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The total cost bounds of the transportation problem with varying demand and supply

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  • Liu, Shiang-Tai

Abstract

A transportation problem is a linear programming problem based on a network structure consisting of a finite numbers of nodes and arcs attached to them. In real world applications, the supply and demand quantities in the transportation problem are sometimes hardly specified precisely because of changing economic conditions. This paper investigates the transportation problem when the demand and supply quantities are varying. A pair of mathematical programs is formulated to calculate the objective value. The derived result is also in range, where the total transportation cost would appear. In addition to allowing for simultaneous changes in supply and demand values, the total cost bounds are calculated directly. Due to the structure of the transportation problem, the largest total transportation cost may not occur at the highest total quantities shipped. Since the total cost bounds are derived, it would be beneficial to decision-making.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jomega:v:31:y:2003:i:4:p:247-251
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    Citations

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    Cited by:

    1. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. D’Ambrosio, C. & Gentili, M. & Cerulli, R., 2020. "The optimal value range problem for the Interval (immune) Transportation Problem," Omega, Elsevier, vol. 95(C).
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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