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On solving fully rough multi-objective fractional transportation problem: development and prospects

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Abstract

In these days, rough set theory has emerged as an invaluable tool for expressing uncertainty in various optimization problems as it takes into account both the consistency and the expertise of all the involved experts and thus leads to more realistic decisions. In view of this characteristic of the rough set theory, in this study, a fractional transportation problem in rough environment is investigated which is of great benefit because of being able to study the relative efficiency in various fields such as transportation, resource allocation, information theory, education, administration, etc. In particular, for many real-life transportation problems the objective may be interpreted as the ratio of physical and economic values, such as profit/cost, delivery speed/wastage, actual cost/standard cost, actual time/standard time, etc. A new methodology has been developed to solve the multi-objective fractional transportation problem with rough parameters in which, firstly, the problem is decomposed into two sub-models namely, the upper interval model and the lower interval model. Then the upper interval model is decomposed into two crisp fractional transportation problems to characterize the possibly Pareto-optimal solution and the lower interval model is decomposed into two crisp fractional transportation problems to characterize the surely Pareto-optimal solution, respectively. The proposed methodology incorporates the variable transformation method to address the non-linearity of the objective functions. Thereafter, the Pareto-optimal solution of the linearized model is obtained by using the weighted-sum method. The proposed approach provides a wide range for the obtained optimal compromise solution and allows the decision-maker to choose the best one as per the practical uses. At last, a case study is solved to demonstrate the applicability of the proposed methodology.

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Acknowledgements

The first author is thankful to the Ministry of Human Resource Development, India, for providing financial support to carry out this work. The authors would also like to thank the anonymous reviewers and the associate editor for their insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India

    Shivani & Deepika Rani

  2. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

    Ali Ebrahimnejad

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  1. Shivani
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  2. Deepika Rani
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  3. Ali Ebrahimnejad
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Correspondence to Ali Ebrahimnejad.

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Shivani, Rani, D. & Ebrahimnejad, A. On solving fully rough multi-objective fractional transportation problem: development and prospects. Comp. Appl. Math. 42, 266 (2023). https://doi.org/10.1007/s40314-023-02400-z

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