Robust fuzzy programming: Difference between revisions

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Revision as of 15:29, 19 July 2019

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{{Orphan|date=June 2016}}

'''Robust fuzzy programming (ROFP)''' is a powerful [[mathematical optimization]] approach to deal with optimization problems under [[uncertainty]]. This approach is firstly introduced at 2012 by Pishvaee, Razmi & Torabi<ref name=":0">{{Cite journal|title = Robust possibilistic programming for socially responsible supply chain network design: A new approach|url = http://www.sciencedirect.com/science/article/pii/S0165011412001819|journal = Fuzzy Sets and Systems|date = 2012-11-01|pages = 1–20|volume = 206|series = Theme : Operational Research|doi = 10.1016/j.fss.2012.04.010|first = M. S.|last = Pishvaee|first2 = J.|last2 = Razmi|first3 = S. A.|last3 = Torabi}}</ref> in the Journal of Fuzzy Sets and Systems. ROFP enables the decision makers to be benefited from the capabilities of both [[fuzzy set|fuzzy]] mathematical programming and [[robust optimization]] approaches. At 2016 Pishvaee and Fazli<ref name=":1">{{Cite journal|title = Novel robust fuzzy mathematical programming methods|url = http://www.sciencedirect.com/science/article/pii/S0307904X15003686|journal = Applied Mathematical Modelling|date = 2016-01-01|pages = 407–418|volume = 40|issue = 1|doi = 10.1016/j.apm.2015.04.054|first = Mir Saman|last = Pishvaee|first2 = Mohamadreza|last2 = Fazli Khalaf}}</ref> put a significant step forward by extending the ROFP approach to handle flexibility of constraints and goals.ROFP is able to achieve a ''robust solution'' for an optimization problem under uncertainty.

== Definition of robust solution ==

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* [[Supply chain management]] such as the work by Pishvaee et al.<ref name=":0" /> which addresses the design of a social responsible supply chain network under epistemic uncertainty.

* Healthcare management such as the works by Zahiri et al.<ref>{{Cite journal|title = A robust possibilistic programming approach to multi-period ___location–allocation of organ transplant centers under uncertainty|url = http://www.sciencedirect.com/science/article/pii/S0360835214001533|journal = Computers & Industrial Engineering|date = 2014-08-01|pages = 139–148|volume = 74|doi = 10.1016/j.cie.2014.05.008|first = Behzad|last = Zahiri|first2 = Reza|last2 = Tavakkoli-Moghaddam|first3 = Mir Saman|last3 = Pishvaee}}</ref> and Mousazadeh et al.<ref>{{Cite journal|title = A robust possibilistic programming approach for pharmaceutical supply chain network design|url = http://www.sciencedirect.com/science/article/pii/S0098135415002203|journal = Computers & Chemical Engineering|date = 2015-11-02|pages = 115–128|volume = 82|doi = 10.1016/j.compchemeng.2015.06.008|first = M.|last = Mousazadeh|first2 = S. A.|last2 = Torabi|first3 = B.|last3 = Zahiri}}</ref> which consider the planning of an organ transplantation network and a pharmaceutical supply chain, respectively.

* [[Energy planning]] such as Bairamzadeh et al.<ref>{{Cite journal|title = Multiobjective Robust Possibilistic Programming Approach to Sustainable Bioethanol Supply Chain Design under Multiple Uncertainties|journal = Industrial & Engineering Chemistry Research|date = 2015-12-22|pages = 237–256|volume = 55|issue = 1|doi = 10.1021/acs.iecr.5b02875|language = EN|first = Samira|last = Bairamzadeh|first2 = Mir Saman|last2 = Pishvaee|first3 = Mohammad|last3 = Saidi-Mehrabad}}</ref> which uses a multi-objective possibilistic programming model to deal with the design of a bio-ethanol production-distribution network. Also in another research, Zhou et al.<ref>{{Cite journal|title = A robust possibilistic mixed-integer programming method for planning municipal electric power systems|url = http://www.sciencedirect.com/science/article/pii/S0142061515002653|journal = International Journal of Electrical Power & Energy Systems|date = 2015-12-15|pages = 757–772|volume = 73|doi = 10.1016/j.ijepes.2015.06.009|language = EN|first = Y.|last = Zhou|first2 = Y.P.|last2 = Li|first3 = G.H.|last3 = Huang}}</ref> developed a robust possibilistic programming model to deal with the planning problem of municipal electric power system.

* [[Sustainability]] such as Xu and Huang<ref>{{Cite journal|title = Development of an Improved Fuzzy Robust Chance-Constrained Programming Model for Air Quality Management|journal = Environmental Modeling & Assessment|date = 2015-10-15|pages = 535–548|volume = 20|issue = 5|doi = 10.1007/s10666-014-9441-3|language = EN|first = Ye|last = Xu|first2 = Guohe|last2 = Huang}}</ref> which employ ROFP to cope with an air quality management problem.