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Fuzzy Approach for Three Level Linear Programming Problems

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Authors:
Hegazy Zaher, Naglaa Ragaa Saeid, Ahmed Serag
10.5120/ijca2016908205

Hegazy Zaher, Naglaa Ragaa Saeid and Ahmed Serag. Article: Fuzzy Approach for Three Level Linear Programming Problems. International Journal of Computer Applications 133(16):30-34, January 2016. Published by Foundation of Computer Science (FCS), NY, USA. BibTeX

@article{key:article,
	author = {Hegazy Zaher and Naglaa Ragaa Saeid and Ahmed Serag},
	title = {Article: Fuzzy Approach for Three Level Linear Programming Problems},
	journal = {International Journal of Computer Applications},
	year = {2016},
	volume = {133},
	number = {16},
	pages = {30-34},
	month = {January},
	note = {Published by Foundation of Computer Science (FCS), NY, USA}
}

Abstract

This study presents a proposed fuzzy approach for solving three level linear programming problems. This approach does not increase the complexities of original problems and usually solves a multilevel programming problem in less number of iterations. Numerical examples are used to compare the proposed approach with several approaches in the literature.

References

  1. A. Baky, Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach, Applied Mathematical Modeling, 34 (2010) 2377–2387.
  2. H. P. Benson, On the Structure and Properties of a Linear Multilevel Programming Problem, Journal of Optimization Theory and Applications, 60 (1989) 353–373.
  3. J. Bracken and J.M. McGill, Mathematical programs with optimization problems in the constraints Operations Research, 21 (1973) 37-44.
  4. W. Candler and R. D. Norton, Multilevel Programming and Development Policy, World Bank Staff, Working Paper 258, (1977) Washington, DC.
  5. E. Anderson and N. Joglekar, A Hierarchical Product Development Planning Framework, Production and Operations Management, 14 (3) (2005)344-361.
  6. E.S. Lee and H.S. Shih, Fuzzy and Multi-Level Decision Making, 1st edition, London: Springer, 2001, Chapters 1, 2.
  7. G. Anandalingam, A Mathematical Programming Model of Decentralized Multi- Level Systems, Journal of Operational Research Society, 39 (11) (1988) 1021–1033.
  8. G. Anandalingam and T.L. Friesz, Hierarchical Optimization: an Introduction, Annals of Operations Research, 34 (1) (1992) 1–11.
  9. S. S. HSU, et al., A Neural Network Approach to Multiobjective and Multilevel Programming Problems, Computers and Mathematics with Applications, 48(2004) 95-108.
  10. J. F. Bard and J. E. Falk, an Explicit Solution to the Multi-Level Programming Problems, Computers and Operations Research, 9 (1982) 77–100.
  11. J. Falk, A Linear Max-Min Problem, Mathematical Programming, 5 (1973) 169-181.
  12. M. Kassa, et al., A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems. An International Journal of Optimization and Control: Theories & Applications, 3(2) (2013)133-144.
  13. K. Lachhwani, et al., Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach, 2012.
  14. D. LI, et al., Multilevel Dynamic Programming for General Multiple Linear-Quadratic Controls in Discrete-Time Systems, Computers Math. Applic, 27 (1994) 59-66.
  15. M.S. Osman, et al., A multi-level Nonlinear Multi-Objective Decision Making under Fuzziness, J. Appl. Math. Comp., 153 (2004) 239–252.
  16. M.S. Osman, et al., A Compromise Weighted Solution for Multilevel Linear Programming Problems, Journal of Engineering Research and Applications, 3 (2013) 927-936.
  17. M. Mari´c, An efficient Genetic Algorithm for Solving the multi-Level Uncapacitated Facility Location Problem, Computing and Informatics, 29 (2010) 183–201.
  18. O. Ben-Ayed and C.E. Blair, Computational Difficulties of Bi-level Linear Programming, Operations Research, 38(1988) 556–560.
  19. O. Ben-Ayed, Bi-Level Linear Programming, Computers and Operations Research, 20 (1993) 485–501.
  20. R. E. Bellman and L.A. Zadeh, Decision-Making in a Fuzzy Environment, Manage. Sci., 17 (1970) 141–164.
  21. M. Sakawa, et al., Interactive Fuzzy Programming for Multilevel Linear Programming Problems, Computers Math. Applic, 36 (1998) 71-86.
  22. H.S. Shih, et al., Fuzzy Approach for Multi-Level Programming Problems, Computers and Operations Research, 23 (1) (1996) 73–91.
  23. H.S. Shih and E.S. Lee, Compensatory Fuzzy Multiple Level Decision Making , Fuzzy Sets and Systems, 14 (2000) 71–87.
  24. H.S. Shih, et al., An Interactive Approach for Integrated Multilevel Systems in a Fuzzy Environment, Mathematical and Computer Modeling, 36 (2002) 569-585.
  25. S. Sinha, Fuzzy Mathematical Programming Applied to Multi-Level Programming Problems, Computers and Operations Research, 30 (2003) a 1259–1268.
  26. S. Sinha, Fuzzy Programming Approach to Multi-Level Programming Problems, Fuzzy Sets and Systems, 136 (2003) b 189–202.
  27. D. J. White, Multilevel Programming, Rational Reaction Sets, and Efficient Solutions, Journal of Optimization Theory and Applications, 87 (1995) 727–746.
  28. Y.J. Lai, Hierarchical Optimization: a Satisfactory Solution, Fuzzy Sets and Systems, 77(1996) 321–335.
  29. L. Zhang, A Fuzzy Algorithm for Solving a Class of Bi-Level Linear Programming Problem, Appl. Math. Inf. Sci., 8, (2014) 1823-1828.

Keywords

Bi-level programming, Three-level programming, Multi-level programming, Tri-level algorithm, Fuzzy Programming