Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
A Parametric Technique Based on Simplex for Treating Stochastic Multicriteria Linear Programming Problem
Current Issue
Volume 6, 2019
Issue 1 (March)
Pages: 1-5   |   Vol. 6, No. 1, March 2019   |   Follow on         
Paper in PDF Downloads: 47   Since May 9, 2019 Views: 936   Since May 9, 2019
Authors
[1]
Adel Mefleh Widyan, Department of Mathematics, Faculty of Science, Qassim University, Buraidah, Saudi Arabia.
Abstract
Most of works treats the stochastic multicriteria optimization linear programming problem (SMOLPP) by transforming it to a deterministic one and solve it to obtain the efficient solutions. This paper introduced a new parametric technique based on the simplex algorithm for decomposing the parametric space of SMOLPP. The mathematical expectation approach will be used to transform the stochastic model with random variable in the objective functions to a deterministic one. Then, using the nonnegative weighted sum approach to scalarize the problem. A set of all efficient solutions can be determined using the proposed approach. A numerical example will be given to illustrate the proposed algorithm.
Keywords
Stochastic Optimization, Multicriteria Programming, Parametric Study, Simplex Techniques
Reference
[1]
A. Charnes and W. W. Cooper, Chance-constrained programming. Management Science 5 (1959) 73-79.
[2]
A. M. Widyan, Obtaining the Efficient Solutions for Multicriterion Programming Problems with Stochastic Parameters, Journal of Natural Sciences and Mathematics, Qassim University, Vol. 9, No. 1, (2016) 17-25.
[3]
J. Fliege, H. Xu, Stochastic Multiobjective Optimization: Sample Average Approximation and Applications, Journal of Optimization Theory and Applications, (2011) 151: 135–162.
[4]
Dinh The Luc, Multiobjective Linear Programming, Springer International Publishing Switzerland, (2016).
[5]
P. L. Yu, M. Zeleny, The Techniques of Linear Multiobjective Programming, R. A. I. R. O. Ser. Verte 8 (V-3) (1974) 51–71.
[6]
A. M. Widyan, Decomposition the Parametric Space in Stochastic Multiobjective Programming problem, Journal of Global Research in Mathematical Archives (JGRMA), Vol. 4, No. 2, (2017) 6 -15.
[7]
N. Bryson, Applications of the Parametric Programming Procedure, European Journal of Operational Research 54 (1991) 66-73.
[8]
J. A. Filar, K. E. Avrachenkov, E. Altman, An Asymptotic Simplex Method for Parametric Linear Programming, Conference: Information, Decision and Control, IEEE Xplore, (1999) 427 – 432.
[9]
M. Ehrgott, J. Puerto, A. M. Rodriguez-Chia, Primal-Dual Simplex Method for Multiobjective Linear Programming, J. Optim Theory Appl. (2007) 134: 483-497.
[10]
Brigit Rudloff, Firdevs Ulus, Robert Vanderbei, A Parametric Simplex Algorithm for Linear Vector Optimization Problems, Math. Program., Ser. A (2017) 163: 213-242.
[11]
M. A. Abo-Sinna, M. L. Hussein, An algorithm for decomposing the parametric space in multiobjective dynamic programming problems, European Journal of Operational Research 73 (1994) 532-538.
[12]
Andrzej Ruszczynski, Some Advances in Decomposition Methods for Stochastic Linear Programming, Annals of Operations Research 85 (1999) 153-172.
[13]
Matthias Ehrgott, Multicriteria Optimization, 2nd Edition, Springer, Heidelberg, (2005).
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
CONTACT US
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
E-mail:
LET'S GET IN TOUCH
Name
E-mail
Subject
Message
SEND MASSAGE
Copyright © 2013-, Open Science Publishers - All Rights Reserved