IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v95y2020ics0305048318307448.html
   My bibliography  Save this article

The optimal value range problem for the Interval (immune) Transportation Problem

Author

Listed:
  • D’Ambrosio, C.
  • Gentili, M.
  • Cerulli, R.

Abstract

We address the problem of finding the range of the optimal cost of a transportation problem when supply and demand vary over an interval. We consider the specific version of a transportation problem with supply inequality constraints and demand equality constraints under the assumption that the transportation costs are immune against the transportation paradox. We investigate some theoretical properties of the problem which constitute the basis of a novel solution algorithm. Our results show that the proposed algorithm hugely outperforms the best existing solution approaches.

Suggested Citation

  • D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    • Handle: RePEc:eee:jomega:v:95:y:2020:i:c:s0305048318307448
    DOI: 10.1016/j.omega.2019.04.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048318307448
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2019.04.002?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. Ocotlán Díaz-Parra & Jorge A. Ruiz-Vanoye & Beatriz Bernábe Loranca & Alejandro Fuentes-Penna & Ricardo A. Barrera-Cámara, 2014. "A Survey of Transportation Problems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, March.
    2. 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.
    3. 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.
    4. A. Charnes & W. W. Cooper, 1954. "The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems," Management Science, INFORMS, vol. 1(1), pages 49-69, October.
    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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Sumati Mahajan & S. K. Gupta, 2021. "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Annals of Operations Research, Springer, vol. 296(1), pages 211-241, January.
    7. 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.
    8. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    9. P. Senthil Kumar, 2018. "Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(2), pages 73-100, April.
    10. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
    11. 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.
    12. P. Senthil Kumar, 2016. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 5(4), pages 121-146, October.
    13. 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.
    14. Charles, V. & Udhayakumar, A. & Rhymend Uthariaraj, V., 2010. "An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems," European Journal of Operational Research, Elsevier, vol. 201(2), pages 390-398, March.
    15. Mie Augier & Michael Prietula, 2007. "Perspective---Historical Roots of the A Behavioral Theory of the Firm Model at GSIA," Organization Science, INFORMS, vol. 18(3), pages 507-522, June.
    16. 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.
    17. Zoltan Lakner & Anna Kiss & Bela Vizvari & Jozsef Popp, 2021. "Trade Liberalisation and Sustainability: A Case Study of Agro-Food Transport Optimisation," European Research Studies Journal, European Research Studies Journal, vol. 0(1), pages 822-839.
    18. Marjorie B. Gassner, 1991. "Biproportional Delegations," Journal of Theoretical Politics, , vol. 3(3), pages 321-342, July.
    19. Muwafaq Mohammed Alkubaisi, 2015. "Modified VOGEL Method to Find Initial Basic Feasible Solution (IBFS) Introducing a New Methodology to Find Best IBFS," Business and Management Research, Business and Management Research, Sciedu Press, vol. 4(2), pages 22-36, June.
    20. P. Senthil Kumar, 2020. "Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 37(3), pages 418-451.

    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:jomega:v:95:y:2020:i:c:s0305048318307448. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.