
    6. Goel, Asvin & Meisel, Frank, 2013. "Workforce routing and scheduling for electricity network maintenance with downtime minimization," European Journal of Operational Research, Elsevier, vol. 231(1), pages 210-228.
    7. Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.
    8. Rivera, Juan Carlos & Murat Afsar, H. & Prins, Christian, 2016. "Mathematical formulations and exact algorithm for the multitrip cumulative capacitated single-vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 249(1), pages 93-104.
    9. Wang, Shaojun & Sarker, Bhaba R. & Mann, Lawrence & Triantaphyllou, Evangelos, 2004. "Resource planning and a depot location model for electric power restoration," European Journal of Operational Research, Elsevier, vol. 155(1), pages 22-43, May.
    10. Paraskevopoulos, Dimitris C. & Laporte, Gilbert & Repoussis, Panagiotis P. & Tarantilis, Christos D., 2017. "Resource constrained routing and scheduling: Review and research prospects," European Journal of Operational Research, Elsevier, vol. 263(3), pages 737-754.
    11. Julia Rieck & Jürgen Zimmermann, 2010. "A new mixed integer linear model for a rich vehicle routing problem with docking constraints," Annals of Operations Research, Springer, vol. 181(1), pages 337-358, December.
    12. Dumez, Dorian & Lehuédé, Fabien & Péton, Olivier, 2021. "A large neighborhood search approach to the vehicle routing problem with delivery options," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 103-132.
    13. Shoshana Anily, 1996. "The vehicle‐routing problem with delivery and back‐haul options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 415-434, April.
    14. Timo Gschwind & Stefan Irnich & Christian Tilk & Simon Emde, 2020. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Journal of Scheduling, Springer, vol. 23(3), pages 363-377, June.
    15. Zhang, Jian & Woensel, Tom Van, 2023. "Dynamic vehicle routing with random requests: A literature review," International Journal of Production Economics, Elsevier, vol. 256(C).
    16. Chu, Feng & Labadi, Nacima & Prins, Christian, 2006. "A Scatter Search for the periodic capacitated arc routing problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 586-605, March.
    17. László A. Végh, 2017. "A Strongly Polynomial Algorithm for Generalized Flow Maximization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 179-211, January.
    18. Lu, Jiawei & Nie, Qinghui & Mahmoudi, Monirehalsadat & Ou, Jishun & Li, Chongnan & Zhou, Xuesong Simon, 2022. "Rich arc routing problem in city logistics: Models and solution algorithms using a fluid queue-based time-dependent travel time representation," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 143-182.
    19. Chase C. Murray & Mark H. Karwan, 2010. "An extensible modeling framework for dynamic reassignment and rerouting in cooperative airborne operations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 634-652, October.
    20. Jesica Armas & Peter Keenan & Angel A. Juan & Seán McGarraghy, 2019. "Solving large-scale time capacitated arc routing problems: from real-time heuristics to metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 135-162, February.

    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:239:y:2014:i:1:p:80-88. 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.