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Solving Stochastic Fuzzy Transportation Problem with Mixed Constraints Using the Weibull Distribution

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  • T.K. Buvaneshwari
  • D. Anuradha

Abstract

The development in the industries has necessitated the growth of transportation methods. Due to the variation in the transportation systems, many problems seem to arise in the present times. One such problem is the stochastic fuzzy transportation problem (SFTP). The SFTP is a chance‐constrained programming (CCP) problem with probabilistic constraints where supply and demand are randomness, and the objective function is in fuzzy nature. In this paper, we have developed three models for the SFTP, where the constraints are mixed type following Weibull distribution (WD). The aim of the research work is to optimize the transportation cost in FTP under probabilistic mixed constraints. In order to achieve this, the cost coefficient of the fuzzy objective function is converted to alpha cut representation, and the probabilistic mixed constraints are converted to deterministic form by using the WD. The proposed models are illustrated by providing a numerical example, and the problem is solved using Lingo software. It is worth pointing out that these models are constructed from different points of view. The decision‐maker’s (DM’s) preference has the final say in the usage of the models. A sensitivity analysis (SA) is performed to explore the sensitivity of the parameters in the proposed model.

Suggested Citation

  • T.K. Buvaneshwari & D. Anuradha, 2022. "Solving Stochastic Fuzzy Transportation Problem with Mixed Constraints Using the Weibull Distribution," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6892342
    DOI: 10.1155/2022/6892342
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    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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    4. 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.
    5. 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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