Aula Formulação Binários-2023 1

Prof. Volmir – UFPR 1 Introdução • Divisibility Assumption of Linear Programming: Decision variables in a linear programming model are allowed to have any values, including fractional values, that satisfy the functional and nonnegativity constraints. • Since the number of “products” must have an integer value, the divisibility assumption is violated. https://people.eng.unimelb.edu.au/pstuckey/COMP90046/lec/s5_mip.pdf Prof. Volmir – UFPR 2 http://personal.lse.ac.uk/WILLIAHP/talks/he_Problem_with_Integer_Programming.ppt http://www.baskent.edu.tr/~sureten/MS(integer programming).ppt Prof. Volmir – UFPR 3 Prof. Volmir – UFPR 4 http://home.ubalt.edu/ntsbarsh/ECON/Integer.ppt Prof. Volmir – UFPR 5 Prof. Volmir – UFPR 6 THE ALABAMA PARADOX https://academic.oup.com/teamat/article-abstract/1/2/69/1685642?redirectedFrom=PDF Prof. Volmir – UFPR 7 Formulações - binário VVaarriiáávveeiiss BBiinnáárriiaass ((SSIIM M--NNÃÃOO,, YYEESS--NNOO,, GGOO--NNOO--GGOO,, 00--11)) https://cs.stanford.edu/~ermon/cs325/slides/MIP2.ppt Prof. Volmir – UFPR 8 Prof. Volmir – UFPR 9 Encargos Fixos e Custos de Instalação http://home.ubalt.edu/ntsbarsh/ECON/Integer.ppt Prof. Volmir – UFPR 10 RReellaaççõõeess llóóggiiccaass –– IIm mpplliiccaaççõõeess SSEE--EENNTTÃÃOO Prof. Volmir – UFPR 11 Prof. Volmir – UFPR 12 AAttiivvaarr oouu DDeessaattiivvaarr UUM MAA rreessttrriiççããoo reformulando Seja 4x+3y  12 e 2x + 5x  10 Desativar/Ativar a restrição 2x + 5x  10. Prof. Volmir – UFPR 13 AAttiivvaarr UUM MAA rreessttrriiççããoo ee ddeessaattiivvaarr OOUUTTRRAA rreessttrriiççããoo https://people.eng.unimelb.edu.au/pstuckey/COMP90046/lec/s5_mip.pdf Prof. Volmir – UFPR 14 Outro exemplo Prof. Volmir – UFPR 15 https://laurentlessard.com/teaching/cs524/slides/20%20- %20logic%20constraints%20and%20integer%20variables.pdf Prof. Volmir – UFPR 16 RReepprreesseennttaaççããoo ddee ffuunnççããoo lliinneeaarr ppoorr ppaarrtteess x=0:0.01:2; >> y=x.^2; >> plot(x,y) Prof. Volmir – UFPR 17 RReepprreesseennttaaççããoo ddee vvaalloorreess ddiissccrreettooss http://www.facom.ufms.br/~ricardo/Courses/OP-2008/Lectures/Lec08.pdf Também pode ser usado quando a variável inteira tem limite superior VVaarriiáávveell aassssuum miinnddoo vvaalloorreess ddeessccoonnttíínnuuooss EElliim miinnaaççããoo ddee pprroodduuttooss ddee vvaarriiáávveeiiss , Linearizando Forma 1 ou Forma 2 , ,