Corte e Empacotamento UFSCAR
Transcrição
Corte e Empacotamento UFSCAR
/ (2 1 $ 5 ' 2 -8 1 4 8 (,5 $ 0 2 ' (/2 6' (35 2 * 5 $ 0 $ d 2 0 $ 7(0 È 7,& $ 3$ 5 $ 35 2 %/(0 $ 6 ' (& $ 5 5 (* $ 0 (1 72 ' (& $ ,; $ 6' (1 75 2 ' (& 2 1 7Ç,1 (5 (6 ' LVVHUWDomR GH 0 HVWUDGR DSUHVHQWDGD DR 3URJUDP DGH3yV* UDGXDomRHP (QJHQKDULD GH3URGXomRGD8 QLYHUVLGDGH)HGHUDOGH6mR &DUORV FRP R SDUWH GRV UHTXLVLWRV SDUD REWHQomRGRWtWXORGH0 HVWUHHP (QJHQKDULD GH3URGXomR 2 ULHQWDGRU3URI' U5HLQDOGR0 RUDELWR1 HWR $ JrQFLDV)LQDQFLDGRUDV&$ 3(6H)$ 3(63 6mR& DUORV Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária da UFSCar J957mp Junqueira, Leonardo. Modelos de programação matemática para problemas de carregamento de caixas dentro de contêineres / Leonardo Junqueira. -- São Carlos : UFSCar, 2009. 134 p. Dissertação (Mestrado) -- Universidade Federal de São Carlos, 2009. 1. Pesquisa operacional. 2. Sistema de unitização de cargas. 3. Otimização combinatória. 4. Modelagem matemática. I. Título. CDD: 658.4034 (20 a) $ RVP HXVSDLV 0 DULDH2 VYDOGR $ * 5 $ ' (& ,0 (1 72 6 $ JUDGHoR D WRGRV TXH FRQWULEXtUDP GH DOJXP D P DQHLUD GLUHWD RX LQGLUHWDP HQWHSDUDDUHDOL]DomRGHVWDSHTXHQDREUD(P HVSHFLDOJRVWDULDGHP HQFLRQDU 2 SURIHVVRU5HLQDOGR0 RUDELWR1 HWRSRUWHUP HGDGRDRSRUWXQLGDGHGH UHDOL]DUHVWHWUDEDOKRHSHODRULHQWDomRQRP HVP RVHP SUHFRP P XLWDSDFLrQFLDHERP KXP RU HSHODVLQ~P HUDVOHLWXUDVHFRUUHo}HVGRWH[WR $ SHVTXLVDGRUD' HQLVH6DWR< DP DVKLWDSRUWHUDFRP SDQKDGRWRGDVDVHWDSDV GRGHVHQYROYLP HQWRGHVWHWUDEDOKRHSRUWHUVLGRVHP SUHP XLWRVROtFLWDHSDFLHQWHQDVDMXGDV HP GLYHUVRVP RP HQWRVVHP DVTXDLVHVWHWUDEDOKRGLILFLOP HQWHWHULDVLGRUHDOL]DGR 2 VSURIHVVRUHV$ QWRQLR&DUORV0 RUHWWL+ RUDFLR+ LGHNL< DQDVVHH9 LWyULD 0 DULD 0 LUDQGD 3XUH]D SHORV FRP HQWiULRV VXJHVW}HV H FUtWLFDV IHLWRV QR H[DP H GH TXDOLILFDomRHQDGHIHVDGDGLVVHUWDomRHTXHP HDMXGDUDP DP HOKRUDURQtYHOGHVWHWUDEDOKR 2 SURIHVVRU2 OLQWR&pVDU%DVVLGH$ UD~MRSHORP DWHULDOHQYLDGRLQFOXLQGRXP FyGLJRSDUDDYLVXDOL]DomRGRVSDGU}HVGHHP SDFRWDP HQWRHTXHP XLWRIDFLOLWRXR GHVHQYROYLP HQWRGHVWHWUDEDOKR 2 SURIHVVRU: DOWHU/LEDUGLSRUWHUGHVSHQGLGRXP DSDUWHGRVHXWHP SRHP FRQYHUVDVFRP LJRVREUHFRQFHLWRVGHUHVLVWrQFLDGRVP DWHULDLVHTXHP HDMXGDUDP DP RGHODU DOJXP DVGDVFRQVLGHUDo}HVSUiWLFDVWUDWDGDVQHVWHWUDEDOKR 2 VFROHJDV$ OH[DQGHU$ EXDEDUD' RXJODV-RVp$ OHP -XQLRU0 {QLFDGR $ P DUDO5DIDHO3LDWWL2 LWLFLFDGH3DLYDHWRGRVRVGHP DLVLQWHJUDQWHVGR/DERUDWyULRGH 0 RGHODJHP GR' (38 )6&DUSHODVGLFDVHFRQVHOKRVGDGRVGXUDQWHP HXSURFHVVRGH P HVWUDGR 2 VIXQFLRQiULRVGR' (38 )6&DU5DTXHO2 WWDQL%RULRORH5REVRQ/RSHVGRV 6DQWRVGDVHFUHWDULDGHSyVJUDGXDomRH/HDQGUR&DQDOL5DP RVGRVXSRUWHGHLQIRUP iWLFD SHODVROLFLWXGHHP GLYHUVRVP RP HQWRV $ &$ 3(6HD)$ 3(63SHORDSRLRILQDQFHLUR 0 HXVSDLV0 DULD-RVp=XSLUROL-XQTXHLUDH2 VYDOGR-RVp-XQTXHLUDHP HX LUP mR)DEUtFLR-XQTXHLUDSHODGHGLFDomRHDWHQomRHP WRGRVRVP RP HQWRVVHP DVTXDLVHX GLILFLOP HQWHWHULDFXP SULGRP DLVHVWDHWDSD assim me disse, embora voz alguma ou sopro ou eco ou simples percussão atestasse que alguém, sobre a montanha, a outro alguém, noturno e miserável, em colóquio se estava dirigindo: “O que