CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Dinkelbach Approach for Solving Interval-valued Multiobjective Fractional Programming Problems using Goal Programming

by Mousumi Kumar, Bijay Baran Pal
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 57 - Number 8
Year of Publication: 2012
Authors: Mousumi Kumar, Bijay Baran Pal
10.5120/9133-3321

Mousumi Kumar, Bijay Baran Pal . Dinkelbach Approach for Solving Interval-valued Multiobjective Fractional Programming Problems using Goal Programming. International Journal of Computer Applications. 57, 8 ( November 2012), 12-17. DOI=10.5120/9133-3321

@article{ 10.5120/9133-3321,
author = { Mousumi Kumar, Bijay Baran Pal },
title = { Dinkelbach Approach for Solving Interval-valued Multiobjective Fractional Programming Problems using Goal Programming },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 57 },
number = { 8 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 12-17 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume57/number8/9133-3321/ },
doi = { 10.5120/9133-3321 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:59:53.547938+05:30
%A Mousumi Kumar
%A Bijay Baran Pal
%T Dinkelbach Approach for Solving Interval-valued Multiobjective Fractional Programming Problems using Goal Programming
%J International Journal of Computer Applications
%@ 0975-8887
%V 57
%N 8
%P 12-17
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper presents an interval valued goal programming approach for solving multiobjective fractional programming problems. In the model formulation of the problem, the interval-valued system constraints are converted in to equivalent crisp system. The interval valued fractional objective goals are transformed into linear goals by employing the iterative parametric method which is an extension of Dinkelbach approach. In the solution process, the goal achievement function, termed as 'regret function', is formulated for minimizing the unwanted deviational variables to achieve the goals in their specified ranges and thereby arriving at most satisfactory solution in the decision making environment. To illustrate the proposed approach one numerical example is solved.

References
  1. Bellman, R. E. , Zadeh, L. A. 1973. Decision making in a fuzzy environment. Management Sciences, vol. 17, pp. B141-B164.
  2. Bitran, G. R. 1980. Linear multiobjective problems with interval coefficients. Management Science. vol. 26, pp. 694-706,
  3. Chanas, S. , Kuchta, D. 1996. Multiobjective programming in optimization of interval objective functions – a generalized approach. European Journal of Operational Research. vol. 94, pp. 594-598.
  4. Charnes, A. , Cooper, W. W. 1961. Management Models and Industrial Applications of Linear Programming, Vol. I and II. Wiley, New York.
  5. Charnes, A. , Cooper, W. W. and Ferguson, R. 1955. Optimal estimation of executive compensation by linear programming. Management Science. vol. 1, pp. 138-151.
  6. Craven, B. D. 1988. Fractional Programming. Heldermann Verlag, Berlin.
  7. Dempster, M. A. H. 1980. Stochastic Programming, Academic Press.
  8. Dinkelbach, W. 1967. On Nonlinear Fractional Programming. Management Science. vol. 13, pp. 492 – 498.
  9. Ida, M. 2000. Interval multiobjective programming and mobile robot path planning". In: Mohammadian, M. , Mohammadian, M. , (Eds). New Frontiers in Computational Intelligence and it's Applications. IOS Press, pp. 313-322.
  10. Ida, M. 2003. Portfolio selection problem interval coefficients. Applied Mathematics Letters, vol. 16, pp 709-713.
  11. Ignizio, J. P. 1976. Goal Programming and Extensions, Lexington, Massachusetts, D. C. Health.
  12. Ignizio, J. P. , Cavalier, T. M. 1994. Linear Programming. Prentice Hall, New Jersey.
  13. Inuiguchi, M. Kume, Y. 1991. Goal programming problems with interval coefficients and target intervals. European Journal of Operational Research. vol. 52, pp. 345-361.
  14. Ishibuchi, H. , Thanaka, H. 1990. Multiobjective programming in optimization of interval objective function. European Journal of Operational Research. vol. 48, 219-225.
  15. Jones, D. F. , Tamiz, M. 2010. Practical Goal programming. Springer Books.
  16. Jones, D. F. , Tamiz, M. 2002. Goal programming in the period 1990-2000, in Multiple Criteria Optimization: State of the art annotated bibliographic surveys, M. Ehrgott and X. Gandibleux (Eds. ), pp. 129-170. Kluwer Pub.
  17. Kerfortt, R. B. 1989. Interval mathematical techniques for control theory computation. K. Bowers and J. Lund (eds. ), Computation and Control, Proceedings of the Bozeman Conference, vol. 20 of Progression Systems and Control Theory, Birkhauser, Boston, MA, pp. 169-178.
  18. Kornbluth, J. S. H. , Steuer, R. E. 1981. Multiple Objective Linear Fractional Programming. Management Science, vol. 27, pp. 1024 – 1039.
  19. Lee, S. M. 1972. Goal Programming for Decision Analysis. Auerbach Pub. , Philadelphia.
  20. Liu, B. 2002. Theory and Practice of Uncertain Programming. Physica-Verlag, Heidelberg.
  21. Moore, R. E. 1966. Interval analysis, Prentice-Hall, New Jersey,.
  22. Oliveira, C. and Anunes, C. H. 2007. Multiple objective linear programming models with interval coefficients – an illustrated overview. European Journal of Operational Research. vol. 118, pp. 1434-1463.
  23. Pal, B. B. , Kumar, M. , and Sen, S. 2012. A priority–based goal programming method for solving academic personnel planning problems with interval–valued resource goals in university management system. International Journal of Applied Management System. vol. 4, No. 3, pp. 284-312.
  24. Romero, C. 1986. A survey of generalized goal programming. European Journal of Operational Research, vol. 25, pp. 183–191.
  25. Romero, C. 1991. Handbook of Critical Issues in Goal Programming. Pergamon Press, Oxford.
  26. Romero, C. 2001. Extended Lexicographic Goal Programming: A Unifying Approach. Omega, vol. 29, pp. 63 – 71.
  27. Romero, C. 2004. A General Structure of Achievement Function For a Goal Programming Model. European Journal of Operational Research. vol. 153, pp. 675 – 686.
  28. Schniederjans, M. J. 1995. Goal Programming: Methodology and Applications. Kluwer, Boston.
  29. Sengupta, A. , Pal, T. K. and Chakraborty, D. 2001. Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems, vol. 119, pp. 129-138.
  30. Steuer, R. E. 1981. Algorithm for linear programming problems with interval objectives function coefficients. Management Science. vol. 26, pp. 333 – 348.
  31. Tong, S. 1994. Interval number and fuzzy number linear programming. Fuzzy Sets and Systems, vol. 66, pp. 301–306.
  32. Zimmermann, H. –J. 1978. Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and Systems. vol. 1, pp. 45–55.
Index Terms

Computer Science
Information Sciences

Keywords

Dinkelbach approach Fractional Programming Goal Programming Interval Arithmetic Interval Programming

Powered by PhDFocusTM