IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v323y2023i1d10.1007_s10479-023-05210-y.html
   My bibliography  Save this article

Multi-commodity flow problem on lossy network with partial lane reversals

Author

Listed:
  • Shiva Prakash Gupta

    (Tribhuvan University)

  • Urmila Pyakurel

    (Tribhuvan University)

  • Tanka Nath Dhamala

    (Tribhuvan University)

Abstract

During the transmission of several different commodities from respective sources to the sinks, there may be loss due to leakage, evaporation, or damage. The generalized multi-commodity flow problem on a lossy network deals with the transshipment of these commodities from the origin nodes to the destination nodes − not violating the capacity constraints on each arc with minimum loss. Partial lane reversal strategy makes traffic systematic and smooth by flipping the orientation of necessary road segments that improve the flow value and significantly minimize the loss. In this paper, we introduce maximum generalized static multi-commodity flow, maximum generalized dynamic multi-commodity flow, and generalized earliest arrival multi-commodity flow problems on a lossy network with partial lane reversals, and present algorithms to solve these problems in pseudo-polynomial time complexity. We also present a fully polynomial-time approximation scheme for the maximum generalized dynamic multi-commodity flow problem with partial lane reversals.

Suggested Citation

  • Shiva Prakash Gupta & Urmila Pyakurel & Tanka Nath Dhamala, 2023. "Multi-commodity flow problem on lossy network with partial lane reversals," Annals of Operations Research, Springer, vol. 323(1), pages 45-63, April.
    • Handle: RePEc:spr:annopr:v:323:y:2023:i:1:d:10.1007_s10479-023-05210-y
    DOI: 10.1007/s10479-023-05210-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-023-05210-y
    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/s10479-023-05210-y?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. Jeff L. Kennington, 1978. "A Survey of Linear Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 26(2), pages 209-236, April.
    2. Tomasz Radzik, 1998. "Faster Algorithms for the Generalized Network Flow Problem," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 69-100, February.
    3. William S. Jewell, 1962. "New Methods in Mathematical Programming---Optimal Flow Through Networks with Gains," Operations Research, INFORMS, vol. 10(4), pages 476-499, August.
    4. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    5. Urmila Pyakurel & Hari Nandan Nath & Stephan Dempe & Tanka Nath Dhamala, 2019. "Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    6. Urmila Pyakurel & Stephan Dempe, 2020. "Network Flow with Intermediate Storage: Models and Algorithms," SN Operations Research Forum, Springer, vol. 1(4), pages 1-23, December.
    7. Steffen Rebennack & Ashwin Arulselvan & Lily Elefteriadou & Panos M. Pardalos, 2010. "Complexity analysis for maximum flow problems with arc reversals," Journal of Combinatorial Optimization, Springer, vol. 19(2), pages 200-216, February.
    8. Urmila Pyakurel & Shiva Prakash Gupta & Durga Prasad Khanal & Tanka Nath Dhamala, 2020. "Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-13, October.
    9. Shiva Prakash Gupta & Urmila Pyakurel & Tanka Nath Dhamala, 2022. "Dynamic Multicommodity Contraflow Problem with Asymmetric Transit Times," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-8, February.
    10. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    11. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    12. J. A. Tomlin, 1966. "Minimum-Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 14(1), pages 45-51, February.
    13. Andrew V. Goldberg & Serge A. Plotkin & Éva Tardos, 1991. "Combinatorial Algorithms for the Generalized Circulation Problem," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 351-381, May.
    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. Pyakurel, Urmila & Khanal, Durga Prasad & Dhamala, Tanka Nath, 2023. "Abstract network flow with intermediate storage for evacuation planning," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1178-1193.
    2. Urmila Pyakurel & Stephan Dempe, 2020. "Network Flow with Intermediate Storage: Models and Algorithms," SN Operations Research Forum, Springer, vol. 1(4), pages 1-23, December.
    3. Durga Prasad Khanal & Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2022. "Efficient Algorithms for Abstract Flow with Partial Switching," SN Operations Research Forum, Springer, vol. 3(4), pages 1-17, December.
    4. Urmila Pyakurel & Hari Nandan Nath & Stephan Dempe & Tanka Nath Dhamala, 2019. "Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    5. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    6. Kaj Holmberg & Di Yuan, 2003. "A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 42-57, February.
    7. Weiqi Hong & Zishu Yang & Xu Sun & Jianyu Wang & Pengpeng Jiao, 2022. "Temporary Reversible Lane Design Based on Bi-Level Programming Model during the Winter Olympic Games," Sustainability, MDPI, vol. 14(8), pages 1-17, April.
    8. Kevin D. Wayne, 2002. "A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 445-459, August.
    9. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    10. Tanka Nath Dhamala & Urmila Pyakurel & Ram Chandra Dhungana, 2018. "Abstract Contraflow Models and Solution Procedures for Evacuation Planning," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 89-100, August.
    11. Tomasz Radzik, 1998. "Faster Algorithms for the Generalized Network Flow Problem," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 69-100, February.
    12. László A. Végh, 2017. "A Strongly Polynomial Algorithm for Generalized Flow Maximization," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 179-211, January.
    13. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    14. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
    15. Shahriar Akter & Samuel Fosso Wamba, 2019. "Big data and disaster management: a systematic review and agenda for future research," Annals of Operations Research, Springer, vol. 283(1), pages 939-959, December.
    16. Deepa Mishra & Sameer Kumar & Elkafi Hassini, 2019. "Current trends in disaster management simulation modelling research," Annals of Operations Research, Springer, vol. 283(1), pages 1387-1411, December.
    17. Sarah Root & Amy Cohn, 2008. "A novel modeling approach for express package carrier planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 670-683, October.
    18. László A. Végh, 2014. "Concave Generalized Flows with Applications to Market Equilibria," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 573-596, May.
    19. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    20. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Phase transitions of the price-of-anarchy function in multi-commodity routing games," Transportation Research Part B: Methodological, Elsevier, vol. 182(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:spr:annopr:v:323:y:2023:i:1:d:10.1007_s10479-023-05210-y. 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.