Annals of Operations Research

, Volume 253, Issue 1, pp 599–620 | Cite as

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

  • Sankar Kumar Roy
  • Gurupada Maity
  • Gerhard Wilhelm Weber
  • Sirma Zeynep Alparslan Gök
Article

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.

Keywords

Transportation problem Multi-objective decision making Multi-choice programming Goal programming Conic scalarization Interval uncertainty 

Notes

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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Sankar Kumar Roy
    • 1
  • Gurupada Maity
    • 1
  • Gerhard Wilhelm Weber
    • 2
  • Sirma Zeynep Alparslan Gök
    • 3
  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  3. 3.Department of Mathematics, Faculty of Arts and ScienceSuleyman Demirel UniversityIspartaTurkey

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