Advertisement

Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment

  • Sankar Kumar RoyEmail author
  • Sudipta Midya
Article
  • 10 Downloads

Abstract

This paper analyzes multi-objective fixed-charge solid transportation problem with product blending in intuitionistic fuzzy environment. The parameters of multi-objective fixed-charge solid transportation problem may not be defined precisely because of globalization of the market and other unmanageable factors. So, we often hesitate in prediction of market demand and other parameters connected with transporting systems in a period. Based on these facts, the parameters of the formulated model are chosen as triangular intuitionistic fuzzy number. New ranking method is used to convert intuitionistic fuzzy multi-objective fixed-charge solid transportation problem with product blending to a deterministic form. New intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) is initiated to derive Pareto-optimal solution from the proposed model. Furthermore, we solve the formulated model using intuitionistic fuzzy programming; and a comparison is drawn between the obtained solutions extracted from the approaches. Finally, a practical (industrial) problem is incorporated to illustrate the applicability and feasibility of the proposed study. Conclusions with future research based on the paper are described at last.

Keywords

Fixed-charge solid transportation problem Product blending Multi-objective optimization Intuitionistic fuzzy programming Ranking method Intuitionistic fuzzy TOPSIS 

Notes

Compliance with Ethical Standards

Conflict of interests

The authors have no conflict of interest for the publication of this paper.

