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Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach

by Surapati Pramanik, Partha Pratim Dey
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 25 - Number 11
Year of Publication: 2011
Authors: Surapati Pramanik, Partha Pratim Dey
10.5120/3155-4360

Surapati Pramanik, Partha Pratim Dey . Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach. International Journal of Computer Applications. 25, 11 ( July 2011), 34-40. DOI=10.5120/3155-4360

@article{ 10.5120/3155-4360,
author = { Surapati Pramanik, Partha Pratim Dey },
title = { Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach },
journal = { International Journal of Computer Applications },
issue_date = { July 2011 },
volume = { 25 },
number = { 11 },
month = { July },
year = { 2011 },
issn = { 0975-8887 },
pages = { 34-40 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume25/number11/3155-4360/ },
doi = { 10.5120/3155-4360 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:11:33.631856+05:30
%A Surapati Pramanik
%A Partha Pratim Dey
%T Bi-level Linear Fractional Programming Problem based on Fuzzy Goal Programming Approach
%J International Journal of Computer Applications
%@ 0975-8887
%V 25
%N 11
%P 34-40
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents fuzzy goal programming approach for bi-level linear fractional programming problem with a single decision maker at the upper level and a single decision maker at the lower level. Here, each level has single objective function, which are fractional in nature and the system constraints are linear functions. In the proposed approach, we first construct fractional membership functions by determining individual best solution of the objective functions subject to the system constraints. The fractional membership functions are then transformed into equivalent linear membership functions by first order Taylor polynomial series. Since the objectives of both level decision makers are potentially conflicting in nature, a possible relaxation of both level decisions is considered for avoiding decision deadlock. Then, the fuzzy goal programming approach is used for achieving highest degree of each of the membership goals to the maximum possible by minimizing the negative deviational variables. To demonstrate the efficiency of the proposed approach, an illustrative numerical example is solved and Euclidean distance function is used to obtain compromise optimal solution.

References
  1. Bard, J. F. 1984. Optimality conditions for the bilevel programming problem. Naval Research Logistics Quarterly 31, 13-26.
  2. Bialas, W. F., and Karwan, M. H. 1984. Two level linear programming. Management Science 30, 1004-1020.
  3. Candler, W., and Townsley, R. 1982. A linear two-level programming problem. Computers & Operations Research 9, 59-76.
  4. Fortuni-Amat, J., and McCarl, B. 1981. A representation and economic interpretation of a two-level programming problem. Journal of Operational Research Society 32, 783-792.
  5. Anandalingam, G. 1988. A mathematical programming model of decentralized multi-level systems. Journal of the Operational Research Society 39 (11), 1021-1033.
  6. Lai, Y. J. 1996. Hierarchical optimization: a satisfactory solution. Fuzzy Sets and Systems 77, 321–335.
  7. Shih, H. S., Lai, Y. J., and Lee, E. S. 1996. Fuzzy approach for multi-level programming problem. Computers & Operations Research 23 (1), 73-91.
  8. Shih, H. S., and Lee, E. S. 2000. Compensatory fuzzy multiple level decision making. Fuzzy Sets and Systems 114, 71-87.
  9. Sakawa, M., and Nishizaki, I., and Uemura, Y. 1998. Interactive fuzzy programming for multilevel linear programming problems. Computers and Mathematics with Applications 36, 71-86.
  10. Pramanik, S., and Roy, T. K. 2007. Fuzzy goal programming approach to multi-level programming problems. European Journal of Operational Research 176, 1151-1166.
  11. Thirwani, D., and Arora, S. R. 1993. Bi-level linear fractional programming problem. Cahiers Du Cero 35 (1-2), 135-149.
  12. Sakawa, M., and Nishizaki, I. 2002. Interactive fuzzy programming for decentralized two-level linear fractional programming problem. Fuzzy Sets and Systems 125, 301-315.
  13. Sakawa, M., and Nishizaki, I. 2001. Interactive fuzzy programming for two-level linear fractional programming problem. Fuzzy Sets and Systems 119, 31-40.
  14. Calvete, H. I., and Galé, C. 2004. A note on bi-level linear fractional programming problem. European Journal of Operational Research 152, 296-299.
  15. Calvete, H. I., and Galé, C. 1999. The bi-level linear/linear fractional programming problem. European Journal of Operational Research 114, 188-197.
  16. Mishra, S. 2007. Weighting method for bi-level linear fractional programming problems 183, 296-302.
  17. Ahlatcioglu, M., and Tirayaki, F. 2007. Interactive fuzzy programming for decentralized two-level linear programming problems (DTLLFP). Omega 35, 432-450.
  18. Malhotra, N., and Arora, S. R. 2000. An algorithm to solve linear fractional bilevel programming problem via goal programming. Journal of the Operational Research Society of India (OPSEARCH) 37 (1), 1-13.
  19. Baky, I. A. 2009. Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy Sets and Systems 160, 2701-2713.
  20. Toksarı, M. D. 2010. Taylor series approach for bi-level linear fractional programming problem. Selçuk Journal of Applied Mathematics 11 (1) 63-69.
  21. Yu, P. L. 1973. A class of solutions for group decision problems. Management Science 19, 936-946.
Index Terms

Computer Science
Information Sciences

Keywords

Bi-level programming Bi-level linear fractional programming Fuzzy programming Fuzzy goal programming

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