procuraste em ti ou fora de teu ser restrito e nunca se mostrou, mesmo afetando dar-se ou se rendendo, e a cada instante mais se retraindo, olha, repara, ausculta: essa riqueza sobrante a toda pérola, essa ciência sublime e formidável, mas hermética, essa total explicação da vida, esse nexo primeiro e singular, que nem concebes mais, pois tão esquivo se revelou ante a pesquisa ardente em que te consumiste... vê, contempla, abre teu peito para agasalhá-lo.” IUDJP HQWRGHA Máquina do Mundo GH&DUORV' UXP P RQGGH$ QGUDGH 5 (68 0 2 2 REMHWRGHHVWXGRGHVWHWUDEDOKRpXP FDVRSDUWLFXODUGRVSUREOHP DVGHFRUWHH HP SDFRWDP HQWRFRQKHFLGRFRP RSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHV(VWHVSUREOHP DV FRQVLVWHP HP DUUDQMDU FDL[DV UHWDQJXODUHV RUWRJRQDOP HQWH GHQWUR GH FRQWrLQHUHV RX FDP LQK}HVYDJ}HVIHUURYLiULRVHSDOHWHVGHP DQHLUDDRWLP L]DUXP DIXQomRREMHWLYRSRU H[HP SORP D[LP L]DURDSURYHLWDP HQWRGRHVSDoRGLVSRQtYHORXHQWmRP LQLP L]DURQ~P HURGH FRQWrLQHUHVQHFHVViULRVSDUDFDUUHJDUWRGDVDVFDL[DVGLVSRQtYHLV2 REMHWLYRGHVWHWUDEDOKRp GHVHQYROYHUP RGHORVGHSURJUDP DomRP DWHP iWLFDTXHDERUGHP VLWXDo}HVFRP XP HQWH HQFRQWUDGDV QD SUiWLFD GR FDUUHJDP HQWR GH FRQWrLQHUHV &RQVLGHUDo}HV GH P ~OWLSODV RULHQWDo}HVGDVFDL[DVOLP LWHGHSHVRGRFRQWrLQHUHVWDELOLGDGHGRFDUUHJDP HQWRUHVLVWrQFLD GDVFDL[DVDRHP SLOKDP HQWRHFDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRVVmRWUDWDGDV2 DXWRU QmRWHP FRQKHFLP HQWRGHIRUP XODo}HVP DWHP iWLFDVGLVSRQtYHLVQDOLWHUDWXUDGHFRUWHH HP SDFRWDP HQWRTXHWUDWHP HVWDVFRQVLGHUDo}HVHHVWHWUDEDOKRSUHWHQGHFRQWULEXLUFRP SRVVtYHLVIRUP XODo}HVTXHHP ERUDSRXFRUHDOLVWDVSDUDVHUHP DSOLFDGDVQDSUiWLFDGHVFUHYHP HVWDVVLWXDo}HV([SHULP HQWRVFRP SXWDFLRQDLVFRP RVP RGHORVSURSRVWRVVmRUHDOL]DGRV XWLOL]DQGRRDSOLFDWLYR* $ 0 6&3/(; HH[HP SORVJHUDGRVDOHDWRULDP HQWHHGDOLWHUDWXUD2 V UHVXOWDGRVP RVWUDP TXHRVP RGHORVVmRFRHUHQWHVHUHSUHVHQWDP DGHTXDGDP HQWHDVVLWXDo}HV WUDWDGDVHP ERUDHVWDDERUGDJHP QDVXDYHUVmRDWXDOHVWHMDOLP LWDGDDUHVROYHURWLP DP HQWH DSHQDVSUREOHP DVGHWDP DQKREHP P RGHUDGR1 RHQWDQWRRVP RGHORVSRGHP VHU~WHLVSDUD P RWLYDUSHVTXLVDVIXWXUDVH[SORUDQGRP pWRGRVGHGHFRP SRVLomRP pWRGRVGHUHOD[DomR P pWRGRVKHXUtVWLFRVHQWUHRXWURVSDUDUHVROYHURVSUREOHP DVHP TXHVWmR 3DODYUDVFKDYH3UREOHP DVGH&RUWHH(P SDFRWDP HQWR&DUUHJDP HQWRGH&RQWrLQHUHV 2 WLP L]DomR&RP ELQDWyULD0 RGHODJHP 0 DWHP i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et al.EDVHSDUDHVWHWUDEDOKR )LJXUD ' LVSRVLWLYRVGHXQLWL]DomRGHFDUJD )LJXUD 5HVXP RGRVWLSRVLQWHUP HGLiULRVGH3&(¶VP D[LP L]DomRGDVVDtGDV )LJXUD 5HVXP RGRVWLSRVLQWHUP HGLiULRVGH3&(¶VP LQLP L]DomRGDVHQWUDGDV )LJXUD 3RQWRVGHUHIHUrQFLDSDUDFDL[DVHFRQWrLQHUHV )LJXUD /RFDOL]DomRGHXP DFDL[DGHQWURGRFRQWrLQHU )LJXUD /RFDOL]DomRGRFRQWrLQHUQRHVSDoRGHFRRUGHQDGDVFDUWHVLDQDV )LJXUD /RFDOL]DomRUHODWLYDGHGXDVFDL[DVGHQWURGHXP FRQWrLQHU )LJXUD 3ODQRL H QDSRVLomRt HP UHODomRDRHL[Ry )LJXUD/RFDOL]DomRUHODWLYDGHGXDVFDL[DVGHQWURGHXP FRQWrLQHU )LJXUD([HP SORVGHFDL[DVVHQGRFDUUHJDGDVHP FDP DGDVYHUWLFDLVHKRUL]RQWDLV )LJXUD([HP SORGHFDL[DVVHQGRFDUUHJDGDVHP SLOKDV )LJXUD([HP SORVGHFDL[DVIRUP DQGRXP