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One-stage uncertain linear optimization | ||
| Journal of Hyperstructures | ||
| دوره 7، Spec. 2nd CSC2017، شهریور 2018، صفحه 36-49 اصل مقاله (304.41 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2018.2688 | ||
| نویسندگان | ||
| Zeinab Zarea؛ Alireza Ghaffari-Hadigheh Ghaffari-Hadigheh* | ||
| Department of Applied Mathematics, Azarbaijan Shahid Madani University Tabriz, Iran | ||
| چکیده | ||
| Uncertainty is one of the intrinsic features of natural phenomenon and optimization is not an exception. Parameters in an optimization problem may be inaccurately presented, or due to variation after solving the problem, the current optimal solution may not be optimal or feasible for the new data. One of the approaches towards the uncertainty is the uncertainty theory initiated by Liu in 2007 and completed in 2011. This theory describes the uncertainty originated from human reasoning in mathematical axiomatic words. In this paper, we consider one-stage uncertain linear optimization problem, where the parameters linearly depend on several independent uncertain variables. A solution method is presented which is similar to the branch and bound method for the integer linear program. The presented methodology is explained by simple illustrative examples. | ||
| کلیدواژه‌ها | ||
| Uncertainty Theory؛ One-stage uncertain optimization problem؛ Linear Optimization | ||
| مراجع | ||
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[1] A. Ben-Tal and A. Nemirovski, Robust solutions of linear programming problems contaminated with uncertain data, Mathematical programming, 88(2000), 411-424. [2] J.R. Birge and F. Louveaux, Introduction to stochastic programming, Springer Sci-ence & Business Media,(2011). [3] A. Ghaffari-Hadigheh, Two linear programming models in uncertain environment (in Persian), Journal of Operational Research in Its Applications, 50, 37-51. [4] A. Ghaffari-Hadigheh and N. Mehanfar, Matrix Perturbation and Optimal Partition Invariancy in Linear Optimization, Asia-Pacific Journal of Operational Research,32(2015). [5] A. Ghaffari-Hadigheh and Terlaky Tams, Sensitivity analysis in linear optimiza-tion: Invariant support set intervals, European Journal of Operational Research,169(2006), 1158-1175. [6] B. Liu, Uncertainty theory, Springer, (2007). [7] B. Liu, Uncertainty theory: A branch of mathematics for modeling human uncer-tainty, Springer, 300(2011). [8] G.H. Huang and M.F. Cao, Analysis of Solution Methods for Interval Linear Pro-gramming, Journal of Environmental Informatics, 17(2011). [9] H. Naseri, Fuzzy Simplex Methods for Fuzzy uncertain linear programming, Oper-ations Research and Applications,4(2013). [10] H. Tanaka and K. Asai, Fuzzy linear programming problems with fuzzy numbers,Fuzzy Sets and Systems, 13(1984),1-10. [11] M. Zheng, Y. Yi, Z. Wang and J.F. Chen, Study on two-stage uncertain program-ming based on uncertainty theory, Journal of Intelligent Manufacturing, (2017),633-642. [12] Roos, Cornelis, Terlaky, Tams and Vial, Interior point algorithms for linear opti-mization, Springer Science, (2005). | ||
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