Skip to main content
SpringerLink
Log in

Uncertain multi-objective multi-product solid transportation problems

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

The solid transportation problem is an important generalization of the classical transportation problem as it also considers the conveyance constraints along with the source and destination constraints. The problem can be made more effective by incorporating some other factors, which make it useful in real life situations. In this paper, we consider a fully fuzzy multi-objective multi-item solid transportation problem and present a method to find its fuzzy optimal-compromise solution using the fuzzy programming technique. To take into account the imprecision in finding the exact values of parameters, all the parameters are taken as trapezoidal fuzzy numbers. A numerical example is solved to illustrate the methodology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2

Similar content being viewed by others

References

  1. Schell E D 1955 Distribution of a product by several properties. In: Proceedings of 2nd Symposium in Linear Programing, DCS/comptroller, HQ US Air Force, Washington DC, 615–642

    Google Scholar 

  2. Haley K B 1962 The solid transportation problem. Oper. Res. 10: 448–463

    Article  MATH  Google Scholar 

  3. Zadeh L A 1965 Fuzzy sets. Inf. Control 8: 338–353

    Article  MathSciNet  MATH  Google Scholar 

  4. Bector C R and Chandra S 2010 Fuzzy mathematical programming and fuzzy matrix games, studies in fuzziness and soft computing, 169 Springer, Verlag, Heidelberg

    Google Scholar 

  5. Zimmermann H J 1978 Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1: 45–55

    Article  MathSciNet  MATH  Google Scholar 

  6. Bit A K, Biswal M P and Alam S S 1993 Fuzzy programming approach to multi-objective solid transportation problem. Fuzzy Sets Syst. 57: 183–194

    Article  MathSciNet  MATH  Google Scholar 

  7. Li Y, Ida K and Gen M 1997 Improved genetic algorithm for solving multi-objective solid transportation problem with fuzzy numbers. Comput. Ind. Eng. 33: 589–592

    Article  MathSciNet  Google Scholar 

  8. Liu B and Liu Y K 2002 Expected Value of Fuzzy Variable and Fuzzy Expected Value Models. IEEE Trans. Fuzzy Syst. 10: 445–450

  9. Islam S and Roy T K 2006 A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems. Eur. J. Oper. Res. 173: 387–404

    Article  MathSciNet  MATH  Google Scholar 

  10. Ojha A, Das B, Mondala S and Maiti M 2009 An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality. Math. Comput. Model. 50: 166–178

    Article  MathSciNet  MATH  Google Scholar 

  11. Gupta A, Kumar A and Kaur A 2012 Mehar’s method to find exact fuzzy optimal solution of unbalanced fully fuzzy multi-objective transportation problems. Optim. Lett. 6: 1737–1751

    Article  MathSciNet  MATH  Google Scholar 

  12. Cui Q and Sheng Y 2012 Uncertain programming model for solid transportation problem. Information 15: 342–348

    Google Scholar 

  13. Kundu P, Kar S and Maiti M 2013 Multi-objective multi-item solid transportation problem in fuzzy environment. Appl. Math. Model. 37: 2028–2038

    Article  MathSciNet  Google Scholar 

  14. Baidya A, Bera U K and Maiti M 2014 Solution of multi-item interval valued solid transportation problem with safety measure using different methods. OPSearch 51: 1–22

    Article  MathSciNet  MATH  Google Scholar 

  15. Kundu P, Kar S and Maiti M 2014 Multi-objective solid transportation problems with budget constraint in uncertain environment, Int. J. Syst. Sci. 45: 1668–1682

    Article  MathSciNet  MATH  Google Scholar 

  16. Ebrahimnejad A 2014 A simplified new approach for solving fuzzy transportation problems with generalized trapezoidal fuzzy numbers. Appl. Soft Comput. 19 (2014) 171176

    MathSciNet  Google Scholar 

  17. Kaufmann A and Gupta M M 1985 Introduction to fuzzy arithmetics: Theory and applications. Van Nostrand Reinhold, New York

  18. Liou T S and Wang M J 1992 Ranking fuzzy number with integral values. Fuzzy Sets Syst. 50: 247–255

    Article  MathSciNet  MATH  Google Scholar 

  19. Kumar A and Kaur A 2014 Optimal way of selecting cities and conveyances for supplying coal in uncertain environment. Sādhanā 39: 165–187

  20. Jimenez F and Verdegay J L 1997 Obtaining fuzzy solutions to the fuzzy solid transportation problem with genetic algorithms. Proceedings of sixth IEEE internatonal conference on fuzzy systems, Barcelona, Spain, 1657–1663

    Google Scholar 

  21. Jimenez F and Verdegay J L 1998 Uncertain solid transportation problems. Fuzzy Sets Syst. 100: 45–57

    Article  MathSciNet  Google Scholar 

  22. Jimenez F and Verdegay J L 1999 Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach. Eur. J. Oper. Res. 117: 485–510

    Article  MATH  Google Scholar 

  23. Yang L and Liu L 2007 Fuzzy fixed charge solid transportation problem and algorithm. Appl. Soft Comput. 7: 879–889

    Article  Google Scholar 

  24. Liu S T 2006 Fuzzy total transportation cost measures for fuzzy solid transportation problem. Appl. Math. Comput. 174: 927–941

    MathSciNet  MATH  Google Scholar 

  25. Gen M, Ida K, Li Y and Kubota E 1995 Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm. Comput. Ind. Eng. 29: 537–541

Download references

Acknowledgments

The authors are thankful to the reviewers for their valuable comments and suggestions, which improved the presentation of the paper. The first author is also thankful to CSIR, Government of India, for providing financial support.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247 667, India

    Deepika Rani & T R Gulati

Authors
  1. Deepika Rani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T R Gulati
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Deepika Rani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rani, D., Gulati, T.R. Uncertain multi-objective multi-product solid transportation problems. Sādhanā 41, 531–539 (2016). https://doi.org/10.1007/s12046-016-0491-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-016-0491-x

Keywords

Search

Navigation