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Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities

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  • Khurana, Archana
  • Adlakha, Veena
  • Lev, Benjamin

Abstract

In this paper, we consider a multi-index constrained transportation problem (CTP) of axial constraints with bounds on destination requirements, source availabilities, and multiple types of commodities. The specified problem is converted into a related transportation problem by adding a source, a destination, and a commodity, making it equivalent to a standard axial sum problem. This related problem is transformed into a multi-index transportation problem that can be solved easily. The provided solution method is very useful for transporting heterogeneous commodities. A transportation model may sometimes have various capacity constraints on the flow between pairs of origins and destinations. Moreover, budgetary, political, and emergency situations may impair or enhance the flow between origins and destinations, making it critical for a manager to reevaluate allocations. These considerations have motivated us to explore the multi-index CTP with impaired and enhanced flow. We present several numerical examples to demonstrate the proposed algorithms.

Suggested Citation

  • Khurana, Archana & Adlakha, Veena & Lev, Benjamin, 2018. "Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities," Operations Research Perspectives, Elsevier, vol. 5(C), pages 319-333.
    • Handle: RePEc:eee:oprepe:v:5:y:2018:i:c:p:319-333
    DOI: 10.1016/j.orp.2018.10.001
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    1. A. Charnes & Darwin Klingman, 1970. "Note--The Distribution Problem with Upper and Lower Bounds on the Node Requirements," Management Science, INFORMS, vol. 16(9), pages 638-642, May.
    2. Adlakha, Veena & Kowalski, Krzysztof & Lev, Benjamin, 2010. "A branching method for the fixed charge transportation problem," Omega, Elsevier, vol. 38(5), pages 393-397, October.
    3. Pradip Kundu & Samarjit Kar & Manoranjan Maiti, 2014. "Multi-objective solid transportation problems with budget constraint in uncertain environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1668-1682, August.
    4. K. B. Haley, 1963. "The Multi-Index Problem," Operations Research, INFORMS, vol. 11(3), pages 368-379, June.
    5. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.
    6. Hu, Qian & Zhang, Zhenzhen & Lim, Andrew, 2016. "Transportation service procurement problem with transit time," Transportation Research Part B: Methodological, Elsevier, vol. 86(C), pages 19-36.
    7. D. Klingman & R. Russell, 1975. "Solving Constrained Transportation Problems," Operations Research, INFORMS, vol. 23(1), pages 91-106, February.
    8. 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.
    9. Harvey M. Wagner, 1959. "On a Class of Capacitated Transportation Problems," Management Science, INFORMS, vol. 5(3), pages 304-318, April.
    10. Di, Zhen & Yang, Lixing & Qi, Jianguo & Gao, Ziyou, 2018. "Transportation network design for maximizing flow-based accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 209-238.
    11. Archana Khurana & Tripti Verma, 2015. "On a class of capacitated transshipment problems with bounds on rim conditions," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 251-280.
    12. Dangalchev, Chavdar A., 2000. "Optimization of the transportation expense of a firm with contractual supplies," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 203-217, April.
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    2. Abd Elazeem M. Abd Elazeem & Abd Allah A. Mousa & Mohammed A. El-Shorbagy & Sayed K. Elagan & Yousria Abo-Elnaga, 2021. "Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems," Sustainability, MDPI, vol. 13(3), pages 1-18, January.

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