SDGUmRJXLOKRWLQDGRHQmRJXLOKRWLQDGR )LJXUD([HP SORGHFDL[DVVHQGRFDUUHJDGDVHP FXEyLGHV )LJXUD([HP SORQXP pULFRFRP RVFRQMXQWRVX HY )LJXUD6XSHUFRQWrLQHUIRUP DGRSHODXQLmRGHGRLVFRQWrLQHUHV )LJXUD2 ULHQWDo}HVTXHXP DFDL[DSRGHWHUFRP URWDo}HVHP WRUQRGHWRGRVRVHL[RV )LJXUD0 DSHDP HQWRGRFRQMXQWRGHSRQWRVGDIDFHVXSHULRUGDFDL[Di )LJXUDÈ UHDGHFRQWDWRHQWUHGXDVFDL[DVQRSODQRxy )LJXUD0 DSHDP HQWRGRVFRQMXQWRVGHSRQWRVGDVIDFHVODWHUDOGLUHLWDHODWHUDOGRIXQGRGD FDL[Di )LJXUDÈ UHDVGHFRQWDWRHQWUHGXDVFDL[DVQRVSODQRVyz Hxz )LJXUD&RQMXQWRGHFDL[DVHP SLOKDGDVVREUHXP DFDL[DGHUHIHUrQFLD )LJXUD&DP LQKmRVHQGRGHVFDUUHJDGRDRORQJRGHFLQFRGHVWLQRV )LJXUD([HP SORGHHP SDFRWDP HQWRGDVFDL[DVFRP R3URFHGLP HQWR )LJXUD([HP SORGHHP SDFRWDP HQWRGDVFDL[DVFRP R3URFHGLP HQWR )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRVJUXSRV$ mHRVP RGHORV 0 0 H0 )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRVJUXSRV% mHRVP RGHORV 0 0 H0 )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORHRVP RGHORV0 0 0 H 0 )LJXUD6ROXo}HVREWLGDVSDUDRH[HP SORGH&KHQet al )LJXUD6ROXo}HVREWLGDVSDUDRVH[HP SORVGH/LQVet al / ,67$ ' (7 $ %(/$ 6 7DEHOD &RQVLGHUDo}HVSUiWLFDVDSUHVHQWDGDVSRU%LVFKRIIH5DWFOLIID 7DEHOD 0 RGHORVXWLOL]DGRVQRVH[SHULP HQWRVFRP SXWDFLRQDLV 7DEHOD ' LP HQV}HVL W H GRVFRQWrLQHUHVSDUDRVJUXSRVGHH[HP SORVJHUDGRV DOHDWRULDP HQWH 7DEHOD 1 ~P HURGHHOHP HQWRVGRVSDGU}HVQRUP DLVHQ~P HURGHUHVWULo}HVHYDULiYHLVGRV P RGHORVFRP L W H LJXDLVD 7DEHOD 5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 7DEHOD 5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 7DEHOD 5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 7DEHOD 5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 7DEHOD 5HVXP RGRVH[SHULP HQWRVFRP H[HP SORVGRVJUXSRV$ m 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 7DEHOD5HVXP RGRVH[SHULP HQWRVFRP H[HP SORVGRVJUXSRV% m 7DEHOD5HVXOWDGRVREWLGRVFRP RVJUXSRV$ $ $ $ % % % H% HRV P RGHORV0 H0 7DEHOD5HVXOWDGRVREWLGRVFRP RVJUXSRV$ $ $ $ % % % H% HRV P RGHORV0 H0 7DEHOD5HVXOWDGRVREWLGRVFRP RVWUrVH[HP SORVGH/LQVet alHRVP RGHORV0 H 0 68 0 È 5 ,2 & $ 3Ë78 /2 ,1 752 ' 8 d 2 & $ 3Ë78 /2 & $ 55(* $ 0 (1 72 ' (& 2 1 7Ç,1 (5(6 ,1 752 ' 8 d 2 /2 * Ë67,&$ ' (),1 ,d® (6& 2 1 &(,72 6($ 7,9 ,' $ ' (6 8 1 ,7,=$ d 2 ' (& $ 5* $ ' ,632 6,7,9 2 6' (8 1 ,7,=$ d 2 ' (& $ 5* $ 9 $ 1 7$ * (1 6(' (69 $ 1 7$ * (1 6' $ 8 1 ,7,=$ d 2 ' (& $ 5* $ 352 %/(0 $ 6' (& 2 57(((0 3$ &2 7$ 0 (1 72 352 %/(0 $ 6' (& $ 55(* $ 0 (1 72 ' (& 2 1 7Ç,1 (5(6 & 2 1 6,' (5$ d® (635È 7,&$ 61 2 & $ 55(* $ 0 (1 72 ' (& 2 1 7Ç,1 (5(6 & $ 3Ë78 /2 )2 50 8 /$ d® (6(0 e72 ' 2 6' $ /,7(5$ 78 5$ ,1 752 ' 8 d 2 )2 50 8 /$ d® (60 $ 7(0 È 7,&$ 6 )2 50 8 /$ d 2 ' (% ($ 6/(< )2 50 8 /$ d 2 ' (76$ ,ET AL )2 50 8 /$ d 2 ' (& + (1 ET AL )2 50 8 /$ d 2 ' (+ $ ' -,&2 1 67$ 1 7,1 2 8 (& + ,672 ),' (6 )2 50 8 /$ d 2 ' (% ($ 6/(< 0 e72 ' 2 6' (62 /8 d 2 & $ 3Ë78 /2 0 2 ' (/$ * (0 &2 0 & 2 1 6,' (5$ d® (6$ ' ,&,2 1 $ ,6 ,1 752 ' 8 d 2 0 $ 1 ,38 /$ 1 ' 2 $ )2 50 8 /$ d 2 ' (% ($ 6/(< & 2 1 6,' (5$ 1 ' 2 0 Ò /7,3/$ 62 5,(1 7$ d® (6' $ 6& $ ,; $ 6 & 2 1 6,' (5$ 1 ' 2 /,0 ,7(' (3(62 ' 2 & 2 1 