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Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming for Capacitated Transportation Problem

by A.k. Bhargava, S.r. Singh, Divya Bansal
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 107 - Number 3
Year of Publication: 2014
Authors: A.k. Bhargava, S.r. Singh, Divya Bansal
10.5120/18732-9971

A.k. Bhargava, S.r. Singh, Divya Bansal . Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming for Capacitated Transportation Problem. International Journal of Computer Applications. 107, 3 ( December 2014), 18-23. DOI=10.5120/18732-9971

@article{ 10.5120/18732-9971,
author = { A.k. Bhargava, S.r. Singh, Divya Bansal },
title = { Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming for Capacitated Transportation Problem },
journal = { International Journal of Computer Applications },
issue_date = { December 2014 },
volume = { 107 },
number = { 3 },
month = { December },
year = { 2014 },
issn = { 0975-8887 },
pages = { 18-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume107/number3/18732-9971/ },
doi = { 10.5120/18732-9971 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:40:06.040835+05:30
%A A.k. Bhargava
%A S.r. Singh
%A Divya Bansal
%T Multi-Objective Fuzzy Chance Constrained Fuzzy Goal Programming for Capacitated Transportation Problem
%J International Journal of Computer Applications
%@ 0975-8887
%V 107
%N 3
%P 18-23
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents a multi-objective fuzzy chance constrained capacitated transportation problem based on fuzzy goal programming problem with capacity restrictions on commodities which are shipped from different sources to different destinations. The capacity of each origin and the demand of each destination are considered random in nature with fuzzy normal stochastic parameters following normal distribution with fuzzy mean and fuzzy variance respectively. These inequality constraints are also considered as fuzzy probabilistic in nature assuming to be triangular fuzzy numbers. Further, the supply and demand constraints are converted into equivalent deterministic forms. Then, we define the fuzzy goal tolerance limit of each of the objective functions which are then characterized by the associated membership functions. In the solution process, the fuzzy parameters are defuzzied by applying graded mean integration method which provided a satisfactory result. Further, an illustrative example is solved to demonstrate the effectiveness of the proposed model.

