CFP last date
20 May 2024
Call for Paper
June Edition
IJCA solicits high quality original research papers for the upcoming June edition of the journal. The last date of research paper submission is 20 May 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Multi-Objective Chance Constrained Capacitated Transportation Problem based on Fuzzy Goal Programming

by Surapati Pramanik, Durga Banerjee
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 44 - Number 20
Year of Publication: 2012
Authors: Surapati Pramanik, Durga Banerjee
10.5120/6383-8877

Surapati Pramanik, Durga Banerjee . Multi-Objective Chance Constrained Capacitated Transportation Problem based on Fuzzy Goal Programming. International Journal of Computer Applications. 44, 20 ( April 2012), 42-46. DOI=10.5120/6383-8877

@article{ 10.5120/6383-8877,
author = { Surapati Pramanik, Durga Banerjee },
title = { Multi-Objective Chance Constrained Capacitated Transportation Problem based on Fuzzy Goal Programming },
journal = { International Journal of Computer Applications },
issue_date = { April 2012 },
volume = { 44 },
number = { 20 },
month = { April },
year = { 2012 },
issn = { 0975-8887 },
pages = { 42-46 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume44/number20/6383-8877/ },
doi = { 10.5120/6383-8877 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:36:07.285084+05:30
%A Surapati Pramanik
%A Durga Banerjee
%T Multi-Objective Chance Constrained Capacitated Transportation Problem based on Fuzzy Goal Programming
%J International Journal of Computer Applications
%@ 0975-8887
%V 44
%N 20
%P 42-46
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents chance constrained multi-objective capacitated transportation problem based on fuzzy goal programming problem. Generally, in transportation problem the capacity of each origin and the demand of each destination are random in nature. The inequality constraints representing supplies and demands are probabilistically described. In many real situations, there are capacity restrictions on units of commodities which are shipped from different sources to different destinations. In the model formulation, supply and demand constraints are converted into equivalent deterministic forms. Then, we define the fuzzy goal levels of the objective functions. The fuzzy objective goals are then characterized by the associated membership functions. In the solution process, two fuzzy goal programming models are considered by minimizing negative deviational variables to obtain compromise solution. Distance function is used in order to obtain the most compromise optimal solution. In order to demonstrate the effectiveness of the proposed approach, an illustrative example of chance constrained multi-objective capacitated transportation problem is solved.

References
  1. Hitchcock, F. L. 1941. Distribution of a product from several sources to numerous localities. Journal of Mathematical Physics 20, 224–230.
  2. Koopmans, T. C. 1951. Activity Analysis of Production and Allocation, Cowels Commission Monograph 13, Wiley, New York.
  3. Charnes, A. , and Cooper, W. W. 1954. The stepping stone method for explaining linear programming calculation in transportation problem. Management Science 1, 49-69.
  4. Kantorovitch, L. V. 1960. Mathematical methods in the organization and planning of production. Publication House of the Leningrad State University (in Russian Language), English translation in Management Science 6(4), 366 – 422.
  5. Haley, K. B. 1963. The solid transportation problem. Operation Research 10, 448-463.
  6. Patel, G. , and Tripathy, J. 1989. The solid transportation problem and its variants. International Journal of Management and Systems 5, 17-36.
  7. 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.
  8. Current, J. , and Min, H. 1986. Multiobjective design of transportation networks: taxonomy and annotation. European Journal of Operational Research 26,187-201.
  9. Appa, G. M. 1973. The transportation problem and its variants. Operations Research Quarterly 24, 79-99.
  10. Brigden,M. E. B. 1974. A variant of the transportation problem in which the constraints are of mixed type. Operations Research Quarterly 25, 437-445.
  11. Misra, S. , and Das, C. 1981a. Three-dimensional transportation problem with capacity restriction. NZOR 9, 47-58.
  12. Misra, S. , and Das, C. 1981b. Solid transportation problem with lower and upper bounds on the rim condition-a note. NZOR 9,137-140.
  13. Klingman,D. , Napier,A. , and Stu, J. 1974. NETGEN: a program for generating large scale capacitated assignment, transportation cost network problems. Management Science 20, 814-821.
  14. Wagner, H. M. 1959. ON a class of capacitated transportation problems. Management Science 5, 304-318.
  15. 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.
  16. Dantzig, G. B. 1955. Linear programming under uncertainty. Management Science 1, 197 – 206.
  17. 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.
  18. Charnes, A. , and Cooper, W. W. 1963. Deterministic equivalent for optimizing and satisfying under uncertainty. Operational Research 11(1), 18 – 39.
  19. Hassin, R. , and Zemel, E. 1988. Probabilistic analysis of the capacitated transportation problem. Mathematics of Operation Research 13,80-89.
  20. 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.
  21. 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.
  22. Pramanik, S. and Roy, T. K. 2007. Fuzzy goal programming approach to multilevel programming problems. European Journal of Operational Research 176(2), 1151-1166.
  23. Pramanik, S. and Dey, P. P. 2011. Quadratic bi-level programming problem based on fuzzy goal programming approach. International Journal of Software Engineering & Applications 2(4), 41-59.
  24. Yu, P. L. 1973. A class of solutions for group decision problems. Management Science19, 936-946.
  25. Pramanik, S. and Roy, T. K. 2008. Multiobjective transportation model with fuzzy parameters: a priority based fuzzy goal programming. Journal of Transportation Systems Engineering and Information Technology 8 (3), 40-48.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy Goal Programming Chance Constrained Programming Transportation Problem Capacitated Transportation Problem Randomness Membership Function Multi Objective Decision Making

Powered by PhDFocusTM