7Ç,1 (5 & 2 1 6,' (5$ 1 ' 2 (67$ %,/,' $ ' (' 2 & $ 55(* $ 0 (1 72 & 2 1 6,' (5$ 1 ' 2 5 (6,67Ç1 &,$ ' $ 6& $ ,; $ 6$ 2 (0 3,/+ $ 0 (1 72 & 2 1 6,' (5$ 1 ' 2 & $ 5* $ )5$ &,2 1 $ ' $ (0 0 Ò /7,3/2 6' (67,1 2 6 & $ 3Ë78 /2 5 (68 /7$ ' 2 6& 2 0 38 7$ &,2 1 $ ,6(' ,6&8 66 2 ,1 752 ' 8 d 2 5 (68 /7$ ' 2 6' ((; (0 3/2 6* (5$ ' 2 6$ /($ 72 5,$ 0 (1 7( 5 (68 /7$ ' 2 6' ((; (0 3/2 6' $ /,7(5$ 78 5$ & $ 3Ë78 /2 & 2 1 &/8 6® (6(3(563(&7,9 $ 6)8 78 5$ 6 5 ()(5Ç1 &,$ 6% ,%/,2 * 5È ),&$ 6 $ 3Ç1 ' ,' ($ 0 2 ' (/2 6(0 * $ 0 6±3$ 57(, $ 3Ç1 ' ,' (% 0 2 ' (/2 6(0 * $ 0 6±3$ 57(,, & $ 3Ë78 /2 ,1 75 2 ' 8 d 2 ' HQWUH DV SULQFLSDLV DWLYLGDGHV ORJtVWLFDV GHVWDFDP VH DV DWLYLGDGHV GH DUP D]HQDJHP GHP DQXVHLRGHP DWHULDLVHGHWUDQVSRUWHGHP HUFDGRULDVFRP RFKDYHVSDUDD LQWHJUDomRGHFDGHLDVGHVXSULP HQWRGHVGHRVIRUQHFHGRUHVDWpRVFOLHQWHV&RP RGHFRUUrQFLD GRDSHUIHLoRDP HQWRFRQWtQXRGHVWDVDWLYLGDGHVGHQWURGDVHP SUHVDVQDV~OWLP DVGpFDGDVWrP JDQKDGRGHVWDTXHFRQFHLWRVFRP RRVGHWUDQVSRUWHP XOWLP RGDOHXQLWL]DomRGHFDUJDV (VWHWUDEDOKRDERUGDP pWRGRVFRP XP HQWHHQFRQWUDGRVQDSUiWLFDSDUDDX[LOLDU QDXQLWL]DomRGHP HUFDGRULDVFDUJDVRXP DLVHVSHFLILFDP HQWHQRDUUDQMRGHFDL[DVGHQWURGH FRQWrLQHUHVLVWRpQDFRQWHLQHUL]DomRGHFDUJD2 objeto de estudoGHVWHWUDEDOKRpXP FDVR SDUWLFXODU GRV SUREOHP DV GH FRUWHHHP SDFRWDP HQWRFRQKHFLGRFRP RSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHV1 HVWHVSUREOHP DVJHQHULFDP HQWHFDL[DVUHWDQJXODUHVGHYHP VHUHP SDFRWDGDVRUWRJRQDOP HQWHGHQWURGHXP RXP DLVFRQWrLQHUHV 2 objetivoGHVWHWUDEDOKRpGHVHQYROYHUP RGHORVGHSURJUDP DomRP DWHP iWLFD TXHDERUGHP VLWXDo}HVFRP XP HQWHHQFRQWUDGDVQDSUiWLFDGRFDUUHJDP HQWRGHFRQWrLQHUHV &RQVLGHUDo}HVGHP ~OWLSODVRULHQWDo}HVGDVFDL[DVOLP LWHGHSHVRGRFRQWrLQHUHVWDELOLGDGH GRFDUUHJDP HQWRUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRHFDUJDIUDFLRQDGDHP P ~OWLSORV GHVWLQRV VmR WUDWDGDV 0 XLWDV GHVWDV VLWXDo}HV SUiWLFDV QmR HQFRQWUDP IRUP XODo}HV P DWHP iWLFDVGLVSRQtYHLVQDOLWHUDWXUDGHFRUWHHHP SDFRWDP HQWRHHVWHWUDEDOKRSUHWHQGH FRQWULEXLUFRP P RGHORVGHSURJUDP DomRP DWHP iWLFDTXHHP ERUDSRXFRUHDOLVWDVSDUDVHUHP DSOLFDGRVQHVWDVVLWXDo}HVUHSUHVHQWDP RVSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVFRP HVWDVFRQVLGHUDo}HV $ VjustificativasSDUDRGHVHQYROYLP HQWRGHIRUP XODo}HVTXHGHVFUHYDP VLWXDo}HVSUiWLFDVHP FDUUHJDP HQWRGHFRQWrLQHUHVHVWmRQDVSULQFLSDLVYDQWDJHQVGRHP SUHJR GHVWDIRUP DGHXQLWL]DomRGHFDUJDWDLVFRP RLUHGXomRGHSHUGDVURXERVHDYDULDVGD FDUJDLLUHGXomRGHGHVSHVDVFRP URWXODJHP HP DUFDomRGDVFDUJDVLLLUHGXomRGH GHVSHVDVFRP XWLOL]DomRGHP mRGHREUDSDUDP RYLP HQWDomRGDFDUJDLYDXP HQWRGD UDSLGH]QDVRSHUDo}HVGHFDUUHJDP HQWRHGHVFDUUHJDP HQWRGHYHtFXORVHHP EDUFDo}HVHWF 4 XDQWRjVXDabordagemGHSHVTXLVDHVWHWUDEDOKRSRVVXLXP DDERUGDJHP quantitativaSRLVHVWDpSDUWLFXODUP HQWHP DLVDSURSULDGDSDUDSURGX]LUGHVFREHUWDVHP TXH UHODo}HVGHFDXVDHHIHLWRVmRHVWDEHOHFLGDVHHP TXHRSHVTXLVDGRUP DQLSXODDWLYDP HQWHXP FHQiULRHREVHUYDRVHIHLWRVGHVWDLQWHUYHQomRQDVYDULiYHLVGHLQWHUHVVH%5< 0 $ 1 4 XDQWRDRVHXmétodoGHSHVTXLVDHVWHWUDEDOKRXWLOL]DDmodelagem P DWHP iWLFDFRP RP pWRGRSRLVHVWHSHUP LWHDRSHVTXLVDGRUP DQLSXODUGLUHWDP