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

  • Sankar Kumar Roy
  • Gurupada Maity
  • Gerhard-Wilhelm Weber
Original Paper


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.


Transportation problem Multi-objective decision making Goal programming Grey number Utility function 

Mathematics Subject Classification

90B06 90C29 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Sankar Kumar Roy
    • 1
  • Gurupada Maity
    • 1
  • Gerhard-Wilhelm Weber
    • 2
  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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