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Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

Author

Listed:
  • Abd Elazeem M. Abd Elazeem

    (High Institute of Marketing, Commerce, and Information System, Cairo 11865, Egypt)

  • Abd Allah A. Mousa

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Mohammed A. El-Shorbagy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt)

  • Sayed K. Elagan

    (Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia)

  • Yousria Abo-Elnaga

    (Department of Basic Science, Higher Technological Institute, Tenth of Ramadan City 44629, Egypt)

Abstract

Multi-dimensional transportation problems denoted as multi-index are considered as the extension of classical transportation problems and are appropriate practical modeling for solving real–world problems with multiple supply, multiple demand, as well as different modes of transportation demands or delivering different kinds of commodities. This paper presents a method for detecting the complete nondominated set (efficient solutions) of multi-objective four-index transportation problems. The proposed approach implements weighted sum method to convert multi-objective four-index transportation problem into a single objective four-index transportation problem, that can then be decomposed into a set of two-index transportation sub-problems. For each two-index sub-problem, parametric analysis was investigated to determine the range of the weights values that keep the efficient solution unchanged, which enable the decision maker to detect the set of all nondominated solutions for the original multi-objective multi-index transportation problem, and also to find the stability set of the first kind for each efficient solution. Finally, an illustrative example is presented to illustrate the efficiency and robustness of the proposed approach. The results demonstrate the effectiveness and robustness for the proposed approach to detect the set of all nondominated solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jsusta:v:13:y:2021:i:3:p:1372-:d:488811
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    References listed on IDEAS

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    1. K. B. Haley, 1963. "The Multi-Index Problem," Operations Research, INFORMS, vol. 11(3), pages 368-379, June.
    2. 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.
    3. Junginger, Werner, 1993. "On representatives of multi-index transportation problems," European Journal of Operational Research, Elsevier, vol. 66(3), pages 353-371, May.
    4. Dalbinder Kaur & Sathi Mukherjee & Kajla Basu, 2015. "Solution of a Multi-Objective and Multi-Index Real-Life Transportation Problem Using Different Fuzzy Membership Functions," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 666-678, February.
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