Skip to main content
Log in

Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment

  • Published:
Journal of Transportation Security Aims and scope Submit manuscript


In this paper we introduce “safety factor” in transportation problem. Here we solve Multi Item Interval Valued Solid Transportation Problem (MIIVSTP) with safety factor under Desire Safety Measure (DSM) fuzzy-stochastic and stochastic. When items are transported from origins to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency etc. in some routes specially in developing countries. Due to this reason desired total safety factor is being introduced. Also our goal is to evaluate the solution of MIIVSTP using Global Criteria Method. Here we developed five model with taking DSM as fuzzy-stochastic and stochastic and safety factor as crisp, fuzzy, interval, stochastic, fuzzy-stochastic. Here the transportation costs are intervals, the corresponding multi-objective transportation problem is formulated using “mean and width” technique. Then the problem is converted to a single objective transportation problem taking convex combination of the objectives according to their weights. Finally all the models are solved by Generalized Reduced Gradient (GRG) method using LINGO software. Numerical examples are used to illustrate the model and methodologies.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others


  • Basu M, Pal BB, Kundu A (1994) An algorithm for optimum solution of solid fixed charge transportation problem. Optimization 31:283–291

    Article  Google Scholar 

  • Bit AK, Biswal MP, Alam SS (1993) Fuzzy programming approach to multi-objective solid transportation problem. Fuzzy Set Syst 57:183–194

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jimenez F, Verdegay JL (1998) Uncertain solid transportation problem. Fuzzy Sets and System 100(1–3):45–57

    Google Scholar 

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

    Article  Google Scholar 

  • Kaufmann A, Gupta MM (1991) Introduction to fuzzy arithmetic: theory and applications, Van Nostrand Reinhold, New York

  • Kwakernaak H (1978) Fuzzy random variables - I. Definitions and theorems. Inf Sci 15:1–19

    Article  Google Scholar 

  • Kwakernaak H (1979) Fuzzy random variables -II, algorithms and examples forthe discrete case. Inf Sci 17:253–278

    Article  Google Scholar 

  • Li Y, Ida K, Gen M, Kobuchi R (1997a) Neural network approach for multi-criteria sold transportation problem. Comput Ind Eng 33:465–468

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Liberling H (1981) On finding compromise solutions for multi criteria problems using the fuzzy min-operator. Fuzzy Set Syst 6:105–118

    Article  Google Scholar 

  • Puri ML, Ralescu D (1986) Fuzzy random variables. J Math Anal Appl 114:409–422

    Article  Google Scholar 

  • Sengupta A, Pal TK (2004) Interval-valued transportation problem with multiple penalty factors. Vidyasagar 562 University Journal of physical Science 71–81

  • Sengupta A, Pal TK (2000) On comparing interval numbers. Eur J Oper Res 127:28–43

    Article  Google Scholar 

  • Shell E (1955) Distribution of a product by several properties. Directorate of Management Analysis, Proc. 2nd Symp. On Linear programming, Vol. 2, pp 615–642, DCs/ Comptroller H.Q.U.S.A.F., Washington, DC

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

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

  • Zimmerman J (1978) Fuzzy programming and Linearprogramming with several objective functions. Fuzzy Sets Syst 1:45–55

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to U. K. Bera.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baidya, A., Bera, U.K. & Maiti, M. Multi-item interval valued solid transportation problem with safety measure under fuzzy-stochastic environment. J Transp Secur 6, 151–174 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: