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Genetic algorithm based fuzzy programming approach for multi-objective linear fractional stochastic transportation problem involving four-parameter Burr distribution

Author

Listed:
  • Adane Abebaw Gessesse

    (KIIT, Deemed to be University)

  • Rajashree Mishra

    (KIIT, Deemed to be University)

  • Mitali Madhumita Acharya

    (KIIT, Deemed to be University)

  • Kedar Nath Das

    (NIT Silchar)

Abstract

In real life situations, it is difficult to handle multi-objective linear fractional stochastic transportation problem. It can’t be solved directly using mathematical programming approaches. In this paper, a solution procedure is proposed for the above problem using a genetic algorithm based fuzzy programming method. The supply and demand parameters of the said problem follow four-parameters Burr distribution. The proposed approach omits the derivation of deterministic equivalent form as required in case of classical approach. In the given methodology, initially the probabilistic constraints present in the problem are tackled using stochastic programming combining the strategy adopted in genetic algorithm. Throughout the problem, feasibility criteria is maintained. Then after, the non-dominated solution are obtained using genetic algorithm based fuzzy programming approach. In the proposed approach, the concept of fuzzy programming approach is inserted in the genetic algorithm cycle. The proposed algorithm has been compared with fuzzy programming approach and implemented on two examples. The result shows the efficacy of the proposed algorithm over fuzzy programming approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:ijsaem:v:11:y:2020:i:1:d:10.1007_s13198-019-00928-0
    DOI: 10.1007/s13198-019-00928-0
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    References listed on IDEAS

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    3. Zbigniew Michalewicz & George A. Vignaux & Matthew Hobbs, 1991. "A Nonstandard Genetic Algorithm for the Nonlinear Transportation Problem," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 307-316, November.
    4. S. Dutta & S. Acharya & Rajashree Mishra, 2016. "Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 835-872, December.
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    Cited by:

    1. 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.

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