Absolute point algorithm for solving unbalanced fuzzy transportation problem

K. Rathi, S. Muruganantham

Article ID: 573
Vol 3, Issue 1, 2020

VIEWS - 733 (Abstract) 406 (PDF)

Abstract


 In real time situations, the total availability of goods or product may be more or less than the actual market demand and the unbalanced transportation situation arise more commonly. Such unbalanced Transportation Problems (TP) are solved by introducing dummy source or destination which do not exist in reality. The optimal allocation involves cells from such dummy source or destination and the allocated number of quantities are held back at one or more origins. The paper aims to propose an algorithm based on Absolute Points to solve unbalanced TP under fuzzy environment. The proposed algorithm is advantageous than the existing algorithms  in such a way that it provides the added information of transporting the excess availability from dummy supply point to appropriate destination to meet future demands at minimum cost. Finally, by virtue of the proposed algorithm an example is done to illustrate the practicality and the effectiveness of the proposed algorithm. 


Keywords


Transportation management; fuzzy transportation problem; absolute point; heptagonal fuzzy numbers

Full Text:

PDF


References


1. Adlakha V and Kowalski K 1998 A Quick Sufficient Solution to the More-for-Less Paradox in the Transportation Problem, International Journal of Management Science 26(4):541-547.

2. Arsham H and Khan A B 1989 A simplex-type algorithm for general transportation problems: An alternative to stepping stone. J. Oper. Res. Soc. 40: 581–590.

3. Basirzadeh H 2011 An approach for solving fuzzy transportation problem. Applied Mathematical Science 5: 1549–1566.

4. Das M K and Baruah H K 2007 Solution of the transportation problem in fuzzified form Journal of Fuzzy Mathematics 15: 79–95.

5. Deepika Rani, T R Gulati and Amit Kumar A 2014 A method for unbalanced transportation problems in fuzzy environment 39(3): 573–581.

6. Gani A N, Samuel A E and Anuradha D 2011 Simplex type algorithm for solving fuzzy transportation problem. Tamsui Oxf. J. Math. Sci. 27: 89–98.

7. Hitchcock FL (1941) The distribution of a product from several resources to numerous localities, Journal of Mathematical Physics 20: 224-230.

8. Rathi K and Balamohan S. (2016). A Mathematical Model for Subjective Evaluation of Alternatives in Fuzzy Multi-Criteria Group Decision Making Using COPRAS Method. International Journal of Fuzzy Systems. Vol.19. 10.1007/s40815-016-0256-z.

9. Rathi.K and Balamohan.S (2014) Representation and ranking of fuzzy numbers with Heptagonal membership function using value and ambiguity index, Applied Mathematical Sciences, 87(8): 4309-4321.

10. Saad O M and Abbas S A 2003 A parametric study on transportation problem under fuzzy environment. Journal of Fuzzy Mathematics 11: 115–124.

11. Zadeh L A 1965 Fuzzy sets. Inf. Control, 8: 338–353.




DOI: https://doi.org/10.24294/tm.v1i2.573

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

This site is licensed under a Creative Commons Attribution 4.0 International License.