IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v229y2025icp611-635.html
   My bibliography  Save this article

Two-phase time minimization transportation problem with the restricted flow

Author

Listed:
  • Kaur, Supinder
  • Dahiya, Kalpana
  • Sharma, Anuj

Abstract

Motivated by the hierarchical structure within transportation systems, this paper explores a two-phase time minimization transportation problem with restricted flow (2p−TPF). In this problem, the transportation of products occurs in two distinct phases due to the partition of source–destination links into two separate levels: Level-1 and Level-2 links, with a specified amount of commodity being transported in each phase. For the transportation of a specific quantity of goods during the first phase, only Level-1 links are utilized. Following this, during the second phase of transportation, only Level-2 links are utilized. Transportation is carried out concurrently via numerous source–destination links relevant to each phase. This paper proposes an iterative algorithm (Algorithm-TPF) to find an optimal solution for a two-phase time minimization transportation problem that minimizes the sum of Phase-1 and Phase-2 transportation times. The proposed algorithm solves a solid time minimization transportation problem∖its restricted version at each iteration. Various theoretical results are proven to support the convergence of the algorithm. Numerical examples of various sizes are provided to support the theoretical results. Computational experiments conducted on randomly generated instances demonstrate the algorithm’s efficiency and convergence. The proposed algorithm offers an alternative method for solving two-phase time minimization transportation problems.

