Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 796028, 20 pages
http://dx.doi.org/10.1155/2012/796028
Research Article

Two Weighted Fuzzy Goal Programming Methods to Solve Multiobjective Goal Programming Problem

Department of Mathematics, National Institute of Technology Agartala, Tripura, Jirania 799055, India

Received 4 March 2012; Revised 2 June 2012; Accepted 4 June 2012

Academic Editor: Hak-Keung Lam

Copyright © 2012 Mousumi Gupta and Debasish Bhattacharjee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Charnes, W. W. Cooper, and R. Ferguson, “Optimal estimation of executive compensation by linear programming,” Journal of the Institute of Management Science, vol. 1, pp. 138–151, 1955. View at Google Scholar · View at Zentralblatt MATH
  2. U. K. Bhattacharya, “A chance constraints goal programming model for the advertising planning problem,” European Journal of Operational Research, vol. 192, no. 2, pp. 382–395, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. C. T. Chang, “Multi-choice goal programming,” Omega, vol. 35, pp. 389–396, 2007. View at Publisher · View at Google Scholar
  4. C. T. Chang, “Revised multi-choice goal programming,” Applied Mathematical Modelling, vol. 32, no. 12, pp. 2587–2595, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. Romero, “A survey of generalized goal programming (1970–1982),” European Journal of Operational Research, vol. 25, no. 2, pp. 183–191, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. J. P. Ignizio, Goal Programming and Extensions, Lexington Health Care Center, Lexington, Mass, USA, 1976.
  7. J. P. Ignizio, Introduction to Linear Goal Programming, Sage, Beverly Hills, Calif, USA, 1985.
  8. J. N. D. Gupta and N. U. Ahmed, “A goal programming approach to job evaluation,” Computers & Industrial Engineering, vol. 14, no. 2, pp. 147–152, 1988. View at Publisher · View at Google Scholar
  9. J. S. H. Kornbluth and R. E. Steuer, “Goal programming with linear fractional criteria,” European Journal of Operational Research, vol. 8, no. 1, pp. 58–65, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Charnes and W. W. Cooper, “Programming with linear fractional functionals,” Naval Research Logistics Quarterly, vol. 9, pp. 181–186, 1962. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. H. L. Li, “A global approach for general 0-1 fractional programming,” European Journal of Operational Research, vol. 73, pp. 590–596, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. S. F. Tantawy, “A new procedure for solving linear fractional programming problems,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 969–973, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH
  14. R. E. Bellman and L. A. Zadeh, “Decision-making in a fuzzy environment,” Journal of the Institute of Management Science, vol. 17, pp. B141–B164, 1970. View at Google Scholar
  15. H. Tanaka, T. Okuda, and K. Asai, “On fuzzy-mathematical programming,” Journal of Cybernetics, vol. 3, no. 4, pp. 37–46, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. H. J. Zimmermann, “Fuzzy programming and linear programming with several objective functions,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 45–55, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. M. K. Luhandjula, “Fuzzy approaches for multiple objective linear fractional optimization,” Fuzzy Sets and Systems, vol. 13, no. 1, pp. 11–23, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. R. Narasimhan, “Goal programming in a fuzzy environment,” Decision Sciences, vol. 11, pp. 325–336, 1980. View at Publisher · View at Google Scholar
  19. E. L. Hannan, “On fuzzy goal programming,” Decision Sciences, vol. 12, pp. 522–531, 1981. View at Publisher · View at Google Scholar
  20. H. A. Barough, “A multi-objective goal programming approach to a fuzzy transportation problem: the case of a general contractor company,” The Journal of Mathematics and Computer Science, vol. 2, no. 1, pp. 9–19, 2011. View at Google Scholar
  21. H. Y. Kanga and A. H. I. Lee, “Inventory replenishment model using fuzzy multiple objective programming: a case study of a high-tech company in Taiwan,” Applied Soft Computing, vol. 10, pp. 1108–1118, 2010. View at Publisher · View at Google Scholar
  22. R. T. Moghaddam, B. Javadi, F. Jolai, and A. Ghodratnama, “The use of a fuzzy multi-objectivelinear programming for solving a multi-objective single-machine scheduling problem,” Applied Soft Computing, vol. 10, pp. 919–925, 2010. View at Google Scholar
