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Multi-objective two-stage grey transportation problem using utility function with goals

Author

Listed:
  • Sankar Kumar Roy

    (Vidyasagar University)

  • Gurupada Maity

    (Vidyasagar University)

  • Gerhard-Wilhelm Weber

    (Middle East Technical University)

Abstract

Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-016-0464-5
    DOI: 10.1007/s10100-016-0464-5
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    References listed on IDEAS

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

    1. Soumen Kumar Das & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2020. "An exact and a heuristic approach for the transportation-p-facility location problem," Computational Management Science, Springer, vol. 17(3), pages 389-407, October.
    2. Vishal Kashav & Chandra Prakash Garg & Rupesh Kumar, 2023. "Ranking the strategies to overcome the barriers of the maritime supply chain (MSC) of containerized freight under fuzzy environment," Annals of Operations Research, Springer, vol. 324(1), pages 1223-1268, May.
    3. Erfan Babaee Tirkolaee & Alireza Goli & Selma Gütmen & Gerhard-Wilhelm Weber & Katarzyna Szwedzka, 2023. "A novel model for sustainable waste collection arc routing problem: Pareto-based algorithms," Annals of Operations Research, Springer, vol. 324(1), pages 189-214, May.
    4. Tooraj Karimi & Arvin Hojati & Jeffrey Yi-Lin Forrest, 2022. "A new methodology for sustainability measurement of banks based on rough set theory," 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. 30(1), pages 415-431, March.
    5. Bo Yan & Xiaoxu Chen & Qin Yuan & Xiaotai Zhou, 2020. "Sustainability in fresh agricultural product supply chain based on radio frequency identification under an emergency," 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. 28(4), pages 1343-1361, December.
    6. Arabi, Mahsa & Gholamian, Mohammad Reza, 2023. "Resilient closed-loop supply chain network design considering quality uncertainty: A case study of stone quarries," Resources Policy, Elsevier, vol. 80(C).
    7. 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.
    8. Selma Gütmen & Sankar Kumar Roy & Gerhard-Wilhelm Weber, 2024. "An overview of weighted goal programming: a multi-objective transportation problem with some fresh viewpoints," 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. 32(3), pages 557-568, September.
    9. Shyamali Ghosh & Karl-Heinz Küfer & Sankar Kumar Roy & Gerhard-Wilhelm Weber, 2023. "Type-2 zigzag uncertain multi-objective fixed-charge solid transportation problem: time window vs. preservation technology," 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(1), pages 337-362, March.
    10. Soumen Kumar Das & Magfura Pervin & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2023. "Multi-objective solid transportation-location problem with variable carbon emission in inventory management: a hybrid approach," Annals of Operations Research, Springer, vol. 324(1), pages 283-309, May.
    11. Duygu Üçüncü & Süreyya Akyüz & Erdal Gül, 2024. "A novel auto-pruned ensemble clustering via SOCP," 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. 32(3), pages 819-841, September.
    12. Erfan Babaee Tirkolaee & Zahra Dashtian & Gerhard-Wilhelm Weber & Hana Tomaskova & Mehdi Soltani & Nasim Sadat Mousavi, 2021. "An Integrated Decision-Making Approach for Green Supplier Selection in an Agri-Food Supply Chain: Threshold of Robustness Worthiness," Mathematics, MDPI, vol. 9(11), pages 1-30, June.
    13. Zheng, Xiao-Xue & Chang, Ching-Ter, 2021. "Topology design of remote patient monitoring system concerning qualitative and quantitative issues," Omega, Elsevier, vol. 98(C).

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