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A KKM approach for inverse capacitated transportation problem in neutrosophic environment

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Abstract

Inverse optimization is one of the interesting areas in both fundamental and applied research. This paper introduces a new approach, named as Khalifa, Kumar, and Mirjalili (KKM) approach, for solving the inverse capacitated transportation problem (ICTP) in a neutrosophic environment. The problem is considered with unit transportation cost associated with the single-valued trapezoidal neutrosophic numbers. Using the proposed KKM approach, the objective of the research work is to make the transportation cost as low as possible, which can lead to an optimal feasible solution. Based on the score function, the neutrosophic problem is first converted into an equivalent deterministic problem and then into a linear programming (LP) problem. Afterwards, by applying the dual and optimality conditions the inverse problem is obtained. In the end, an illustrative example is given to support the proposed approach and to gain more insights.

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Acknowledgements

The authors would like to thank the Editor-in-Chief and anonymous referees for their suggestions and helpful comments that have led to an improvement both in the quality and clarity of the paper.

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Author notes

  1. Hamiden Abd El-Wahed Khalifa

    Present address: Mathematics Department, College of Science and Arts, Al-Badaya, Qassim University, Buraydah, Saudi Arabia

Authors and Affiliations

  1. Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt

    Hamiden Abd El-Wahed Khalifa

  2. Mathematics Division, School of Advanced Sciences and Languages (SASL), VIT Bhopal University, Bhopal, 466 114, India

    Pavan Kumar

  3. Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Fortitude Valley, Brisbane, QLD, 4006, Australia

    Seyedali Mirjalili

  4. YFL (Yonsei Frontier Lab), Yonsei University, Seoul, South Korea

    Seyedali Mirjalili

Authors
  1. Hamiden Abd El-Wahed Khalifa
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  2. Pavan Kumar
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  3. Seyedali Mirjalili
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Corresponding author

Correspondence to Pavan Kumar.

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Khalifa, H.A.EW., Kumar, P. & Mirjalili, S. A KKM approach for inverse capacitated transportation problem in neutrosophic environment. Sādhanā 46, 166 (2021). https://doi.org/10.1007/s12046-021-01682-5

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  • DOI: https://doi.org/10.1007/s12046-021-01682-5

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