64Kb - DComp
Transcrição
64Kb - DComp
Capítulo V: O MÉTODO SIMPLEX REVISADO 1 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP 0e72'26,03/(;5(9,6$'2 F1RUPDOPHQWHQ!!PLVWRpQ~PHURGHYDULiYHLVPXLWRPDLRUTXHRQ~PHURGH UHVWULo}HV $ F$SUiWLFDUHYHODTXHR6,03/(;UHVROYHXP3/FRPPDPSLYRWHDPHQWRV F&RQFOXHVHTXHKiFROXQDVTXHQXQFDVmRXVDGDVQmRGLVWDQWHDFDGD LQWHUDomRHIHWXDPVHFiOFXORVVREUHVHXVHOHPHQWRV F2FRUUHDVVLPGHVSHUGtFLRGHWHPSRHPHPyULD F$LGpLDHQWmRpQmRJXDUGDUQDPHPyULDUiSLGD³FRUH´GRFRPSXWDGRUR TXDGURFRPSOHWRSLYRWHDGR ∧ F ∧ $ ∧ E F'LVSRQGRVHGH$+SRGHVHHIHWXDUXPDSURJUDPDomR6,03/(;GDtQDVFHR 0e72'26,03/(;5(9,6$'2 321726 %È6,&26 6(FRQRPLDGHPHPyULDUiSLGD 6*XDUGDVH$EFQDPHPyULDOHQWDGLVFRILWD 6$WXDOL]DomRGH$+ 2 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP $78$/,=$d2'$,19(56$'$0$75,='(%$6( 0DWUL]GHSLYRWHDPHQWR3UV ([HPSOR ∧ 0DWUL]$ QD LWHUDomRN ∧ 0DWUL]$ QD LWHUDomRN ∧ $ ∧ $ ∧ $ ∧ ∧ $ $ ∧ $ ∧ ∧ $ $ ∧ eIiFLOYHUTXHDRSHUDomRGHDWXDOL]DomRGH$FRQVLVWHQDPXOWLSOLFDomR SHODPDWUL]3 ∧ ∧ $ $ ∧ ∧ ∧ $ $N $N ∧ ∧ $ $ 30$75,='(3,927($0(172 3 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP 6,03/(;5(9,6$'2 ',$*5$0$'(%/2&26 1$0(0Ï5,$5È3,'$',63®(66( + tQGLFHGDVYDULiYHLVEiVLFDV ∧ E YDORUGDVROXomREiVLFD F+ FXVWRGDVYDULiYHLVEiVLFDV $+ PDWUL]LQYHUVDGDEDVH &$/&8/$9(725 08/7,3/,&$'25 π F+$+ &$/&8/$ FM F+π$, ∧ ∧ (VFROKDXPFV! FROXQDYDULiYHOV DHQWUDUQDEDVH ∧ $V 7RGRVRV ∧ F, 62/8d2Ï7,0$ ),1,7$ &DOFXOD $+$V &DOFXODOLQKDUGHEORTXHLR YDULiYHODVDLUGDEDVH 'HWHUPLQD3UVHID]DWXDOL]Do}HV + +UV→+¶ ∧ ∧ 3UVE→E¶ F+→F+ 3UV$+→$+ 62/8d2,1),1,7$ QmRKiEORTXHLR 3('('$'26$0(0Ï5,$/(17$ 4 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP (;(03/26,03/(;5(9,6$'2 [[[[ [[[[ [[[[ [[[ [L!L 0D[] VD 3 [[[[ [[[[[ [[[[[ [[[[ [L!L 0D[] )250$ 3$'52 VD ,1,&,$/,=$d2 + ^` ∧ E F+ $+ 5 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP ,7(5$d2 π ● ∧ F ● F+$+ Fπ$ ! &ROXQDDHQWUDUQDEDVHV ● ∧ $ ● $+$ /LQKDGHEORTXHLR ● [ [ [ ;⇒U Ι 6 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP 3UV 3 ● $78$/,=$d®(6 ● ++ ^`→+¶ ^` 3UVE ∧ → E ∧ F+ 3UVE ∧ 7 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP ,7(5$d2 π ● ∧ F ● F+$+ Fπ$ ! &ROXQDDHQWUDUQDEDVHV ● ∧ $ ● $+$ /LQKDGHEORTXHLR ● [ [ [ ;⇒U Ι 8 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP 3UV 3 ● $78$/,=$d®(6 ● + + ^`→+¶¶ ^` 3UVE ∧ F+ 3UV$+ 9 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP ,7(5$d2 F+ π ● $+ π ∧ F Fπ$ ∧ F Fπ$ ∧ F Fπ$ ∧ Fπ$ ● F ∧ 72'26 FK⇒ 62/8d2Ï7,0$ ),1,7$ 10 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP [[[[[[[ 6,03/(;&2080 [[[[[[[ 11 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP [[[[[[[ 12 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP 6,03/(; &/È66,&2 ,'e,$ %È6,&$ $LQWHUDomR.VH DSRLDWRWDOPHQWHHP GDGRVSURYHQLHQWHV GDLQWHUDomR. 5$=2→ 6,03/(; 5(9,6$'2 $LQWHUDomR.VH DSRLDHPGDGRVGD LQWHUDomR=(52 (&2120,$'(0(0Ï5,$ ( (&2120,$'(&È/&8/2 13 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP eDIRUPDSUHSDUDGD GDLQWHUDomR. (6758785$ '( '$'26 ∧ F, ∧, $ ([LJHRFRQKHFLPHQWRDWXDOL]DGR ∧ GH$++F+EH] $OpPGLVWRGHQWURGHFDGDLWHUDomR ∧ pQHFHVViULRRFiOFXORGH πH$V ∧ E $LQIRUPDomRGHYHVHU DWXDOL]DGDDFDGD LQWHUDomR 3,927($0(172 14 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP (;3/,&$d2'26,03/(;5(9,6$'2 &202&$5$&7(5,=$5$62/8d2%È6,&$ [+ $+E ] F+$+E 7(67('(27,0$/,'$'( ∧ F, F, π $, &20 π F+ $+ 6$%(02648(6( ∧ F,→Ï7,02 &DVRFRQWUiULRHVFROKHVHXPDYDULiYHO ∧ [VSDUDHQWUDUQDEDVHFV! 15 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP &È/&8/2'2%/248(,2 ∧ ∧V [+ E$ [V! 6HQGR[VRPDLRUSRVVtYHO &20 ∧ $+E E ∧V + V $ $ $ $78$/,=$5(6758785$'('$'26 $+1292 3UV$+$17,*$ +$17,*2 ++U+U+P +1292 ++UV+P ∧ ∧ ∧ E1292 E $17,*2$V[V ∧ ]1292 ]$17,*2FV[V 16 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP &RPRYLPRVSURFHVVDVHWRGDLWHUDomRN VHPQHFHVVLGDGHGHXPDHVWUXWXUDGHGDGRV FRPSOHWDGDLWHUDomRN 20e72'26,03/(;&/È66,&2 ,7(5$d2 ,7(5$d2 ,7(5$d2 ,7(5$d2 ,7(5$d2 ,7(5$d2 20e72'26,03/(;5(9,6$'2 ,7(5$d2 ,7(5$d2 17 Departamento de Engenharia de Sistemas - (DENSIS) FEEC/UNICAMP
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