Suggested Citation

  • Kaur, Supinder & Dahiya, Kalpana & Sharma, Anuj, 2025. "Two-phase time minimization transportation problem with the restricted flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 611-635.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:611-635
    DOI: 10.1016/j.matcom.2024.09.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003859
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.09.030?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Peter L. Hammer, 1969. "Time‐minimizing transportation problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 16(3), pages 345-357, September.
    2. K. B. Haley, 1963. "The Multi-Index Problem," Operations Research, INFORMS, vol. 11(3), pages 368-379, June.
    3. Yolanda Hinojosa & Justo Puerto & Francisco Saldanha-da-Gama, 2014. "A two-stage stochastic transportation problem with fixed handling costs and a priori selection of the distribution channels," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1123-1147, October.
    4. K. B. Haley, 1962. "New Methods in Mathematical Programming---The Solid Transportation Problem," Operations Research, INFORMS, vol. 10(4), pages 448-463, August.
    5. Prabhjot Kaur & Anuj Sharma & Vanita Verma & Kalpana Dahiya, 2022. "An alternate approach to solve two-level hierarchical time minimization transportation problem," 4OR, Springer, vol. 20(1), pages 23-61, March.
    6. Dipak Barman & Anjana Kuiri & Barun Das, 2021. "A two-vehicle two-stage solid transportation problem with bi-fuzzy coefficients through genetic algorithm," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 18(4), pages 444-464.
    7. Vikas Sharma & Kalpana Dahiya & Vanita Verma, 2010. "Capacitated Two-Stage Time Minimization Transportation Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(04), pages 457-476.
    8. Sherali, Hanif D., 1982. "Equivalent weights for lexicographic multi-objective programs: Characterizations and computations," European Journal of Operational Research, Elsevier, vol. 11(4), pages 367-379, December.
    9. Singh, Gurwinder & Singh, Amarinder, 2023. "Extension of Particle Swarm Optimization algorithm for solving two-level time minimization transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 727-742.
    10. Fanrong Xie & Zuoan Li, 2022. "An iterative solution technique for capacitated two-stage time minimization transportation problem," 4OR, Springer, vol. 20(4), pages 637-684, December.
    11. Paul, Jomon A. & Zhang, Minjiao, 2019. "Supply location and transportation planning for hurricanes: A two-stage stochastic programming framework," European Journal of Operational Research, Elsevier, vol. 274(1), pages 108-125.
    12. Sharma, Anuj & Verma, Vanita & Kaur, Prabhjot & Dahiya, Kalpana, 2015. "An iterative algorithm for two level hierarchical time minimization transportation problem," European Journal of Operational Research, Elsevier, vol. 246(3), pages 700-707.
    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. Supinder Kaur & Ekta Jain & Kalpana Dahiya, 2025. "Two-level solid transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 62(1), pages 423-447, March.
    2. Fanrong Xie & Zuoan Li, 2022. "An iterative solution technique for capacitated two-stage time minimization transportation problem," 4OR, Springer, vol. 20(4), pages 637-684, December.
    3. Prabhjot Kaur & Anuj Sharma & Vanita Verma & Kalpana Dahiya, 2022. "An alternate approach to solve two-level hierarchical time minimization transportation problem," 4OR, Springer, vol. 20(1), pages 23-61, March.
    4. Singh, Gurwinder & Singh, Amarinder, 2023. "Extension of Particle Swarm Optimization algorithm for solving two-level time minimization transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 727-742.
    5. Singh, Bikramjit & Singh, Amarinder, 2023. "Hybrid particle swarm optimization for pure integer linear solid transportation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 243-266.
    6. Yu, Xinyao & Chen, Jie & Zhu, Ning & Ma, Shoufeng & Peng, Binbin, 2025. "A robust stochastic approach to relief pre-positioning for earthquake response under event-wise uncertainties," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 198(C).
    7. Fan, Yu & Shao, Jianfang & Wang, Xihui & Liang, Liang, 2024. "Contract design between relief organisations and private-sector vendors: A humanitarian logistics framework," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 182(C).
    8. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.
    9. Wang, Gang, 2024. "Order assignment and two-stage integrated scheduling in fruit and vegetable supply chains," Omega, Elsevier, vol. 124(C).
    10. P. Senthil Kumar, 2019. "PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global Scientific Publishing, vol. 10(2), pages 20-53, April.
    11. Yu, Wuyang, 2023. "A robust model for emergency supplies prepositioning and transportation considering road disruptions," Operations Research Perspectives, Elsevier, vol. 10(C).
    12. Lamghari, Amina & Ferland, Jacques A., 2011. "Assigning judges to competitions of several rounds using Tabu search," European Journal of Operational Research, Elsevier, vol. 210(3), pages 694-705, May.
    13. Gurupada Maity & Sankar Kumar Roy & Jose Luis Verdegay, 2019. "Time Variant Multi-Objective Interval-Valued Transportation Problem in Sustainable Development," Sustainability, MDPI, vol. 11(21), pages 1-15, November.
    14. Fanrong Xie & Anuj Sharma & Zuoan Li, 2022. "An alternate approach to solve two-level priority based assignment problem," Computational Optimization and Applications, Springer, vol. 81(2), pages 613-656, March.
    15. Sherali, Hanif D. & Narayanan, Arvind & Sivanandan, R., 2003. "Estimation of origin-destination trip-tables based on a partial set of traffic link volumes," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 815-836, November.
    16. Laura Laguna-Salvadó & Matthieu Lauras & Uche Okongwu & Tina Comes, 2019. "A multicriteria Master Planning DSS for a sustainable humanitarian supply chain," Annals of Operations Research, Springer, vol. 283(1), pages 1303-1343, December.
    17. Amir Akbari & Paul I. Barton, 2018. "An Improved Multi-parametric Programming Algorithm for Flux Balance Analysis of Metabolic Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 502-537, August.
    18. Xie, Fanrong & Butt, Muhammad Munir & Li, Zuoan & Zhu, Linzhi, 2017. "An upper bound on the minimal total cost of the transportation problem with varying demands and supplies," Omega, Elsevier, vol. 68(C), pages 105-118.
    19. Shaoqing Geng & Yu Gong & Hanping Hou & Jianliang Yang & Bhakti Stephan Onggo, 2024. "Resource management in disaster relief: a bibliometric and content-analysis-based literature review," Annals of Operations Research, Springer, vol. 343(1), pages 263-292, December.
    20. Zhang, Yuwei & Li, Zhenping & Zhao, Yuwei, 2023. "Multi-mitigation strategies in medical supplies for epidemic outbreaks," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:matcom:v:229:y:2025:i:c:p:611-635. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.