Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method
- 1 Department of Basic Sciences and Humanities, University of Asia Pacific, Dhaka, Bangladesh
- 2 General Education Department, City University, Dhaka, Bangladesh
- 3 Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
Abstract
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various method s as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.
- Zadeh, L.A. (1965) Fuzzy Sets and Systems. In: Fox, J., Ed., System Theory (Microwave Research Institute Symposia Series XV), Polytechnic Press, Brooklyn, 29-37.
- Zimmermann, H.-J. (1978) Fuzzy Programming and Linear Programming with Several Objective Functions. Fuzzy Sets and System, 1, 45-55. https://doi.org/10.1016/0165-0114(78)90031-3
- Tanaka, H. and Asai, K. (1984) Fuzzy Linear Programming Problems with Fuzzy Numbers. Fuzzy Sets and Systems, 13, 1-10. https://doi.org/10.1016/0165-0114(84)90022-8
- Thakre, P.A., et al. (2009) Solving Fuzzy Linear Programming Problem as MOLPP. World Congress on Engineering 2009, London, 1-3 July 2009, 1-10.
- Mahdavi-Amiri, N., et al. (2009) Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems. Iranian Journal of Operational Research, 1, 68-84.
- Nasseri, S.H. and Alizadeh, Z. (2011) Solving Linear Programming Problem with Fuzzy Right Hand Sides: A Penalty Method. The Journal of Mathematics and Computer Science, 3, 318-328. https://doi.org/10.22436/jmcs.03.03.05
- Mishmast Nehi, H. and Hajmohamadi, H. (2011) A Ranking Function Method Solving Fuzzy Multi-Objective Linear Programming. Annals of Fuzzy Mathematics and Informatics, 3, 31-38.
- Kiruthiga, M. and Loganathan, C. (2015) Fuzzy MOLPP Using Fuzzy Programming Model. International Journal of Science, Engineering and Technology Research, 4, Issue 7.
- 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 (IOSR-JM), 13, 39-52. https://doi.org/10.9790/5728-1303013952
- Sen, C. (1983) A New Approach for Multi Objective Rural Development Planning. The Indian Economic Journal, 30, 91-96.
- Nahar, S., Akter, M. and Alim, M.A. (2022) Solving Fuzzy Multi-Objective Linear Programming Problem by Applying Statistical Method. American Journal of Operation Research, 12, 293-309. https://doi.org/10.4236/ajor.2022.126016