References
  1. Chowdary, B. V. and Slomp J. 2002. Production planning under dynamic product environment: A multi-objective goal programming approach, Research Report, University of Groningen.
  2. Sen, N. and Nandi M. 2012. A goal programming approach to rubber plantation planning in Tripura. Applied Mathematical Science 6 (124), 6171-6179.
  3. Hitchcock, F. L. 1941. Distribution of product from several sources to numerous localities. Journal of Mathematical Physics 20, 224-230.
  4. Charnes, A. and Cooper W. W. 1954. The stepping stone method for explaining linear programming calculation in transportation problem. Management Science 1, 49-69.
  5. Haley, K. B. 1963. The solid transportation problem. Operational Research 10, 448-463.
  6. Ringuest, J. L. and Rinks D. B. 1987. Interactive solutions for the linear multi-objective transportation problem. European Journal of Operational Research 32, 96-106.
  7. Current, J. and Min H. 1986. Multiobjective design of transportation networks: Taxonomy and annotation. European Journal of Operational Research 26, 187-201.
  8. Misra, S. and Das C. 1981a. Three-dimensional transportation problem with capacity restriction. New Zealand Operational Research 9, 47-58.
  9. Misra, S. and Das C. 1981b. Solid transportation problem with lower and upper bounds on the rim condition–A note. New Zealand Operational Research 9, 137-140.
  10. Narasimhan, R. 1980. Goal programming in a fuzzy environment. Decision Sciences 11, 325-336.
  11. Narasimhan, R. 1981. On fuzzy goal programming–Some comments. Decision Sciences 12, 532-538.
  12. Narasimhan, R. 1982. A geometric averaging procedure for constructing super transitive approximation to binary comparison matrices. Fuzzy Sets and Systems 8, 53-61.
  13. Hannan, E. L. 1981. Linear programming with multiple fuzzy goals. Fuzzy Sets and Systems 6, 235-248.
  14. Hannan, E. L. 1981. On fuzzy goal programming. Decision Sciences 12, 522-531.
  15. Hannan, E. L. 1982. Contrasting fuzzy goal programming and fuzzy multicriteria programming. Decision Sciences 13, 337-339.
  16. Ignizio, J. P. 1982. On the (re) discovery of fuzzy goal programming. Decision Sciences 13, 331-336.
  17. Rubin, P. A. and Narasimhan R. 1984. Fuzzy goal programming with nested priorities. Fuzzy Sets and Systems 14, 115-129.
  18. Tiwari, R. N. , Rao J. R. and Dharmar S. 1985. Some aspects of fuzzy goal programming, International Symposium on Mathematical Modeling of Ecological Environmental and Biological Systems, Kanpur, India.
  19. Tiwari, R. N. , Dharmar S. and Rao J. R. 1987. Fuzzy goal programming–An additive model. Fuzzy Sets and Systems 24, 27-34.
  20. Tiwari, R. N. , Dharmar S. and Rao J. R. 1986. Priority structure in fuzzy goal programming. Fuzzy Sets and Systems 19, 251-259.
  21. Chanas, S. and Kuchta D. 2002. Fuzzy goal programming–One notion, many meanings. Control and Cybernetics 31 (4), 871-890.
  22. Dantzig, G. B. and Mandansky A. 1961. On the solution of two-stage linear programs under uncertainty. In I. J. Neyman, Editor, Proc. 4th Berkeley Symp. Math. Stat. Prob. , 165-176.
  23. Dantzig, G. B. 1955. Linear programming under uncertainty. Management Science 1, 197-206.
  24. Hassin, R. and Zemel E. 1988. Probabilistic analysis of the capacitated transportation problem. Mathematics of Operation Research 13, 80-89.
  25. Bit, A. K. , Biswal M. P. and Alam S. S. 1992. Fuzzy programming approach to multi-criteria decision making transportation problem. Fuzzy Sets and Systems 50, 135-141.
  26. Bit, A. K. , Biswal M. P. and Alam S. S. 1994. Fuzzy programming approach to chance constrained multi-objective transportation problem. The Journal of Fuzzy Mathematics 2, 117-130.
  27. Chen, H. and Hsieh C. H. 1999. Graded mean integration representation of generalized fuzzy numbers. Journal of Chinese Fuzzy System Association 5 (2), 1-7.
  28. Pramanik, S. and Roy T. R. 2005. A fuzzy goal programming approach for multi-objective capacitated transportation problem. Tamsui Oxford Journal of Management Sciences 21, 75-88.
  29. Pramanik, S. and Banerjee D. 2012. Multi-objective chance constrained capacitated transportation problem based on fuzzy goal programming. International Journal of Computer Applications (0975-8887) 44 (20), 42-46.
  30. Kumar, M. and Pal B. B. 2013. Fuzzy goal programming to chance constrained multilevel programming problems. International Journal of Advanced Computer Research 3 (1), 193-200.
  31. Gunes, M. and Umarosman N. 2005. Fuzzy goal programming approach on computation of the fuzzy arithmetic mean. Mathematical and Computational Applications 10 (2), 221-220.
  32. Nayebi, M. A. , Sharifi M. , Shahriari M. R. and Zarabadipour O. 2012. Fuzzy-chance constrained multi-objective programming applications for inventory control model. Applied Mathematical Sciences 6 (5), 209-228.
  33. Zimmermann, H. -J. 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems 1, 45-55.
  34. Pramanik, S. and Dey P. P. 2011. Quadratic bi-level programming problem based on fuzzy goal programming approach. International Journal of Software Engineering and Applications 2 (4), 41-59.
  35. Scharge, L. 2013. Lingo 11. 0. Lindo Systems Inc. Website: What's Best! http://www. lindo. com/.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy goal programming fuzzy chance constrained programming capacitated transportation problem multi objective decision making graded mean integration method.

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