Advertisement

Novel multi-objective, multi-item and four-dimensional transportation problem with vehicle speed in LR-type intuitionistic fuzzy environment

  • Sarbari Samanta
  • Dipak Kumar JanaEmail author
  • Goutam Panigrahi
  • Manoranjan Maiti
Original Article
  • 11 Downloads

Abstract

In this paper, we present some novel multi-objective, multi-item and four-dimensional transportation problems in LR-type intuitionistic fuzzy environment. Here, for the first time, the speed of different vehicles and rate of disturbance of speed due to the road condition of different routes for the time minimization objective are introduced. Furthermore, three models are presented under three different conditions. The reduced deterministic models are obtained on implementation of a defuzzification approach by using the accuracy function. Moreover, a new method for converting multi-objective problem into single-objective one is proposed and also we use convex combination method. The models are illustrated by some numerical examples and optimal results are presented.

Keywords

Four-dimensional transportation problem Intuitionistic fuzzy number LR-type intuitionistic fuzzy number Accuracy function 

Notes

Compliance with ethical standards

Funding

We declared that research work was done by self-finance. No institutional fund has been provided.

Conflict of interest

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

Ethical approval

The authors declared that this article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. 1.
    Hitchcock FL (1941) The distribution of a product from several sources to numerous localities. J Math Phys 20:224–230MathSciNetCrossRefGoogle Scholar
  2. 2.
    Houthakker HS (1955) On the numerical solution of the transportation problem. J Oper Res Soc Am 3(2):210–214MathSciNetzbMATHGoogle Scholar
  3. 3.
    Adlakha V, Kowalski K (1998) A quick sufficient solution to the more-for-less paradox in the transportation problems. Omega 26:541–547CrossRefGoogle Scholar
  4. 4.
    Arsham H, Khan AB (1989) A simplex type algorithm for general transportation problems: an alternative to stepping-stone. J Oper Res Soc 40:581–590CrossRefGoogle Scholar
  5. 5.
    Juman ZAMS, Hoque MA (2015) An efficient heuristic to obtain a better initial feasible solution to the transportation problem. Appl Soft Comput 34:813–826CrossRefGoogle Scholar
  6. 6.
    Haley K (1962) The solid transportation problem. Oper Res 10:448–463CrossRefGoogle Scholar
  7. 7.
    Bhatia HL (1981) Indefinite quadratic solid transportation problem. J Inf Optim Sci 2(3):297–303MathSciNetzbMATHGoogle Scholar
  8. 8.
    Pandian P, Anuradha D (2010) A new approach for solving solid transportation problems. Appl Math Sci 4:3603–3610MathSciNetzbMATHGoogle Scholar
  9. 9.
    Pandian P, Kavitha K (2012) Sensitivity analysis in solid transportation problems. Appl Math Sci 6(136):6787–6796MathSciNetzbMATHGoogle Scholar
  10. 10.
    Pramanik S, Jana DK, Mait M (2016) Bi-criteria solid transportation problem with substitutable and damageable items in disaster response operations on fuzzy rough environment. Socio Econ Plan Sci 55:1–13CrossRefGoogle Scholar
  11. 11.
    Bera S, Giri PK, Jana DK, Basu K, Maiti M (2018) Multi-item 4D-TPs under budget constraint using rough interval. Appl Soft Comput 71:364–385CrossRefGoogle Scholar
  12. 12.
    Zimmermann HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1(1):45–55MathSciNetCrossRefGoogle Scholar
  13. 13.
    Jiménez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Sets Syst 100(1–3):45–57MathSciNetCrossRefGoogle Scholar
  14. 14.
    Pramanik S, Jana DK, Maiti M (2013) Multi-objective solid transportation problem in imprecise environments. J Transp Secur 6(2):131–150CrossRefGoogle Scholar
  15. 15.
    Pramanik S, Jana DK, Maiti M (2015) A fixed charge multi-objective solid transportation problem in random fuzzy environment. J Intell Fuzzy Syst 28(6):2643–2654MathSciNetCrossRefGoogle Scholar
  16. 16.
    Pramanik S, Jana DK, Maiti K (2014) A multi objective solid transportation problem in fuzzy, bi-fuzzy environment via genetic algorithm. Int J Adv Oper Manag 6:4–26Google Scholar
