IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v104y2021ics0305048321001018.html
   My bibliography  Save this article

An improved heuristic approach for the interval immune transportation problem

Author

Listed:
  • Carrabs, Francesco
  • Cerulli, Raffaele
  • D’Ambrosio, Ciriaco
  • Della Croce, Federico
  • Gentili, Monica

Abstract

We study the problem of determining the bounds of the optimal cost of a transportation problem when the capacity of the suppliers and the demand of the customers vary over an interval. We consider transportation costs such that the transportation paradox does not arise. We design a new heuristic approach based on some polyhedral properties of the problem and provide a novel integer linear programming mathematical formulation to solve it exactly. Our computational results, carried out on benchmark instances from the literature and on some new instances, show that our heuristic algorithm greatly outperforms the best solution approaches currently used.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:jomega:v:104:y:2021:i:c:s0305048321001018
    DOI: 10.1016/j.omega.2021.102492
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048321001018
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2021.102492?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. Elif Garajová & Milan Hladík & Miroslav Rada, 2019. "Interval linear programming under transformations: optimal solutions and optimal value range," 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. 27(3), pages 601-614, September.
    4. J W Chinneck & K Ramadan, 2000. "Linear programming with interval coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 209-220, February.
    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.
    7. 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.
    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.

    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. 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. 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. M. A. Hoque & Z. A. M. S. Juman, 2024. "Decreased minimum total transportation–inventory cost bounds assuming variability in supplies and demands," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 1888-1905, December.
    4. Jana Novotná & Milan Hladík & Tomáš Masařík, 2020. "Duality Gap in Interval Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 565-580, February.
    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. 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.
    7. Figueroa–García, Juan Carlos & Hernández, Germán & Franco, Carlos, 2022. "A review on history, trends and perspectives of fuzzy linear programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    8. Soyster, A.L. & Murphy, F.H., 2013. "A unifying framework for duality and modeling in robust linear programs," Omega, Elsevier, vol. 41(6), pages 984-997.
    9. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
    10. Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    11. Giove, Silvio & Funari, Stefania & Nardelli, Carla, 2006. "An interval portfolio selection problem based on regret function," European Journal of Operational Research, Elsevier, vol. 170(1), pages 253-264, April.
    12. 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.
    13. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    14. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    15. Palash Sahoo, 2024. "Solution of a single-objective based three-stage 4DTP model with information crowdsourcing under disaster relief scenario: a hybrid random type-2 fuzzy approach," 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. 15(10), pages 4668-4713, October.
    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. Oliveira, Carla & Antunes, Carlos Henggeler, 2011. "A multi-objective multi-sectoral economy–energy–environment model: Application to Portugal," Energy, Elsevier, vol. 36(5), pages 2856-2866.
    18. Gouveia, M.C. & Henriques, C.O. & Dias, L.C., 2023. "Eco-efficiency changes of the electricity and gas sectors across 28 European countries: A value-based data envelopment analysis productivity approach," Socio-Economic Planning Sciences, Elsevier, vol. 87(PB).
    19. Henriques, C.O. & Marcenaro-Gutierrez, O.D. & Lopez-Agudo, Luis Alejandro, 2020. "Getting a balance in the life satisfaction determinants of full-time and part-time European workers," Economic Analysis and Policy, Elsevier, vol. 67(C), pages 87-113.
    20. Yang, Dongfeng & Jiang, Chao & Cai, Guowei & Yang, Deyou & Liu, Xiaojun, 2020. "Interval method based optimal planning of multi-energy microgrid with uncertain renewable generation and demand," Applied Energy, Elsevier, vol. 277(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:eee:jomega:v:104:y:2021:i:c:s0305048321001018. 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.