Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions
In this paper, a new statistical averaging technique is proposed for finding an optimal solution to a multi-objective linear fractional programming problem (MOLFPP) and multi-objective linear programming problem (MOLPP) by using new arithmetic averaging method and new geometric averaging method. It is significantly noticeable same characteristics among all the technique while taking maximum or minimum among all optimized values for multi-objective functions using simplex algorithm. The characteristics provided from the problems are verified by the numerical examples.
References
[1]
Abdil-Kadir, M.S. and Sulaiman, N.A. (1993) An Approach for Multi Objective Fractional Programming Problem. Journal of the College of Education, 3, 1-5.
[2]
Hamad-Amin, A.O. (2008) An Adaptive Arithmetic Average Transformation Technique for Solving MOLPP. MSc. Thesis, University of Koya, Koya.
[3]
Nahar, S. and Alim, M.A. (2017) A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique. IOSR Journal of Mathematics, 13, 39-52. https://doi.org/10.9790/5728-1303013952
[4]
Nahar, S. and Alim, M.A. (2017) A New Statistical Averaging Method to Solve Multi-Objective Linear Programming Problem. International Journal of Science and Research, 6, 623-629.
[5]
Saha, S.K., Hossain, M.R., Uddin, M.K. and Mondal, R.N. (2015) A New Approach of Solving Linear Fractional Programming Problem (LFP) by Using Computer Algorithm. Open Journal of Optimization, 4, 74-86. https://doi.org/10.4236/ojop.2015.43010
[6]
Sen, C. (1983) A New Approach for Multi Objective Rural Development Planning. The Indian Economic Journal, 30, 91-96.
[7]
Sing, H.C. (1981) Optimality Condition in Functional Programming. Journal of Optimization Theory and Application, 33, 287-294. https://doi.org/10.1007/BF00935552
[8]
Sulaiman, N.A. and Mustafa, R.B. (2016) Using Harmonic Mean to Solve Multi-Objective Linear Programming Problems. American Journal of Operations Research, 6, 25-30. https://doi.org/10.4236/ajor.2016.61004
[9]
Sulaiman, N.A. and Othman, A.Q. (2007) Optimal Transformation Technique to Solve Multi-Objective Linear Programming Problem. Journal of University of Kirkuk, 2, 122-131.
[10]
Sulaiman, N.A. and Sadiq, G.W. (2006) Solving the Linear Multi-Objective Programming Problems; Using Mean and Median Value. Al-Rafiden Journal of Computer Sciences and Mathematics, 3, 69-83. https://doi.org/10.33899/csmj.2006.164037
[11]
Lotfi, F., Noora, A., Jahanshahloo, G., Khodabakhshi, M. and Payan, A. (2010) A Linear Programming Approach to Test Efficiency in Multi-Objective Linear Fractional Programming Problems. Applied Mathematical Modelling, 34, 4179-4183. https://doi.org/10.1016/j.apm.2010.04.015
[12]
Porchelvi, R., Vasanthi, L. and Hepzibah, R. (2014) On Solving Multi-Objective Fractional Linear Programming Problems. International Journal of Current Research, 6, 8095-8102.
