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Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables

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Listed:
  • S. Dutta

    (KIIT University)

  • S. Acharya

    (KIIT University)

  • Rajashree Mishra

    (KIIT University)

Abstract

This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:53:y:2016:i:4:d:10.1007_s12597-016-0264-7
    DOI: 10.1007/s12597-016-0264-7
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    References listed on IDEAS

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    1. Islam, Sahidul & Roy, Tapan Kumar, 2006. "A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 387-404, September.
    2. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    3. Liu, Shiang-Tai & Kao, Chiang, 2004. "Solving fuzzy transportation problems based on extension principle," European Journal of Operational Research, Elsevier, vol. 153(3), pages 661-674, March.
    4. Abd El-Wahed, Waiel F. & Lee, Sang M., 2006. "Interactive fuzzy goal programming for multi-objective transportation problems," Omega, Elsevier, vol. 34(2), pages 158-166, April.
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    Cited by:

    1. 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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