IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v68y2017icp105-118.html
   My bibliography  Save this article

An upper bound on the minimal total cost of the transportation problem with varying demands and supplies

Author

Listed:
  • Xie, Fanrong
  • Butt, Muhammad Munir
  • Li, Zuoan
  • Zhu, Linzhi

Abstract

In general cases, to find the exact upper bound on the minimal total cost of the transportation problem with varying demands and supplies is an NP-hard problem. In literature, there are only two approaches with several shortcomings to solve the problem. In this paper, the problem is formulated as a bi-level programming model, and proven to be solvable in a polynomial time if the sum of the lower bounds for all the supplies is no less than the sum of the upper bounds for all the demands; and a heuristic algorithm named TPVDS-A based on genetic algorithm is developed as an efficient and robust solution method of the model. Computational experiments on benchmark and new randomly generated instances show that the TPVDS-A algorithm outperforms the two existing approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jomega:v:68:y:2017:i:c:p:105-118
    DOI: 10.1016/j.omega.2016.06.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048316303346
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2016.06.007?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. Borisovsky, P. & Dolgui, A. & Eremeev, A., 2009. "Genetic algorithms for a supply management problem: MIP-recombination vs greedy decoder," European Journal of Operational Research, Elsevier, vol. 195(3), pages 770-779, June.
    2. 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.
    3. 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.
    4. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    5. Vancroonenburg, Wim & Della Croce, Federico & Goossens, Dries & Spieksma, Frits C.R., 2014. "The Red–Blue transportation problem," European Journal of Operational Research, Elsevier, vol. 237(3), pages 814-823.
    6. Adlakha, Veena & Kowalski, Krzysztof, 1998. "A quick sufficient solution to the More-for-Less paradox in the transportation problem," Omega, Elsevier, vol. 26(4), pages 541-547, August.
    7. Dahiya, Kalpana & Verma, Vanita, 2007. "Capacitated transportation problem with bounds on RIM conditions," European Journal of Operational Research, Elsevier, vol. 178(3), pages 718-737, May.
    8. Das, S. K. & Goswami, A. & Alam, S. S., 1999. "Multiobjective transportation problem with interval cost, source and destination parameters," European Journal of Operational Research, Elsevier, vol. 117(1), pages 100-112, August.
    9. Sonia & Munish Puri, 2004. "Two level hierarchical time minimizing transportation problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 301-330, December.
    10. 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.
    11. Hwang, Hark-Chin & Kang, Jangha, 2016. "Two-phase algorithm for the lot-sizing problem with backlogging for stepwise transportation cost without speculative motives," Omega, Elsevier, vol. 59(PB), pages 238-250.
    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)

    Citations

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


    Cited by:

    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. Dai, Jingqi & Li, Zongmin, 2023. "An equilibrium approach towards sustainable operation of a modern coal chemical industrial park," Omega, Elsevier, vol. 120(C).
    3. 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.
    4. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    5. P. Senthil Kumar, 2024. "An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems," 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(9), pages 4370-4403, September.
    6. 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.
    7. 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.
    8. 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.

    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. 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. 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.
    3. 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.
    4. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    5. 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.
    6. 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.
    7. 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.
    8. Wang, Gang, 2024. "Order assignment and two-stage integrated scheduling in fruit and vegetable supply chains," Omega, Elsevier, vol. 124(C).
    9. 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.
    10. S. K. Bharati & Rita Malhotra, 2017. "Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle," 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. 8(2), pages 1442-1449, November.
    11. 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).
    12. 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.
    13. 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.
    14. Richard L. Church, 2018. "Tobler’s Law and Spatial Optimization," International Regional Science Review, , vol. 41(3), pages 287-310, May.
    15. 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.
    16. 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.
    17. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    18. Mhand Hifi & Rym M'Hallah, 2005. "An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems," Operations Research, INFORMS, vol. 53(1), pages 140-150, February.
    19. 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.
    20. Pérez-Mesa, Juan Carlos & Galdeano-Gómez, Emilio & Salinas Andújar, Jose A., 2012. "Logistics network and externalities for short sea transport: An analysis of horticultural exports from southeast Spain," Transport Policy, Elsevier, vol. 24(C), pages 188-198.

    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:68:y:2017:i:c:p:105-118. 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.