International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN. 

Solution of Multi-Objective Linear Programming Problem by using Relaxation Method

    , ,

Author Affiliations

  • 1Department of Mathematics, Bhagwant University Ajmer, India
  • 2Department of Mathematics, Bhagwant University Ajmer, India
  • 3Department of Mathematics, Engineering College Ajmer, India

Res. J. Mathematical & Statistical Sci., Volume 12, Issue (2), Pages 1-3, September,12 (2024)

Abstract

In this study, the relaxation method is presented for solving multi-objective linear programming problems. Generally, relaxation method is used to solve simultaneous linear equations in which coefficient matrix is a square matrix along with the condition that the elements of the principal diagonal dominate the other elements of that particular row. An illustrative example is given at the end to demonstrate the method. It is an easy method as compared to other methods to solve multi-objective linear programming problems available in the literature.

References

  1. Saul, I. (1963)., Linear Programming: Methods and Applications., McGraw-Hill Book Company.
  2. Goberna, M. A., Hernández, L., & Todorov, M. I. (2005)., On linear inequality systems with smooth coefficients., Journal of optimization theory and applications, 124, 363-386.
  3. Hu, H. (1994)., A projection method for solving infinite systems of linear inequalities., Advances in optimization and approximation, 186-194.
  4. Gass, S. I. (2003)., Linear programming: methods and applications., Courier Corporation.
  5. Kamboo, N. S. (1995)., Mathematical Programming Technique., Affiliated East-West Press Pvt. Ltd., New Delhi (India).
  6. Kwak, N. K. (1973)., Mathematical programming with business applications.,
  7. Agmon, S. (1954)., The relaxation method for linear inequalities., Canadian Journal of Mathematics, 6, 382-392.
  8. González-Gutiérrez, E., & Todorov, M. I. (2012)., A relaxation method for solving systems with infinitely many linear inequalities., Optimization Letters, 6(2), 291-298.
  9. Jeroslow, R. G. (1979)., Some relaxation methods for linear inequalities., Cahiers du Cero, 21, 43-53.
  10. Motzkin, T. S., & Schoenberg, I. J. (1954)., The relaxation method for linear inequalities., Canadian Journal of Mathematics, 6, 393-404.
  11. Temple, G. (1939)., The general theory of relaxation methods applied to linear systems., Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 169(939), 476-500.