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A Multi-Objective Stochastic Solid Transportation Problem with the Supply, Demand, and Conveyance Capacity Following the Weibull Distribution

Author

Listed:
  • Amrit Das

    (Department of Mathematics, VIT University, Vellore 632014, India
    Department of Industrial Engineering, Pusan National University, Busan 46241, Korea)

  • Gyu M. Lee

    (Department of Industrial Engineering, Pusan National University, Busan 46241, Korea)

Abstract

This study addresses a multi-objective stochastic solid transportation problem (MOSSTP) with uncertainties in supply, demand, and conveyance capacity, following the Weibull distribution. This study aims to minimize multiple transportation costs in a solid transportation problem (STP) under probabilistic inequality constraints. The MOSSTP is expressed as a chance-constrained programming problem, and the probabilistic constraints are incorporated to ensure that the supply, demand, and conveyance capacity are satisfied with specified probabilities. The global criterion method and fuzzy goal programming approach have been used to solve multi-objective optimization problems. Computational results demonstrate the effectiveness of the proposed models and methodology for the MOSSTP under uncertainty. A sensitivity analysis is conducted to understand the sensitivity of parameters in the proposed model.

Suggested Citation

  • Amrit Das & Gyu M. Lee, 2021. "A Multi-Objective Stochastic Solid Transportation Problem with the Supply, Demand, and Conveyance Capacity Following the Weibull Distribution," Mathematics, MDPI, vol. 9(15), pages 1-21, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1757-:d:601484
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    References listed on IDEAS

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    1. Dipanjana Sengupta & Amrit Das & Uttam Kumar Bera & Anirban Dutta, 2021. "A Humanitarian Green Supply Chain Management Considering Minimum Cost and Time," International Journal of Business Analytics (IJBAN), IGI Global, vol. 8(2), pages 63-82, April.
    2. A. C. Williams, 1963. "A Stochastic Transportation Problem," Operations Research, INFORMS, vol. 11(5), pages 759-770, October.
    3. Moddassir Khan Nayeem & Gyu M. Lee, 2021. "Robust Design of Relief Distribution Networks Considering Uncertainty," Sustainability, MDPI, vol. 13(16), pages 1-24, August.
    4. 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.
    5. A. Charnes & W. W. Cooper, 1959. "Chance-Constrained Programming," Management Science, INFORMS, vol. 6(1), pages 73-79, October.
    6. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.
    7. Adane Abebaw Gessesse & Rajashree Mishra & Mitali Madhumita Acharya & Kedar Nath Das, 2020. "Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 93-109, February.
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