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Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal

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Abstract

This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.

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Acknowledgments

The second author is very much thankful to University Grants Commission (UGC) of India for providing financial support to continue this research work under [JRF(UGC)] scheme: Sanctioned letter number [F.17-130/1998(SA-I)] dated 26/06/2014. The authors are also very much thankful to the anonymous reviewers for their comments to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, 721102, India

    Sankar Kumar Roy & Gurupada Maity

  2. Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Gerhard Wilhelm Weber

  3. Department of Mathematics, Faculty of Arts and Science, Suleyman Demirel University, 32260, Isparta, Turkey

    Sirma Zeynep Alparslan Gök

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  1. Sankar Kumar Roy
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  2. Gurupada Maity
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  3. Gerhard Wilhelm Weber
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  4. Sirma Zeynep Alparslan Gök
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Correspondence to Sankar Kumar Roy.

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Roy, S.K., Maity, G., Weber, G.W. et al. Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Ann Oper Res 253, 599–620 (2017). https://doi.org/10.1007/s10479-016-2283-4

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