  17. 17.
    Samanta S, Jana DK (2019) A multi-item transportation problem with mode of transportation preference by MCDM method in interval type-2 fuzzy environment. Neural Comput Appl 31(2):605–617CrossRefGoogle Scholar
  18. 18.
    Jana DK, Pramanik S, Maiti M (2016) Mean and CV reduction methods on Gaussian type-2 fuzzy set and its application to a multilevel profit transportation problem in a two-stage supply chain network. Neural Comput Appl 28(9):2703–2726CrossRefGoogle Scholar
  19. 19.
    Attanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefGoogle Scholar
  20. 20.
    Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86(3):299–306MathSciNetCrossRefGoogle Scholar
  21. 21.
    Yager RR (2009) Some aspects of intuitionistic fuzzy sets. Fuzzy Optim Decis Mak 8(1):67–90MathSciNetCrossRefGoogle Scholar
  22. 22.
    Guha D, Chakraborty D (2010) A theoretical development of distance measure for intuitionistic fuzzy numbers. Int J Math Math Sci.  https://doi.org/10.1155/2010/949143 MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Beliakov G, Bustince H, James S, Calvo T, Fernandez J (2012) Aggregation for atanassovs intuitionistic and interval valued fuzzy sets: the median operator. IEEE Trans Fuzzy Syst 20(3):487–498CrossRefGoogle Scholar
  24. 24.
    Hajiagha SHR, Mahdiraji HA, Hashemi SS, Zavadskas EK (2015) Evolving a linear programming technique for MAGDM problems with interval valued intuitionistic fuzzy information. Expert Syst Appl 42(23):9318–9325CrossRefGoogle Scholar
  25. 25.
    Chakraborty D, Jana DK, Roy TK (2014) A new approach to solve intuitionistic fuzzy optimization problem using possibility, necessity, and credibility measures. Int J Eng Math.  https://doi.org/10.1155/2014/593185 CrossRefzbMATHGoogle Scholar
  26. 26.
    Chakraborty D, Jana DK, Roy TK (2015) A new approach to solve multi-objective multi-choice multi-item Atanassov’s intuitionistic fuzzy transportation problem using chance operator. J Intell Fuzzy Syst 28:843–865MathSciNetCrossRefGoogle Scholar
  27. 27.
    Chakraborty D, Jana DK, Roy TK (2015) Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem. OPSEARCH 52(3):431–471MathSciNetCrossRefGoogle Scholar
  28. 28.
    Chakraborty D, Jana DK, Roy TK (2016) Expected value of intuitionistic fuzzy number and its application to solve multi-objective multi-item solid transportation problem for damageable items in intuitionistic fuzzy environment. J Intell Fuzzy Syst 30:1109–1122CrossRefGoogle Scholar
  29. 29.
    Jana DK (2016) Novel arithmetic operations on type-2 intuitionistic fuzzy and its applications to transportation problem. Pac Sci Rev A Nat Sci Eng 18:178–189Google Scholar
  30. 30.
    Singh V, Yadav SP (2017) Development and optimization of unrestricted LR-type intuitionistic fuzzy mathematical programming problems. Expert Syst Appl 80:147–161CrossRefGoogle Scholar
  31. 31.
    Kaur J, Kumar A (2013) Mehar’s method for solving fully fuzzy linear programming problems with L-R fuzzy parameters. Appl Math Model 37:7142–7153MathSciNetCrossRefGoogle Scholar
  32. 32.
    Ghanbari R, Amiri NM, Yousefpour R (2010) Exact and approximate solutions of fuzzy LR linear systems: new algorithms using a least squares model and the ABS approach. Iran J Fuzzy Syst 7(2):1–18MathSciNetzbMATHGoogle Scholar
  33. 33.
    Nagoorgani A, Ponnalagu R (2012) A new approach on solving intuitionistic fuzzy linear programming problem. Appl Math Sci 6:3467–3474MathSciNetzbMATHGoogle Scholar
  34. 34.
    Tanino T, Tanaka T, Inuiguchi M (2003) Multi-objective programming and goal programming: theory and applications. Springer, BerlinCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Sarbari Samanta
    • 1
    • 2
  • Dipak Kumar Jana
    • 1
    Email author
  • Goutam Panigrahi
    • 2
  • Manoranjan Maiti
    • 3
  1. 1.Department of Applied SciencesHaldia Institute of TechnologyHaldia, Purba MedinipurIndia
  2. 2.Department of MathematicsNational Institute of TechnologyDurgapurIndia
  3. 3.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia

Personalised recommendations