HQWHDV YDULiYHLVLQGHSHQGHQWHVGRSUREOHP DHP TXHVWmRHVHEDVHDUHP XP FRQMXQWRGHYDULiYHLV TXHYDULDP GHQWURGHXP GRP tQLRHVSHFtILFRHP TXHP RGHORVGHUHODo}HVFDXVDLVHQWUHDV YDULiYHLVLQGHSHQGHQWHVHGHSHQGHQWHVVmRGHVHQYROYLGRVDQDOLVDGRVHWHVWDGRV$ OpP GLVVR HVWHP pWRGRSHUP LWHDRSHVTXLVDGRUVHEDVHDUQDFRQVWUXomRGHP RGHORVREMHWLYRVTXH H[SOLTXHP RFRP SRUWDP HQWRGHSURFHVVRVRSHUDFLRQDLVGDYLGDUHDORXTXHSRVVDP DSUHHQGHU RVSUREOHP DVGHWRP DGDGHGHFLVmR%(575$ 1 ' )5$ 1 62 2 $ )LJXUDLOXVWUDRP RGHORGH0 LWURIIet al.EDVHSDUDHVWHWUDEDOKR )LJXUD0 RGHORGH0 LWURIIet al.EDVHSDUDHVWHWUDEDOKR )RQWHDGDSWDGRGH%HUWUDQGH)UDQVRR ,VWRpQR³URWHLUR´GHVWHWUDEDOKRHVWiDDSOLFDomRGDP RGHODJHP VREUHXP P RGHORFRQFHLWXDOLQLFLDODUHVROXomRGRP RGHORFLHQWtILFRREWLGRDWUDYpVGDP RGHODJHP HD UHDOLP HQWDomRGDVROXomRGHVWHP RGHORFLHQWtILFRQRP RGHORFRQFHLWXDOLQLFLDO $ hipóteseSULQFLSDOGHVWHWUDEDOKRpDGHTXHpSRVVtYHOHP SUHJDUD SURJUDP DomRP DWHP iWLFDSDUDP RGHODUVLWXDo}HVFRP XP HQWHHQFRQWUDGDVQDSUiWLFDGR FDUUHJDP HQWRGHFRQWrLQHUHV (VWHWUDEDOKRHVWiHVWUXWXUDGRHP VHLVFDStWXORV 1 RFDStWXORpDSUHVHQWDGRRFRQWH[WRHP TXHHVWmRLQVHULGRVRVSUREOHP DV HVWXGDGRV3ULP HLUDP HQWHVmRDSUHVHQWDGRVEUHYHP HQWHRVFRQFHLWRVGHORJtVWLFDHGH XQLWL]DomRGHFDUJDVEHP FRP RRVGLVSRVLWLYRVP DLVFRP XP HQWHXWLOL]DGRVSDUDXQLWL]DU P HUFDGRULDVHDVYDQWDJHQVHGHVYDQWDJHQVGDXWLQL]DomR(P VHJXLGDpDSUHVHQWDGDXP D EUHYHGLVFXVVmRGRVSUREOHP DVGHFRUWHHHP SDFRWDP HQWRHHP SDUWLFXODUGRVSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHVHGDVFRQVLGHUDo}HVSUiWLFDVTXHSRGHP VHUOHYDGDVHP FRQVLGHUDomRTXDQGRVHGHVHMDP RGHODUHVWHVSUREOHP DV 1 RFDStWXORpDSUHVHQWDGDSULP HLUDP HQWHXP DUHYLVmRGDVIRUP XODo}HV P DWHP iWLFDVGLVSRQtYHLVQDOLWHUDWXUDHTXHSRGHP VHUXWLOL]DGDVSDUDP RGHODUSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHV(P VHJXLGDpDSUHVHQWDGDXP DEUHYHGLVFXVVmRGHDOJXQV P pWRGRVGHVROXomRGLVSRQtYHLVQDOLWHUDWXUDSDUDVHUHVROYHUHVWHVSUREOHP DV 1 RFDStWXORVmRDSUHVHQWDGDVH[WHQV}HVGHXP P RGHORGHSURJUDP DomR P DWHP iWLFDGDOLWHUDWXUDGHFRUWHHHP SDFRWDP HQWRGHP RGRDDERUGDUVLWXDo}HVFRP XP HQWH HQFRQWUDGDV QD SUiWLFD GR FDUUHJDP HQWR GH FRQWrLQHUHV &RQVLGHUDo}HV GH P ~OWLSODV RULHQWDo}HVGDVFDL[DVOLP LWHGHSHVRGRFRQWrLQHUHVWDELOLGDGHGRFDUUHJDP HQWRUHVLVWrQFLD GDVFDL[DVDRHP SLOKDP HQWRHFDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRVVmRWUDWDGDV 1 RFDStWXORVmRDSUHVHQWDGRVRVUHVXOWDGRVREWLGRVGRVH[SHULP HQWRV FRP SXWDFLRQDLVUHDOL]DGRVFRP DOJXQVGRVP RGHORVLP SOHP HQWDGRVQDOLQJXDJHP GH P RGHODJHP * $ 0 6HUHVROYLGRVFRP Rsolver&3/(; FRP H[HP SORVJHUDGRVDOHDWRULDP HQWH HGDOLWHUDWXUD 1 RFDStWXORILQDOP HQWHVmRGLVFXWLGDVDVFRQFOXV}HVGHVWHWUDEDOKRHDV SHUVSHFWLYDVSDUDSHVTXLVDVIXWXUDV & $ 3Ë78 /2 & $ 5 5 (* $ 0 (1 72 ' (& 2 1 7Ç,1 (5 (6 ,1 75 2 ' 8 d 2 1 HVWHFDStWXORpDSUHVHQWDGRRFRQWH[WRHP TXHHVWmRLQVHULGRVRVSUREOHP DV HVWXGDGRV3ULP HLUDP HQWHVmRDSUHVHQWDGRVEUHYHP HQWHRVFRQFHLWRVGHORJtVWLFDHGH XQLWL]DomRGHFDUJDVEHP FRP RRVGLVSRVLWLYRVP DLVFRP XP HQWHXWLOL]DGRVSDUDXQLWL]DU P HUFDGRULDVHDVYDQWDJHQVHGHVYDQWDJHQVGDXWLQL]DomR(P VHJXLGDpDSUHVHQWDGDXP D EUHYHGLVFXVVmRGRVSUREOHP DVGHFRUWHHHP SDFRWDP HQWRHHP SDUWLFXODUGRVSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHVHGDVFRQVLGHUDo}HVSUiWLFDVTXHSRGHP VHUOHYDGDVHP FRQVLGHUDomRTXDQGRVHGHVHMDP RGHODUHVWHVSUREOHP DV / 2 * Ë67,& $ ' (),1 ,d ® (6& 2 1 & (,72 6($ 7,9 ,' $ ' (6 $ VRULJHQVGDORJtVWLFDUHP HWHP jDQWLJXLGDGH$ HWLP RORJLDGDSDODYUD ORJtVWLFDYHP GRJUHJRlogistikéHGRODWLP P RGHUQRlogistaHpUHODWLYRDRFiOFXOR7UDWDYDVH GHXP DGHQRP LQDomRGDGDSHORVJUHJRVjSDUWHGDDULWP pWLFDHGDiOJHEUDFRQFHUQHQWHjV TXDWURRSHUDo}HVRXDLQGDXP FRQMXQWRGHVLVWHP DVGHDOJRULWP RVDSOLFDGRVjOyJLFD1 R HQWDQWRDHWLP RORJLDGDSDODYUDORJtVWLFDWDOFRP RWHP VLGRHP SUHJDGDQRV~OWLP RVVpFXORV YHP GRIUDQFrVlogistiqueHWUDWDYDVHGDSDUWHGDDUWHGDJXHUUDTXHWUDWDGRSODQHMDP HQWRH GDUHDOL]DomRGHLSURMHWRHGHVHQYROYLP HQWRREWHQomRDUP D]HQDP HQWRWUDQVSRUWH GLVWULEXLomRUHSDUDomRP DQXWHQomRHHYDFXDomRGHP DWHULDOSDUDILQVRSHUDWLYRVRX DGP LQLVWUDWLYRVLLUHFUXWDP HQWRLQFRUSRUDomRLQVWUXomRHDGHVWUDP HQWRGHVLJQDomR WUDQVSRUWHEHP HVWDUHYDFXDomRKRVSLWDOL]DomRHGHVOLJDP HQWRGHSHVVRDOLLLDTXLVLomRRX FRQVWUXomRUHSDUDomRP DQXWHQomRHRSHUDomRGHLQVWDODo}HVHDFHVVyULRVGHVWLQDGRVDDMXGDU RGHVHP SHQKRGHTXDOTXHUIXQomRP LOLWDULYFRQWUDWRRXSUHVWDomRGHVHUYLoRV)(55(,5$ 1 DVHP SUHVDVDORJtVWLFDSRGHVHUYLVWDFRP RDFRP SHWrQFLDTXHYLQFXODD RUJDQL]DomRDVHXVFOLHQWHVHIRUQHFHGRUHVLVWRpXP HVIRUoRLQWHJUDGR±SODQHMDP HQWR LP SOHP HQWDomRHFRQWUROHGRIOX[RHILFLHQWHHHFRQRP LFDP HQWHHILFD]GHP DWpULDVSULP DV HVWRTXHHP SURFHVVRSURGXWRVDFDEDGRVHLQIRUP Do}HVUHODWLYDVGHVGHRSRQWRGHRULJHP DWp RSRQWRGHFRQVXP R±FRP RREMHWLYRGHDMXGDUDFULDUYDORUSDUDRFOLHQWHSHORP HQRUFXVWR WRWDOSRVVtYHOH[LVWLQGRSDUDVDWLVID]HUDVQHFHVVLGDGHVGRVFOLHQWHVHIDFLOLWDQGRDVRSHUDo}HV UHOHYDQWHVGHSURGXomRHP DUNHWLQJ2 YDORUHP ORJtVWLFDpH[SUHVVRSULQFLSDOP HQWHHP WHUP RVGHWHP SRHOXJDU3URGXWRVHVHUYLoRVQmRWrP YDORUDP HQRVTXHHVWHMDP VREDSRVVH GRFOLHQWHTXDQGRWHP SRHRQGHOXJDUHOHVGHVHMDP FRQVXP LORV%2 : (562 ; &/2 66 %$ //2 8 $ ORJtVWLFDWHP FRP RP LVVmRGLVSRUDP HUFDGRULDRXRVHUYLoRFHUWRQROXJDU FHUWRQRWHP SRFHUWRHQDVFRQGLo}HVGHVHMDGDVDRP HVP RWHP SRHP TXHIRUQHFHDP DLRU FRQWULEXLomRjHP SUHVD$ VDWLYLGDGHVORJtVWLFDVSRGHP VHUGLYLGLGDVHP HVVHQFLDLVHGH DSRLR$ VDWLYLGDGHVHVVHQFLDLVVmRWDP EpP GHQRP LQDGDVDWLYLGDGHVSULP iULDVHLQFOXHP JHVWmRGHHVWRTXHVSURFHVVDP HQWRGHSHGLGRVHWUDQVSRUWH$ VDWLYLGDGHVGHDSRLRVmR WDP EpP GHQRP LQDGDV DWLYLGDGHV VHFXQGiULDV H LQFOXHP DUP D]HQDJHP P DQXVHLR GH P DWHULDLVHP EDODJHQVGHSURWHomRSURJUDP DomRGHSURGXWRVHP DQXWHQomRGHLQIRUP DomR %$ //2 8 1 HVWHWUDEDOKRDVDWLYLGDGHVORJtVWLFDVP DLVGLUHWDP HQWHUHODFLRQDGDVVmRDV DWLYLGDGHVGHDUP D]HQDJHP GHP DQXVHLRGHP DWHULDLVGHHP EDODJHQVGHSURWHomRHGH WUDQVSRUWH7RGDVHVWDVDWLYLGDGHVHQYROYHP DLGpLDGHP HUFDGRULDVRXFDUJDVTXHGHYHP VHU GHYLGDP HQWHDUP D]HQDGDVP DQXVHDGDVHP EDODGDVHWUDQVSRUWDGDV$ VFDUJDVSRGHP VHU FODVVLILFDGDVEDVLFDP HQWHHP 0 ' ,& x &DUJD* HUDOFDUJDHP EDUFDGDFRP P DUFDGHLGHQWLILFDomRHFRQWDJHP GHXQLGDGHV SRGHQGRVHUsoltaLWHQVDYXOVRVHP EDUFDGRVVHSDUDGDP HQWHHP HP EUXOKRVIDUGRV SDFRWHVVDFDVFDL[DVWDP ERUHVHWFRXunitizadaDJUXSDP HQWRGHYiULRVLWHQVHP XQLGDGHVGHWUDQVSRUWH x &DUJDD* UDQHOFDUJDOtTXLGDRXVHFDHP EDUFDGDHWUDQVSRUWDGDVHP