Main Article Content

Abstract

The objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given.

Keywords

Interval Transportation problems New interval arithmetic ASM methods Best candidate method . Improved ASM method Zero suffix method Zero point method

Article Details

How to Cite
Ganesan, R., & N, M. (2023). A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems. Pakistan Journal of Statistics and Operation Research, 19(3), 569-583. https://doi.org/10.18187/pjsor.v19i3.3983

References

    1. Ahmad, H. A. (2012). The best candidates method for solving optimization problems. Journal of computer science, 8(5):711.
    2. Das, S., Goswami, A., and Alam, S. (1999). Multiobjective transportation problem with interval cost, source and destination parameters. European Journal of Operational Research, 117(1):100–112.
    3. Ganesan, K. and Veeramani, P. (2005). On arithmetic operations of interval numbers. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 13(06):619–631.
    4. Gomah, T. I. G. E. M. and Samy, I. (2009). Solving transportation problem using object-oriented model. IJCSNS, 9(2):353.
    5. Hammer, P. L. (1969). Time-minimizing transportation problems. Naval Research Logistics Quarterly, 16(3):345–357.
    6. Keerthana, G. and Ramesh, G. (2019). A new approach for solving integer interval transportation problem with mixed constraints. In Journal of Physics: Conference Series, volume 1377, page 012043. IOP Publishing.
    7. Ma, M., Friedman, M., and Kandel, A. (1999). A new fuzzy arithmetic. Fuzzy sets and systems, 108(1):83–90.
    8. Man, E. L. and Baharum, A. (2011). A qualitative approach of identifying major cost influencing factors in palm oil mills and the relations towards production cost of crude palm oil. American Journal of Applied Sciences, 8(5):441.
    9. Murugesan, R. and Essakiyammal, T. (2020). Some challenging transportation problems to the asm method. Advances in Mathematics: Scientific Journal, 9(6):3357–3367.
    10. Murugesan, S., Kumar, and Ramesh, B. (2013). New optimal solution to fuzzy interval transportation problem. International Journal of Engineering Science and Technology, 3(1):188–192.
    11. Nirmala, T., Datta, D., Kushwaha, H., and Ganesan, K. (2011). Inverse interval matrix: A new approach. Applied Mathematical Sciences, 5(13):607–624.
    12. Pandian, P. and Natarajan, G. (2010). A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems. Applied mathematical sciences, 4(2):79–90.
    13. Patel, J. and Dhodiya, J. (2017). Solving multi-objective interval transportation problem using grey situation decision-making theory based on grey numbers. International Journal of Pure and Applied Mathematics, 113(2):219–233.
    14. Quddoos, A., Javaid, S., and Khalid, M. (2016). A revised version of asm-method for solving transportation problem. International Journal Agriculture, Statistics, Science, 12(1):267–272.
    15. Rani, D. and Kumar, A. G. (2010). Fuzzy Programming Technique for Solving Different Types of Multi Objective Transportation Problem. PhD thesis.
    16. Sengupta, A. and Pal, T. (2003). Interval-valued transportation problem with multiple penalty factors. VU Journal of Physical Sciences, 9:71–81.
    17. Sengupta, A. and Pal, T. K. (2000). On comparing interval numbers. European Journal of Operational Research, 127(1):28–43.
    18. Sudha, G., Ramesh, G., and Ganesan, K. (2021). A new approach for solving the fixed charge transportation problems with interval parameters. Annals of the Romanian Society for Cell Biology, 25(6):1147–1155.
    19. Sudha, S. V. (2012). A genetic based neuro fuzzy technique for process grain sized scheduling of parallel jobs. Journal of Computer Science, 8(1):48–54.
    20. Szwarc, W. (1971). Some remarks on the time transportation problem. Naval Research Logistics Quarterly, 18(4):473–485.
    21. Yao-guo, D., Zheng-Xin, W., Xue-mei, L., and Ning, X. (2009). The optimization model of objective weight in grey situation decision. In 2009 IEEE International Conference on Grey Systems and Intelligent Services (GSIS 2009), pages 1025–1028. IEEE.