Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems
Asian Journal of Probability and Statistics,
In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a single LPP by using various techniques and then the solution of LPP thus formed is recovered by Gauss elimination technique. MOLPP is concerned with the linear programming problems of maximizing or minimizing, the linear objective function having more than one objective along with subject to a set of constraints having linear inequalities in nature. Modeling of Gauss elimination technique of inequalities is derived for numerical solution of linear programming problem by using concept of bounds. The method is quite useful because the calculations involved are simple as compared to other existing methods and takes least time. The same has been illustrated by a numerical example for each technique discussed here.
- Multi-objective linear programming problem
- Gauss elimination technique
- objective function
- Chandra Sen’s technique
- averaging techniques
- new averaging techniques
- AHA simplex algorithm
How to Cite
Sulaiman NA, Sadiq GW. Solving the linear multi-objective programming problems; using mean and median value. Al-Rafiden Journal of Computer Sciences and Mathematics, University of Mosul. 2006;3(1):69-83.
Sulaiman NA, Hamadameen AQ. Optimal transformation technique to solve multi-objective linear programming problem. Journal of University of Kirkuk. 2008;2(2):39-52.
Hamad-Amin AO. An adaptive arithmetic average transformation technique for solving MOLPP. M.Sc. Thesis, University of Koya, Koya, Iraq; 2008.
Sulaiman NA, Mustafa RB. Using harmonic mean to solve multi-objective linear programming problems. American Journal of Operations Research. 2016;6:25-30.
Nahar S, Alim MA. A new statistical averaging method to solve multi-objective linear programming problem. International Journal of Science and Research. 2017;6(8):623-629.
Kohler DA. Translation of a report by Fourier on his work on linear inequalities. OPSEARCH. 1973;10:38-42.
Williams HP. Fourier’s method of linear programming and its dual. American Mathematical Monthly. 1986;93:681-695.
Kanniapaan P, Thangvel K. Modified Fourier’s method of solving LPP. OPSEARCH. 1998;35:45-56.
Sharma KC, Bhargava S. Gauss method to solve linear programming problems. Applied Science Periodical. 2003;3(1):45-49.
Jain S, Mangal A. Modified Fourier elimination technique for fractional programming problem. Acharya Nagarjuna International Journal of Mathematics & Information Technology. 2004;1(2):121-131.
Jain S, Mangal A. Gauss elimination technique for fractional programming problem. Journal of Indian Society of Statistics and Operations Research. 2008;XXIX:1-4.
Jain S, Mangal A. Extended Gauss elimination technique for integer solution of linear fractional programming. Journal of Indian Mathematical Society. 2008;75:37-46.
Jain S, Mangal A. Extended modified Fourier elimination technique for integer solution of fractional programming problem. Varahmihir Journal of Mathematical Sciences. 2008;8(1):179-186.
Jain S. Modeling of Gauss elimination technique for multi-objective linear programming problem. Journal of Novel Applied Sciences. 2012;1(1):25-29.
Jain S. Modeling of Fourier elimination technique for multi-objective fractional programming problem. International Journal of Development Research and Quantitative Techniques. 2013;3(1):30-35.
Jain S. Modeling of Gauss elimination technique for multi-objective fractional programming problem. South Asian Journal of Mathematics. 2014;4(3):148-153.
Ansari AH. Easy simplex (AHA Simplex) algorithm. Journal of Applied Mathematics and Physics. 2019;7:23-30.
Jain S, Mangal A. A comment on S Nahar & Md. Abdul Alim (2017): A new statistical averaging method to solve multi-objective linear programming problem. International Journal of Science and Research. 2020;9(5):573-576.
Abstract View: 656 times
PDF Download: 432 times