Solving A Quadratic Fractional Integer Programming Problem Using Linearization

  • Gaur, Anuradha (Department of Mathematics, Maharaja Agrasen College, University of Delhi) ;
  • Arora, S.R. (Department of Mathematics, Hans Raj College, University of Delhi)
  • Published : 2008.11.30

Abstract

This paper concentrates on reduction of a Quadratic Fractional Integer Programming Problem (QFIP) to a 0-1 Mixed Linear Programming Problem (0-1 MLP). The solution technique is based on converting the integer variables to binary variables and then the resulting Quadratic Fractional 0-1 Programming Problem is linearized to a 0-1 Mixed Linear Programming problem. It is illustrated with the help of a numerical example and is solved using the LINDO software.

Keywords

References

  1. Balas, E., "An additive algorithm for solving linear programs with zero‐One Variables," Operations Research 13 (1965)
  2. Balinski, M. L., "Integer Programming: Methods, Uses, Computation," Management Science 12 (1965)
  3. Beale, E. M., "Survey of Integer Programming," Operational Research Quarterly 16 (1965)
  4. Change, C. T., "An efficient linearization approach for mixed integer problem," European Journal of Operational Research 123 (2000)
  5. Chang, C. T., "On the polynomial mixed 0‐1 fractional programming problems," European Journal of Operational Research, 131 (2001) https://doi.org/10.1016/S0377-2217(00)00104-1
  6. Craven, B. D., Fractional Programming, Helderman, Berlin, 1988
  7. Glover, Fred, "Improved Linear Integer Programming Formulations of Non‐ Linear Integer Problems," Management Science 22, 4 (1975)
  8. Li, H. L., "A global approach for general 0‐1 fractional programming," European Journal of Operational Research 73 (1994)
  9. Martos, B., Nonlinear Programming: Theory and Methods, North‐Holland, Amsterdam, 1975
  10. Shaible, S., "Fractional Programming: Applications and Algorithms", European Journal of Operational Research 7 (1981)
  11. Wu, T. H., "A Note on a global approach for general 0‐1 fractional programming," European Journal of Operational Research 101 (1997)
  12. Chaovalitowangse, W., P. M. Pardalas, O. A. Prokopyev, "A New linearization technique for multiquadratic 0‐1 programming problems," Operation Research Letters 32 (2004)