Skip to main content
SpringerLink
Log in

Multi-objective Solid Transportation Problem in Uncertain Environment

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

Although new information technologies decrease information and transaction costs, transportation problem of physical goods is still relevant. Globalization of trade increased the uncertainty that companies are facing, it also increased the importance of supply chain management in world economies drastically. Because transportation systems are crucial for operation management, the problem of finding efficient and sustainable solutions under such uncertain environments needs to be studied. Thus, this paper focuses on “multi-objective solid transportation problem (STP) in uncertain environment” and presents some approaches to find the compromised optimal solution of multi-objective STP. Then, compatible with uncertainty, fuzzy programming and some techniques of the fuzzy set theory are implemented to solve the problem by using Maple 17.02. A numerical example is executed and presented here to illustrate suggested procedures.

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

Similar content being viewed by others

References

  • Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):B-141

    Article  MathSciNet  MATH  Google Scholar 

  • Bit AK, Biswal MP, Alam SS (1993) Fuzzy programming approach to multiobjective solid transportation problem. Fuzzy Sets Syst 57(2):183–194

    Article  MathSciNet  MATH  Google Scholar 

  • Chanas S, Kuchta D (1996) Multiobjective programming in optimization of interval objective functions—a generalized approach. Eur J Oper Res 94(3):594–598

    Article  MATH  Google Scholar 

  • Dalman H, Gonce Köçken H, Sivri M (2013) A solution proposal to indefinite quadratic interval transportation problem. New Trends Math Sci 1(2):07–12

    Google Scholar 

  • Dalman H, Nuran G, Sivri M (2016) A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty. Int J Fuzzy Syst 18(4):716–729

    Article  MathSciNet  Google Scholar 

  • El-Wahed WFA, Lee SM (2006) Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34(2):158–166

    Article  Google Scholar 

  • Haley K (1962) The solid transportation problem. Oper Res 10:448–463

    Article  MATH  Google Scholar 

  • Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20(2):224–230

    Article  MathSciNet  MATH  Google Scholar 

  • Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225

    Article  MATH  Google Scholar 

  • Jimenez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Sets Syst 100(1):45–57

    Article  MathSciNet  Google Scholar 

  • Jiménez F, Verdegay JL (1999) Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach. Eur J Oper Res 117(3):485–510

    Article  MATH  Google Scholar 

  • Kundu P, Samarjit K, Manoranjan M (2014) Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci 45(8):1668–1682

    Article  MathSciNet  MATH  Google Scholar 

  • Ma WX, Fan E (2011) Linear superposition principle applying to Hirota bilinear equations. Comput Math Appl 61(4):950–959

    Article  MathSciNet  MATH  Google Scholar 

  • Ma WX, Lee JH (2009) A transformed rational function method and exact solutions to the 3 + 1 dimensional Jimbo-Miwa equation. Chaos Solitons Fract 42(3):1356–1363

    Article  MathSciNet  MATH  Google Scholar 

  • Mohamed RH (1997) The relationship between goal programming and fuzzy programming. Fuzzy Sets Syst 89(2):215–222

    Article  MathSciNet  Google Scholar 

  • Mohyud-Din ST, Aslam Noor M, Noor KI (2009a) Traveling wave solutions of seventh-order generalized KdV equations using He’s polynomials. Int J Nonlinear Sci Numer Simul 10(2):227–234

    Article  MATH  Google Scholar 

  • Mohyud-Din ST, Noor MA, Noor KI (2009b) Some relatively new techniques for nonlinear problems. Math Probl Eng 2009:234849. doi:10.1155/2009/234849

    MathSciNet  MATH  Google Scholar 

  • Mohyud-Din ST, Yildirim A, Demirli G (2011a) Analytical solution of wave system in R n with coupling controllers. Int J Numer Methods Heat Fluid Flow 21(2):198–205

    Article  MathSciNet  MATH  Google Scholar 

  • Mohyud-Din ST, Yildirim A, Sariaydin S (2011b) Numerical soliton solution of the Kaup-Kupershmidt equation. Int J Numer Methods Heat Fluid Flow 21(3):272–281

    Article  MathSciNet  MATH  Google Scholar 

  • Moore RE (1966) Interval analysis, vol 4. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Noor MA et al (2006) An iterative method with cubic convergence for nonlinear equations. Appl Math Comput 183(2):1249–1255

    MathSciNet  MATH  Google Scholar 

  • Pramanik S, Dipak KJ, Maiti M (2013) Multi-objective solid transportation problem in imprecise environments. J Transp Secur 6(2):131–150

    Article  Google Scholar 

  • Sakawa M (1993) Fuzzy sets and interactive multiobjective optimization. Plenum Press, New York

    Book  MATH  Google Scholar 

  • Shell E (1955) Distribution of a product by several properties. Directorate of Management Analysis. In: Proceedings of the Second Symposium in Linear Programming, vol 2

  • Tiwari RN, Dharmar S, Rao JR (1987) Fuzzy goal programming—an additive model. Fuzzy Sets Syst 24(1):27–34

    Article  MathSciNet  MATH  Google Scholar 

  • Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Gelisim University, Avcılar, 34310, Istanbul, Turkey

    Hasan Dalman

  2. Department of Mathematical Engineering, Yildiz Technical University, Esenler, 34210, Istanbul, Turkey

    Mustafa Sivri

Authors
  1. Hasan Dalman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mustafa Sivri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hasan Dalman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dalman, H., Sivri, M. Multi-objective Solid Transportation Problem in Uncertain Environment. Iran J Sci Technol Trans Sci 41, 505–514 (2017). https://doi.org/10.1007/s40995-017-0254-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-017-0254-5

Keywords

Search

Navigation