  23. R. H. Mohamed, “The relationship between goal programming and fuzzy programming,” Fuzzy Sets and Systems, vol. 89, no. 2, pp. 215–222, 1997. View at Publisher · View at Google Scholar
  24. B. B. Pal, B. N. Moitra, and U. Maulik, “A goal programming procedure for fuzzy multiobjective linear fractional programming problem,” Fuzzy Sets and Systems, vol. 139, no. 2, pp. 395–405, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. D. Toksari, “Taylor series approach to fuzzy multiobjective linear fractional programming,” Information Sciences, vol. 178, no. 4, pp. 1189–1204, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. C. T. Chang, “Binary fuzzy goal programming,” European Journal of Operational Research, vol. 180, no. 1, pp. 29–37, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. A. Payan, F. Hosseinzadeh Lotfi, A. A. Noora, G. R. Jahanshahloo, and M. Khodabakhshi, “A linear programming approach to test efficiency in multi-objective linear fractional programming problems,” Applied Mathematical Modelling, vol. 34, no. 12, pp. 4179–4183, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. A. Kumar, J. Kaur, and P. Singh, “A new method for solving fully fuzzy linear programming problems,” Applied Mathematical Modelling, vol. 35, no. 2, pp. 817–823, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. C. T. Chang, “A goal programming approach for fuzzy multiobjective fractional programming problems,” International Journal of Systems Science, vol. 40, no. 8, pp. 867–874, 2009. View at Publisher · View at Google Scholar
  30. F. Arıkan and Z. Güngör, “A two-phase approach for multi-objective programming problems with fuzzy coefficients,” Information Sciences, vol. 177, no. 23, pp. 5191–5202, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  31. M. G. Iskander, “Using the weighted max-min approach for stochastic fuzzy goal programming: a case of fuzzy weights,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 456–461, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  32. M. Gupta and D. Bhattacharya, “Goal programming and fuzzy goal programming techniques in the bank investment plans under the scenario of maximizing profit and minimizing risk factor: a case study,” Advances in Fuzzy Mathematics, vol. 5, no. 2, pp. 111–119, 2010. View at Google Scholar
  33. M. Gupta and D. Bhattacharjee, “Min sum weighted fuzzy goal programming model in investment management planning: a case study,” International Research Journal of Finance and Economics, no. 56, pp. 76–81, 2010. View at Google Scholar
  34. P. K. De and B. Yadav, “An algorithm to solve multi-objective assignment problem using interactive fuzzy goal programming approach,” International Journal of Contemporary Mathematical Sciences, vol. 6, no. 34, pp. 1651–1662, 2011. View at Google Scholar
  35. S. Mishra, “Weighting method for bi-level linear fractional programming problems,” European Journal of Operational Research, vol. 183, no. 1, pp. 296–302, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. S. M. Lee and W. F. Abd El-Wahed, “Interactive fuzzy goal programming for multiobjective transportation problems,” Omega, vol. 34, pp. 158–1166, 2006. View at Publisher · View at Google Scholar
  37. S.-Y. Li, C.-F. Hu, and C.-J. Teng, “A fuzzy goal programming approach to multi-objective optimization problem with priorities,” European Journal of Operational Research, vol. 176, no. 3, pp. 1319–1333, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  38. S. R. Arora and R. Gupta, “Interactive fuzzy goal programming approach for bilevel programming problem,” European Journal of Operational Research, vol. 194, no. 2, pp. 368–376, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  39. Y. Z. Mehrjerdi, “Solving fractional programming problem through fuzzy goal setting and approximation,” Applied Soft Computing Journal, vol. 11, no. 2, pp. 1735–1742, 2011. View at Publisher · View at Google Scholar · View at Scopus
  40. R. N. Tiwari, S. Dharmar, and J. R. Rao, “Fuzzy goal programming—an additive model,” Fuzzy Sets and Systems, vol. 24, no. 1, pp. 27–34, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  41. M. Gupta and D. Bhattacharjee, “An approach to solve the fuzzy multi objective linear fractional goal programming problem,” Journal of Statistics and Mathematics, vol. 2, no. 1, pp. 23–36, 2011. View at Google Scholar
  42. C. R. Bector and S. Chandra, Fuzzy Mathematical Programming and Fuzzy matrix Games, Springer, 2005.