Skip to main content

Advertisement

SpringerLink
Log in

A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper is based on two mathematical models for multi-item multi-stage solid transportation problem with budget on total transportation cost in Gaussian type-2 fuzzy environment considering the fixed opening charge and operating cost in distribution center. The first model is about transportation of breakable/damageable items, and the second one considers non breakable/damageable items. The main aspect here is to develop the mathematical formulation of multi stage related solid transportation problem where several items are available for transportation. In order to deal with the Gaussian type-2 fuzziness, two chance-constrained programming models are developed based on generalized credibility measures for the objective function as well as the constraints sets with the help of the CV-based reductions method. Finally the reduced model is turned into its equivalent parametric programming problem. The problem is of high complexity and is difficult to find the optimal solution by any classical method and hence a time and space based meta-heuristic Genetic Algorithm has been proposed. Also the equivalent crisp models are solved using GA and LINGO 13.0 and after comparison, GA results are better. The proposed models and techniques are finally illustrated by providing numerical examples. Some sensitivity analysis and particular cases are presented and discussed. Degrees of efficiency is also evaluated for both the techniques.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Klose A, Drexl A (2005) Facility location models for distribution system design. Eur J Oper Res 162 (1):4–29

    Article  MathSciNet  MATH  Google Scholar 

  2. Sahin G, Sural H (2007) A review of hierarchical facility location models. Comput Oper Res 34(8):2310–2331

    Article  MathSciNet  MATH  Google Scholar 

  3. Melo MT, Nickel S, Saldanha-da-Gama F (2009) Facility location and supply chain management-a review. Eur J Oper Res 196(2):401–412

    Article  MathSciNet  MATH  Google Scholar 

  4. Fox M, Barbuceanu M, Teigen R (2000) Agent-oriented supply chain management. Int J Flex Manuf Syst 12(2):165– 188

    Article  Google Scholar 

  5. Raj KAD, Rajendran C (2012) A genetic algorithm for solving the fixed-charge transportation model: two-stage problem. Comput Oper Res 39(9):2016–2032

    Article  MATH  Google Scholar 

  6. Liu C-H (2011) Using genetic algorithms for the coordinated scheduling problem of a batching machine and two-stage transportation. Appl Math Comput 217(24):10095–10104

    MathSciNet  MATH  Google Scholar 

  7. Tang L, Gong H (2008) A hybrid two-stage transportation and batch scheduling problem. Appl Math Model 32(12):2467–2479

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhu H (2012) A two stage scheduling with transportation and batching. Inf Process Lett 112:728–731

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu C, Fan Y, Ordonez F (2009) A two-stage stochastic programming model for transportation network protection. Comput Oper Res 36:1582–1590

    Article  MathSciNet  MATH  Google Scholar 

  10. Zeballosa LJ, Méndeza CA, Barbosa-Povoab AP, Novaisc AQ (2013) Multi-stage stochastic optimization of the design and planning of a closed-loop supply chain. Computer Aided Chemical Enggnering 32:691–696

    Article  Google Scholar 

  11. Maggionia F, Perbolib G, Tadeib R (2014) The multi-path traveling salesman problem with stochastic travel costs: building realistic instances for City Logistics Applications. Transportation Research Procedia 3:528–536

    Article  Google Scholar 

  12. Pasandideha SHR, Niakib STA, Asadia K (2015) Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA. Inf Sci 292:57–74

    Article  MathSciNet  Google Scholar 

  13. Giri PK, Maiti MK, Maiti M Fully fuzzy fixed charge multi-item solid transportation problem. Appl Soft Comput. doi:10.1016/j.asoc.2014.10.003. article in press

  14. Ertogral K (2008) Multi-item single source ordering problem with transportation cost: a Lagrangian decomposition approach. Eur J Oper Res 191(1):156–165

    Article  MathSciNet  MATH  Google Scholar 

  15. Kundu P, Kar S, Maiti M (2013) Multi-objective multi-item solid transportation problem in fuzzy environment. Appl Math Model 37(4):2028–2038

    Article  MathSciNet  Google Scholar 

  16. Kundu P, Kar S, Maiti M (2014) A Fixed charge transportation problem with type-2 fuzzy variables. Inf Sci 255:170–186

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu ZQ, Liu YK (2010) Type-2 fuzzy variables and their arithmetic. Soft Comput 14:729–747

    Article  MATH  Google Scholar 

  18. Karnik NN, Mendel JM (2001) Centriod of a type-2 fuzzy set. Inf Sci 132:195–220

    Article  MathSciNet  MATH  Google Scholar 

  19. Qin R, Liu Y, Liu Z (2011) Methods of critical value reduction for type-2 fuzzy variables and their applications. J Comput Appl Math 235:1454–1481

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu P, Yang L, Wang L, Li S (2014) A solid transportation problem with type-2 fuzzy variables. Appl Soft Comput 24:543–558

    Article  Google Scholar 

  21. Mendel JM, Robert I, John B (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2)

  22. Zadeh L (1975) The concept of a linguistic variable and its application to appromximate resoning - I. Inf Sci 8:199–249

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu B, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10:445–450

    Article  Google Scholar 

  24. Yager RR (1981) A procedure for ordering fuzzy subsets of the unit interval. Inf Sci 24:143–161

    Article  MathSciNet  MATH  Google Scholar 

  25. Gani NA, Razak AK (2006) Two stage fuzzy transportation problem. J Phys Sci 10:63–69

    Google Scholar 

  26. Tang L, Gong H (2008) A hybrid two-stage transportation and batch scheduling problem. Appl Math Model 32:2467–2479

    Article  MathSciNet  MATH  Google Scholar 

  27. Ritha W, Vinotha JM (2009) Multi-objective two stage fuzzy transportation problem. J Phys Sci 13:107–120

    Google Scholar 

  28. Sudhakar VJ, Kumar VN (2010) Solving the multiobjective two stage fuzzy transportation problem by zero suffix method. Journal of Mathematics Research 2(4):135–140

    Article  MATH  Google Scholar 

  29. Brezin I, Cickov Z, Pekár J, Reiff M (2010) Multi-stage transportation problem with capacity limit. International Journal of Lean Thinking 1(1):42–57

    Google Scholar 

  30. Vignaux GA, Michalewicz ZA (1991) Genetic algorithm for the linear transpotation problem. IEEE Trans Syst Man Cybern 21:445–452

    Article  MathSciNet  MATH  Google Scholar 

  31. Kuo RJ, Huang CC (2009) Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Comput Math Appl 58(4):678–685

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank to the editor and the anonymous reviewers for their suggestions which have led to an improvement in both the quality and clarity of the paper. Dr. Bera acknowledges the financial assistance from Department of Science and Technology, New Delhi under the Research Project (F.No. SR/S4/MS:761/12).

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Agartala, Jirania, West Tripura, 799046, India

    Amrit Das & Uttam Kumar Bera

  2. Department of Applied Mathematics, Vidyasagar University, Midnapore, 721102, WB, India

    Manoranjan Maiti

Authors
  1. Amrit Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Uttam Kumar Bera
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manoranjan Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Uttam Kumar Bera.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A., Bera, U.K. & Maiti, M. A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters. Appl Intell 45, 923–951 (2016). https://doi.org/10.1007/s10489-016-0794-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-016-0794-y

Keywords

Search

Navigation