On Bottleneck-Rough Cost Interval Integer Transportation Problems

  • A. AkilbashaEmail author
  • G. Natarajan
  • P. Pandian
Conference paper
Part of the Trends in Mathematics book series (TM)


An innovative method, namely, level maintain method, is proposed for finding all efficient solutions to a bottleneck-rough cost interval integer transportation problem in which the unit transportation cost, supply, and demand parameters are rough interval integers and the transportation time parameter is an interval integer. The solving procedure of the suggested method is expressed and explained with a numerical example. The level maintain method will dispense the necessary determined support to decision-makers when they are handling time-related logistic problems in rough nature.


  1. 1.
    Akilbasha, A., Natarajan, G., Pandian, P.: Finding an optimal solution of the interval integer transportation problems with rough nature by split and separation method. International Journal of Pure and Applied Mathematics. 106, 1–8 (2016)CrossRefGoogle Scholar
  2. 2.
    Chanas, S., Delgado, M., Verdegayand, J.L., Vila, M.A.: Interval and fuzzy extensions of classical transportation problems. TranspPlann Technol. 17, 203–218 (1993)Google Scholar
  3. 3.
    Hongwei Lu., Guohe Huang., Li He.: An inexact rough-interval fuzzy linear programming method for generating conjunctive water-allocation strategies to agricultural irrigation systems. Applied Mathematical Modelling. 35, 4330–4340 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Kundu, P., Kar, S., Maiti, M.: Some solid transportation model with crisp and rough costs. World Academy of Science, Engineering and Technology. 73, 185–192 (2013)Google Scholar
  5. 5.
    Moore, R.E.: Method and applications of interval analysis. SLAM, Philadelphia, PA (1979)CrossRefGoogle Scholar
  6. 6.
    Pandian, P., Natarajan, G.: A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Appl. Math. Sci. 4, 79–90 (2010)zbMATHGoogle Scholar
  7. 7.
    Pandian, P., Natarajan, G.: A new method for finding an optimal solution for transportation problems. International Journal of Math. Sci. & Engg. Appls. 4, 59–65 (2010)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Pandian, P., Natarajan, G.: A new method for finding an optimal solution of fully interval integer transportation problems. Appl. Math. Sci. 4, 1819–1830 (2010)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Pandian, P., Natarajan, G.: A new method for solving bottleneck-cost transportation problems. International Mathematical Forum. 6, 451–460 (2011)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Pandian, P., Natarajan, G., Akilbasha, A.: Fully rough integer interval transportation problems. International Journal Of Pharmacy and Technology. 8, 13866–13876 (2016)Google Scholar
  11. 11.
    Pawlak, Z.: Rough sets. International Journal of Information and Computer Science. 11, 341–356 (1981)CrossRefGoogle Scholar
  12. 12.
    Sengupta, A., Pal, T.K.: Interval-valued transportation problem with multiple penalty factors. VU Journal of Physical Sciences. 9, 71–81 (2003)Google Scholar
  13. 13.
    Shanmugasundari, M., Ganesan, K.: A novel approach for the fuzzy optimal solution of fuzzy transportation problem. Int. J. Eng. Res. Appl. 3, 1416–1421 (2013)Google Scholar
  14. 14.
    Subhakanta Dash., Mohanty, S.P.: Transportation programming under uncertain environment. International Journal of Engineering Research and Development. 7, 22–28 (2013)Google Scholar
  15. 15.
    Sudhagar, S., Ganesan, K.: A fuzzy approach to transport optimization problem. Optimization and Engineering. 17, 965–980 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Youness, E.: Characterizing solutions of rough programming problems. European Journal of Operational Research. 168, 1019–1029 (2006)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsVellore Institute of TechnologyVelloreIndia

Personalised recommendations