**
Vandana Y. Kakran **
Department of Mathematics and Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India.

**
Jayesh M. Dhodiya **
Department of Mathematics and Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India.

DOI https://doi.org/10.33889/IJMEMS.2021.6.5.085

**Abstract**

This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.

**Keywords-** Capacitated solid transportation problem, Uncertain variable, Optimistic value model, Fuzzy programming technique.

**Citation**

Kakran, V. Y., & Dhodiya, J. M. (2021). Multi-Objective Capacitated Solid Transportation Problem with Uncertain Variables. *International Journal of Mathematical, Engineering and Management Sciences*, *6*(5), 1406-1422. https://doi.org/10.33889/IJMEMS.2021.6.5.085.

**Conflict of Interest**

Both the authors declare that they have no conflict of interest.

**Acknowledgements**

The authors are grateful to all the anonymous referees for their valuable comments and suggestions which helped in improving the quality of the paper. The first author would also like to extend her gratitude to the Council of Scientific & Industrial Research, File No.09/1007(0003)/2017-EMR-I, New Delhi, India for providing financial support to this research work.

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