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

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  • 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
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    References listed on IDEAS

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    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. 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. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
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    Cited by:

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    3. 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.
    4. 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).
    5. 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.
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    7. 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.

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