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Multi-objective two-stage grey transportation problem using utility function with goals

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Abstract

Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.

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Acknowledgements

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 very grateful to the Editor-in-Chief, Professor Ulrike Leopold-Wildburger, and the anonymous reviewers for their valuable and constructive comments which strongly helped to improve the quality of this 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

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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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Correspondence to Sankar Kumar Roy.

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Roy, S.K., Maity, G. & Weber, GW. Multi-objective two-stage grey transportation problem using utility function with goals. Cent Eur J Oper Res 25, 417–439 (2017). https://doi.org/10.1007/s10100-016-0464-5

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