IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v31y2023i3d10.1007_s10100-023-00841-9.html
   My bibliography  Save this article

Interval transportation problem: feasibility, optimality and the worst optimal value

Author

Listed:
  • Elif Garajová

    (Charles University
    Prague University of Economics and Business)

  • Miroslav Rada

    (Prague University of Economics and Business
    Prague University of Economics and Business)

Abstract

We consider the model of a transportation problem with the objective of finding a minimum-cost transportation plan for shipping a given commodity from a set of supply centers to the customers. Since the exact values of supply and demand and the exact transportation costs are not always available for real-world problems, we adopt the approach of interval programming to represent such uncertainty, resulting in the model of an interval transportation problem. The interval model assumes that lower and upper bounds on the data are given and the values can be independently perturbed within these bounds. In this paper, we provide an overview of conditions for checking basic properties of the interval transportation problems commonly studied in interval programming, such as weak and strong feasibility or optimality. We derive a condition for testing weak optimality of a solution in polynomial time by finding a suitable scenario of the problem. Further, we formulate a similar condition for testing strong optimality of a solution for transportation problems with interval supply and demand (and exact costs). Moreover, we also survey the results on computing the best and the worst optimal value. We build on an exact method for solving the NP-hard problem of computing the worst (finite) optimal value of the interval transportation problem based on a decomposition of the optimal solution set by complementary slackness. Finally, we conduct computational experiments to show that the method can be competitive with the state-of-the-art heuristic algorithms.

Suggested Citation

  • Elif Garajová & Miroslav Rada, 2023. "Interval transportation problem: feasibility, optimality and the worst optimal value," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 769-790, September.
    • Handle: RePEc:spr:cejnor:v:31:y:2023:i:3:d:10.1007_s10100-023-00841-9
    DOI: 10.1007/s10100-023-00841-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-023-00841-9
    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/s10100-023-00841-9?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. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    2. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    3. Carrabs, Francesco & Cerulli, Raffaele & D’Ambrosio, Ciriaco & Della Croce, Federico & Gentili, Monica, 2021. "An improved heuristic approach for the interval immune transportation problem," Omega, Elsevier, vol. 104(C).
    4. 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.
    5. Liu, Shiang-Tai, 2003. "The total cost bounds of the transportation problem with varying demand and supply," Omega, Elsevier, vol. 31(4), pages 247-251, August.
    6. Wlodzimierz Szwarc, 1971. "The transportation paradox," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 18(2), pages 185-202, 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. Carrabs, Francesco & Cerulli, Raffaele & D’Ambrosio, Ciriaco & Della Croce, Federico & Gentili, Monica, 2021. "An improved heuristic approach for the interval immune transportation problem," Omega, Elsevier, vol. 104(C).
    2. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    3. Md. Ashraful Babu & M. A. Hoque & Md. Sharif Uddin, 2020. "A heuristic for obtaining better initial feasible solution to the transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 221-245, March.
    4. 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.
    5. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
    6. 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.
    7. Sankar Kumar Roy & Gurupada Maity & Gerhard-Wilhelm Weber, 2017. "Multi-objective two-stage grey transportation problem using utility function with goals," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 417-439, June.
    8. Firoz Ahmad & Ahmad Yusuf Adhami, 2019. "Total cost measures with probabilistic cost function under varying supply and demand in transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 583-602, June.
    9. 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.
    10. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    11. Adlakha, Veena & Kowalski, Krzysztof & Wang, Simi & Lev, Benjamin & Shen, Wenjing, 2014. "On approximation of the fixed charge transportation problem," Omega, Elsevier, vol. 43(C), pages 64-70.
    12. Wu, Laiyun & Kang, Jee Eun & Chung, Younshik & Nikolaev, Alexander, 2021. "Inferring origin-Destination demand and user preferences in a multi-modal travel environment using automated fare collection data," Omega, Elsevier, vol. 101(C).
    13. P.Senthil Kumar, 2018. "PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 7(4), pages 62-99, October.
    14. P. Senthil Kumar, 2020. "Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set," 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. 11(1), pages 189-222, February.
    15. Dai, Jingqi & Li, Zongmin, 2023. "An equilibrium approach towards sustainable operation of a modern coal chemical industrial park," Omega, Elsevier, vol. 120(C).
    16. Joanna Szkutnik-Rogoż & Jarosław Ziółkowski & Jerzy Małachowski & Mateusz Oszczypała, 2021. "Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network," Energies, MDPI, vol. 14(21), pages 1-32, October.

    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:cejnor:v:31:y:2023:i:3:d:10.1007_s10100-023-00841-9. 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.