References

  1. 1.
    Abo-Sinna MA, Amer AH, Ibrahim AS (2008) Extension of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure. Appl Math Model 32:292–302CrossRefzbMATHGoogle Scholar
  2. 2.
    Aggarwal S, Gupta C (2016) Solving intuitionistic fuzzy solid transportation problem via new ranking method based on signed distance, International Journal of Uncertainty. Fuzziness Knowl-Based Syst 24:483–501CrossRefzbMATHGoogle Scholar
  3. 3.
    Angelov PP (1997) Optimization in an intuitionistic fuzzy environments. Fuzzy Sets Syst 86:299–306MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefzbMATHGoogle Scholar
  5. 5.
    Boran FE, Gen S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368CrossRefGoogle Scholar
  6. 6.
    Capuano N, Chiclana F, Fujita H, Viedma EH, Loia V (2018) Fuzzy group decision making with incomplete information guided by social influence. IEEE Trans Fuzzy Syst 26(3):1704– 1718CrossRefGoogle Scholar
  7. 7.
    Chen T, Tsao CY (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst 159:1410–1428MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Das A, Bera UK, Maiti M (2016) A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters, Applied Intelligence.  https://doi.org/10.1007/s10489-016-0794-y
  9. 9.
    Das S, Guha D (2016) A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems. Fuzzy Inf Eng 8:41–74MathSciNetCrossRefGoogle Scholar
  10. 10.
    Grzegrorzewski P (2003) The hamming distance between two intuitionistic fuzzy sets. In: proceedings of the 10th IFSA World Congress, Istanbul, pp s35–38Google Scholar
  11. 11.
    Haley KB (1962) The solid transportation problen. Oper Res 10:448–463CrossRefzbMATHGoogle Scholar
  12. 12.
    Hao Z, Xu Z, Zhao H, Fujita H (2018) A Dynamic weight determination approach based on the intuitionistic fuzzy bayesian network and its application to emergency decision making. IEEE Trans Fuzzy Syst 26 (4):1893–1907CrossRefGoogle Scholar
  13. 13.
    Hirsch WM, Dantzig GB (1968) The Fixed charge problem. Naval Res Logist Q 15:413–424MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hwang CL, Yoon K (1981) Multiple attribute decision making: Methods and Applications. Springer, New YorkCrossRefzbMATHGoogle Scholar
  15. 15.
    Izadikhah M (2009) Using the Hamming distance to extend TOPSIS in a fuzzy environment. J Comput Appl Math 231:200–207MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Jimenez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Sets Syst 100:45–57MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kundu P, Kar S, Maiti M (2013) Multi-objective multi-item solid transportation problem in fuzzy environment. Appl Math Model 37:2028–2038MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kundu P, Kar MB, Kar S, Pal T, Maiti M (2017) A solid transportation model with product blending and parameters as rough variables. Soft Comput 21:2297–2306CrossRefzbMATHGoogle Scholar
  19. 19.
    Li DF (2010) TOPSIS-Based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy set. IEEE Trans Fuzzy Syst 18(2):299–311Google Scholar
  20. 20.
    Liao H, Si G, Xu Z, Fujita H (2018) Hesitant fuzzy linguistic preference utility set and its application in selection of fire rescue plans. Int J Environ Res Publ Health 15(4):664CrossRefGoogle Scholar
  21. 21.
    Li L, Lai KK (2000) A fuzzy approach to the multi-objective transportation problem. Comput Oper Res 27:43–57MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Mahapatra DR, Roy SK, Biswal MP (2010) Multi-objective stochastic transportation problem involving log-normal. J Phys Sci 14:63–76zbMATHGoogle Scholar
  23. 23.
    Maity G, Roy SK (2016) Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand. Int J Manag Sci Eng Manag 11(1):62–70Google Scholar
  24. 24.
    Maity G, Roy SK, Verdegay JL (2016) Multi-objective transportation problem with cost reliability under uncertain environment. Int J Comput Intell Syst 9(5):839–849CrossRefGoogle Scholar
  25. 25.
    Maity G, Roy SK (2017) Multi-objective transportation problem using fuzzy decision variable through multi-choice programming. Int J Oper Res Inf Syst 8(3):82–96CrossRefGoogle Scholar
  26. 26.
    Majumder S, Kundu P, Kar S, Pal T (2018) Uncertain multi-objective multi-item fixed-charge solid transportation problem with budget constraint, Soft Computing, pp 1-23.  https://doi.org/10.1007/s00500-017-2987-7
  27. 27.
    Midya S, Roy SK (2014) Solving single-sink fixed-charge multi-objective multi-index stochastic transportation problem. Am J Math Manag Sci 33(4):300–314Google Scholar
  28. 28.
    Midya S, Roy SK (2017) Analysis of interval programming in different environments and its application to fixed-charge transportation problem, Discrete Mathematics. Algorithm Appl 9(3):1750040. 17 pageszbMATHGoogle Scholar
  29. 29.
    Mitchell HB, Schaefer PA (2000) On ordering fuzzy numbers. Int J Intell Syst 15(11):981–993CrossRefzbMATHGoogle Scholar
  30. 30.
    Nehi HM, Maleki HR (2005) Intuitionistic fuzzy numbers and its applications in fuzzy optimization problem. In: Proceedings of the 9th WSEAS international conference on systems, Athens, pp 1–5Google Scholar
  31. 31.
    Papageorgiou DJ, Toriello A, Nemhauser GL, Savelsbergh MWP (2012) Fixed-charge transportation with product blending. Transp Sci 46(2):281–295CrossRefGoogle Scholar
  32. 32.
    Rani D, Gulati TR, Harish G (2016) Multi-objective non-linear programming problem in intuitionistic fuzzy environment: optimistic and pessimistic view point. Expert Syst Appl 64:228–238CrossRefGoogle Scholar
  33. 33.
    Roy SK, Ebrahimnejad A, Verdegay JL, Das S (2018) New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana 43(3):1–12.  https://doi.org/10.1007/s12046-017-0777-7
  34. 34.
    Roy SK, Maity G, Weber GW (2017) Multi-objective two-stage grey transportation problem using utility function with goals. CEJOR 25:417–439MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Roy SK, Maity G (2017) Minimizing cost and time through single objective function in multi-choice interval valued transportation problem. J Intell Fuzzy Syst 32:1697–1709CrossRefzbMATHGoogle Scholar
  36. 36.
    Roy SK, Maity G, Weber GW, Gök SZA (2017) Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Ann Oper Res 253(1): 599–620MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Roy SK, Midya S, Yu VF (2018) Multi-objective fixed-charge transportation problem with random rough variables, International Journal of Uncertainty. Fuzziness Knowl-Based Syst 26(6):971–996CrossRefGoogle Scholar
  38. 38.
    Sengupta D, Das A, Bera UK (2018) A gamma type-2 defuzzication method for solving a solid transportation problem considering carbon emission, Applied Intelligence.  https://doi.org/10.1007/s10489-018-1173-7
  39. 39.
    Singh SK, Yadav SP (2016) A new approach for solving intuitionistic fuzzy transportation problem of type-2. Ann Oper Res 243:349–363MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Tian X, Xu Z, Fujita H (2018) Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information. Knowl-Based Syst 161:172–184CrossRefGoogle Scholar
  41. 41.
    Vahdani A, Mousavi SM, Moghaddam RT (2011) Group decision making based on novel fuzzy modified TOPSIS method. Appl Math Model 35:4257–4269MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Varghese B, Kuriakose S (2016) Centroid of an intuitionistic fuzzy number. Notes Intuitionistic Fuzzy Sets 18(1):19–24zbMATHGoogle Scholar
  43. 43.
    Wahed WFAE, Lee SM (2006) Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34:158–166CrossRefGoogle Scholar
  44. 44.
    Wang JW, Cheng CH, Cheng HK (2009) Fuzzy hierarchical TOPSIS for supplier selection. Appl Soft Comput 9:377–386CrossRefGoogle Scholar
  45. 45.
    Zadeh LA (1965) Fuzzy Sets. Inf Control 8:338–353CrossRefzbMATHGoogle Scholar
  46. 46.
    Zavardehi SMA, Nezhad SS, Moghaddam RT, Yazdani M (2013) Solving a fuzzy fixed charge solid transportation problen by metaheuristics. Fuzzy Sets Syst 57:183–194Google Scholar
  47. 47.
    Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197CrossRefGoogle Scholar
  48. 48.
    Zhou X, Wang L, Liao H, Wang S, Lev B, Fujita H (2019) A prospect theory-based group decision approach considering consensus for portfolio selection with hesitant fuzzy information. Knowl-Based Syst 168:28–38CrossRefGoogle Scholar
  49. 49.
    Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia

Personalised recommendations