Hungarian Method to Solve Travelling Salesman Problem with Fuzzy Cost

Jadunath Nayak; Sudarsan Nanda; Srikumar Acharya

doi:https://doi.org/10.14445/22315373/IJMTT-V49P544

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 49 | Number 5 | Year 2017 | Article Id. IJMTT-V49P544 | DOI : https://doi.org/10.14445/22315373/IJMTT-V49P544

Hungarian Method to Solve Travelling Salesman Problem with Fuzzy Cost

Jadunath Nayak, Sudarsan Nanda, Srikumar Acharya

Citation :

Jadunath Nayak, Sudarsan Nanda, Srikumar Acharya, "Hungarian Method to Solve Travelling Salesman Problem with Fuzzy Cost," International Journal of Mathematics Trends and Technology (IJMTT), vol. 49, no. 5, pp. 281-284, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V49P544

Abstract

The Travelling Salesman problem is one of the most common problem in O.R. But in real life situation the problem is often not useful due to its crisp nature. Use of fuzzy can make the problem more useful in day to day life. We consider a Travelling Salesman Problem with costs of travelling as trapezoidal fuzzy numbers. Fuzzy ranking function is used to handel trapezoidal fuzzy numbers. Hungering Algorithm is used to solve the problem. An example illustrates the use of the proposed method.

Keywords

Travelling Salesman Problem, Fuzzy.

References

[1] Hadi Basirzadeh. An approach for solving fuzzy transportation problem. Applied Mathematical Sciences, 5(32):1549–1566, 2011.
[2] Norman Biggs, E Keith Lloyd, and Robin J Wilson. Graph Theory, 1736-1936. Oxford University Press, 1976.
[3] Arindam Chaudhuri and Kajal De. Fuzzy multi-objective linear programming for traveling salesman problem. Afr. J. Math. Comp. Sci. Res, 4(2):64–70, 2011.
[4] Péter Földesi and János Botzheim. Modeling of loss aversion in solving fuzzy road transport traveling salesman problem using eugenic bacterial memetic algorithm. Memetic Computing, 2(4):259–271, 2010.
[5] Amit Kumar and Anila Gupta. Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions. Fuzzy Information and Engineering, 3(1):3–21, 2011.
[6] WHAT’S NEW. Encyclopedia> travelling salesman problem.
[7] Hassan Sarhadi and Keivan Ghoseiri. An ant colony system approach for fuzzy traveling salesman problem with time windows. The International Journal of Advanced Manufacturing Technology, 50(9-12):1203–1215, 2010.