DFRQGLFLRQDP HQWR VHP P DUFDGHLGHQWLILFDomRHVHP FRQWDJHP GHXQLGDGHVSRUH[HP SORSHWUyOHR P LQpULRVWULJRIDUHORVHJUmRVHWF x &DUJD)ULJRULILFDGDQHFHVVLWDVHUUHIULJHUDGDRXFRQJHODGDSDUDFRQVHUYDUDVTXDOLGDGHV HVVHQFLDLVGRSURGXWRGXUDQWHRWUDQVSRUWHSRUH[HP SORIUXWDVIUHVFDVSHVFDGRV FDUQHVHWF x &DUJD3HULJRVDDTXHODTXHSRUFDXVDGHVXDQDWXUH]DSRGHSURYRFDUDFLGHQWHV GDQLILFDURXWUDVFDUJDVRXRVP HLRVGHWUDQVSRUWHRXDLQGDJHUDUULVFRVSDUDDVSHVVRDV SRUH[HP SORH[SORVLYRVJDVHVOtTXLGRVRXVyOLGRVLQIODP iYHLVVXEVWkQFLDVR[LGDQWHV LQIHFFLRVDVRXUDGLRDWLYDVFRUURVLYRVHWF x 1 HRJUDQHOFDUUHJDP HQWRIRUP DGRSRUFRQJORP HUDGRVKRP RJrQHRVGHP HUFDGRULDVGH FDUJDJHUDOVHP DFRQGLFLRQDP HQWRHVSHFtILFRFXMRYROXP HRXTXDQWLGDGHSRVVLELOLWDR WUDQVSRUWHHP ORWHVHP XP ~QLFRHP EDUTXHSRUH[HP SORYHtFXORV 1 HVWHWUDEDOKRRWLSRGHFDUJDDVHUHVWXGDGRpD&DUJD* HUDO8 QLWL]DGD 3URGXWRVHSHoDVVmRHP EDODGRVJHUDOP HQWHHP FDL[DVGHSDSHOmRVDFRVSHTXHQDVFDL[DVRX P HVP REDUULVSDUDP DLRUHILFLrQFLDQRP DQXVHLR(VVDVHP EDODJHQVVmRXVDGDVSDUDDJUXSDU SURGXWRVHVmRFKDP DGDVHP EDODJHQVVHFXQGiULDV$ VWUrVIXQo}HVSULQFLSDLVGHXP D HP EDODJHP SRGHP JHUDOP HQWHVHUGHVFULWDVFRP RSURWHomRFRQWUDDYDULDVXWLOLGDGHH HILFLrQFLDHFRP XQLFDomR4 XDQGRDVHP EDODJHQVVHFXQGiULDVVmRDJUXSDGDVHP XQLGDGHV P DLRUHVHVVDIRUP DomRpFKDP DGDXQLWL]DomR%2 : (562 ; &/2 66 8 1 ,7,=$ d 2 ' (& $ 5 * $ 2 WHUP RXQLWL]DomRVLJQLILFDDJUXSDP HQWRGHFDL[DVQXP DFDUJD~QLFD IRUP DQGRXP VyYROXP HSDUDP DQXVHLRRXWUDQVSRUWH&RP RREVHUYDGRQDVHomRDQWHULRU SDUDSURSLFLDUDHILFLrQFLDGRP DQXVHLRSURGXWRVFRP RODWDVJDUUDIDVRXFDL[DVVmR QRUP DOP HQWHMXQWDGRVRX³XQLWL]DGRV´HP XQLGDGHVP DLRUHV$ XQLGDGHLQLFLDODFDL[D P HVWUDDSUHVHQWDGXDVFDUDFWHUtVWLFDVLP SRUWDQWHV(P SULP HLUROXJDUHODVHUYHSDUDSURWHJHU RSURGXWRGXUDQWHRSURFHVVRORJtVWLFR(P VHJXQGROXJDUIDFLOLWDRP DQXVHLRFULDQGRXP SDFRWHGHJUDQGHVGLP HQV}HVHP YH]GHLQ~P HUDVXQLGDGHVSHTXHQDV3RUILP DVFDL[DV P HVWUDVVmRQRUP DOP HQWHFRQVROLGDGDVHP XQLGDGHVP DLRUHVYLVDQGRREWHUP DLRUHILFLrQFLD WDQWRQRP DQXVHLRTXDQWRQRWUDQVSRUWH%2 : (562 ; &/2 66 8 P D RXWUD MXVWLILFDWLYDDIDYRUGDXQLWL]DomRpWDP EpP XP SULQFLSLR IXQGDP HQWDOQRP DQXVHLRGHP DWHULDLV* HUDOP HQWHDHFRQRP LDGRP DQXVHLRGHP DWHULDLVp GLUHWDP HQWHSURSRUFLRQDODRWDP DQKRGDFDUJDP DQXVHDGD,VWRpFRP RDXP HQWRGRWDP DQKR GDFDUJDXP Q~P HURP HQRUGHYLDJHQVpUHTXHULGRSDUDHVWRFDUGHWHUP LQDGDTXDQWLGDGHGH P HUFDGRULDVHQWmRP DLRUpDHFRQRP LD2 Q~P HURGHYLDJHQVUHODFLRQDVHGLUHWDP HQWHDR WHP SRGHP mRGHREUDQHFHVViULRSDUDP RYLP HQWDUDVP HUFDGRULDVDVVLP FRP RRWHP SRTXH RHTXLSDP HQWRGHP DQXVHLRGHP DWHULDLVHVWiHP VHUYLoR%$ //2 8 $ VFDUJDVXQLWL]DGDVDSUHVHQWDP P XLWDVYDQWDJHQV(P SULP HLUROXJDUVmR UHGX]LGRVRWHP SRGHGHVFDUJDHRFRQJHVWLRQDP HQWRQRSRQWRGHGHVWLQR(P VHJXQGROXJDU pIDFLOLWDGRRP DQXVHLRGHP DWHULDLVSHODVLP SOLILFDomRQDYHULILFDomRGDVP HUFDGRULDVHP VXDHQWUDGDHQRUiSLGRSRVLFLRQDP HQWRSDUDDVHSDUDomRGHSHGLGRV&DUJDVXQLWL]DGDV WRP DP VRP HQWHXP TXLQWRGRWHP SRQHFHVViULRQRP DQXVHLRFRQYHQFLRQDO3RU~OWLP RD TXDQWLGDGHGHDYDULDVHP WUkQVLWRSRGHVHUUHGX]LGDSHODDGRomRGHFDUJDVXQLWL]DGDVH HTXLSDP HQWRVHVSHFLDOL]DGRVSDUDRWUDQVSRUWH7RGRVHVVHVIDWRUHVUHGX]HP FXVWRVORJtVWLFRV %2 : (562 ; &/2 66 ' ,632 6,7,9 2 6' (8 1 ,7,=$ d 2 ' (& $ 5 * $ ([LVWHP GLYHUVRVGLVSRVLWLYRVXWLOL]DGRVSDUDXQLWL]DomRRXFRQVROLGDomRGH FDUJD2 VP DLVFRP XP HQWHHQFRQWUDGRVVmR77& x SlingsOLQJDVVmRFLQWDVGHP DWHULDOVLQWpWLFRTXHIRUP DP XP DUHGHXWLOL]DGDV IUHTHQWHP HQWHSDUDVDFDULDSRGHQGRVHJXLUFRP DFDUJDDWpRGHVWLQRILQDORXDSHQDV DWpFRP SDUWLP HQWRVHVSHFtILFRVGHP RGDLVGHWUDQVSRUWHTXDQGRVmRHQWmRUHWLUDGDV x Big-bagsVmRVDFRVGHP DWHULDOVLQWpWLFRFRP IXQGRJHUDOP HQWHFLUFXODURXTXDGUDGR XWLOL]DGRV IUHTHQWHP HQWH SDUD SURGXWRV LQGXVWULDOL]DGRV HP JUmRV H SyV HP VXEVWLWXLomRDVDFDULDSRVVXLQGRJHUDOP HQWHFDSDFLGDGHVXSHULRUjGDVslingsH SRGHQGRVHUUHXWLOL]iYHLV x 3DOHWHVVmRSODWDIRUP DVJHUDOP HQWHGHP DGHLUDP DVSRGHQGRVHUWDP EpP GHDOXP tQLR DoRSROLSURSLOHQRSDSHOmRHWFVXVWHQWDGDVSRUSpVRXYLJDVGRP HVP RP DWHULDO VREUHDVTXDLVP HUFDGRULDVVmRHP SLOKDGDVHSRGHQGRVHUGHVFDUWiYHLVRXUHXWLOL]iYHLV x &RQWrLQHUHVVmRFDL[DVJHUDOP HQWHGHDoRP DVSRGHQGRVHUWDP EpP GHDOXP tQLRRX ILEUDXWLOL]DGDVSDUDDFRQGLFLRQDP HQWRHWUDQVSRUWHGHP HUFDGRULDVGHYHQGRVHU VXILFLHQWHP HQWHIRUWHVSDUDUHVLVWLUDRXVRUHSHWLWLYRHSRGHQGRVHUXWLOL]DGRVFRP R SDUWHLQWHJUDQWHGHGLIHUHQWHVP RGDLVGHWUDQVSRUWHFDP LQK}HVYDJ}HVIHUURYLiULRVRX QDYLRV x 8 /' Unit Load DevicesVmRHTXLSDP HQWRVGHXQLWL]DomRGHFDUJDVDpUHDVRXVHMD VmRRVSDOHWHVHFRQWrLQHUHVXWLOL]DGRVQRWUDQVSRUWHDpUHRSRGHQGRWHUIRUP DWRVH WDP DQKRVGLIHUHQWHVGDTXHOHVXWLOL]DGRVQRWUDQVSRUWHWHUUHVWUHHP DUtWLP R $ )LJXUDLOXVWUDDOJXQVP RGHORVGHVWHVGLVSRVLWLYRVGHXQLWL]DomRGHFDUJD )LJXUD' LVSRVLWLYRVGHXQLWL]DomRGHFDUJD QDVHTrQFLDslingbig-bagSDOHWHFRQWrLQHUH8 /' 9 $ 1 7$ * (1 6(' (69 $ 1 7$ * (1 6' $ 8 1 ,7,=$ d 2 ' (& $ 5 * $ $ XWLOL]DomRGHGLVSRVLWLYRVGHXQLWL]DomRGHFDUJDSRVVXLVXDVYDQWDJHQVH GHVYDQWDJHQV(VWDVVmRDSUHVHQWDGDVDVHJXLU0 ' ,&1 2 9 2 0 ,/Ç1 ,2 9 DQWDJHQV x 5HGXomRGHSHUGDVURXERVHDYDULDVGDFDUJD x 5HGXomRGHGHVSHVDVFRP URWXODJHP HP DUFDomRGDVFDUJDVSRLVQmRpQHFHVViULR UHDOL]DUDVRSHUDo}HVSDUDFDGDLWHP x 5HGXomRGHWD[DVGHHVWLYDFRQIHUrQFLDHFRQVHUWRGDFDUJDQRVORFDLVGHHP EDUTXHH GHVHP EDUTXH x 5HGXomRGHGHVSHVDVFRP XWLOL]DomRGHP mRGHREUDSDUDP RYLP HQWDomRGDFDUJDQDV GHSHQGrQFLDVGDHP SUHVDH[SRUWDGRUD x 5HGXomRGHWD[DVFRP VHUYLoRVGHSURILVVLRQDLVDXW{QRP RVFDSDWD]LDQRVORFDLVGH HP EDUTXHHGHVHP EDUTXH x $ XP HQWRGDUDSLGH]QDVRSHUDo}HVGHFDUUHJDP HQWRHGHVFDUUHJDP HQWRGHYHtFXORVH HP EDUFDo}HVSHUP LWLQGRHP FRQVHTrQFLDRDXP HQWRGDURWDWLYLGDGHGRVP HVP RV x $ XP HQWRGDFDSDFLGDGHGDVLQVWDODo}HVGHDUP D]HQDJHP TXDQGRpSRVVtYHOHP SLOKDURV GLVSRVLWLYRVGHXQLWL]DomR x 3RVVLELOLGDGHGHGHVFRQWRVHIUDQTXLDVFRQFHGLGRVVREUHRYDORUGRIUHWHEiVLFR x 3RVVLELOLGDGHGHDUP D]HQDJHP GDFDUJDHP iUHDVGHVFREHUWDVQRFDVRGRVFRQWrLQHUHV x 3RVVLELOLGDGH GH RSHUDo}HV GH FDUUHJDP HQWR H GHVFDUUHJDP HQWR GH YHtFXORV H HP EDUFDo}HVVREFRQGLo}HVFOLP iWLFDVDGYHUVDVQRFDVRGRVFRQWrLQHUHV x 3RVVLELOLGDGHGHDSOLFDomRGRFRQFHLWRGH³VLVWHP DJOREDOGHWUDQVSRUWHV´QRTXDOD FDUJDVHP RYLP HQWDQDIRUP DXQLWL]DGDDRORQJRGHWRGDDFDGHLD ' HVYDQWDJHQV x (VSDoRVSHUGLGRVGHQWURGDXQLGDGHGHFDUJD x 1 HFHVVLGDGHGHLQYHVWLP HQWRVQDDTXLVLomRGHGLVSRVLWLYRVGHXQLWL]DomRDFHVVyULRV SDUDDIL[DomRGDFDUJDHHTXLSDP HQWRVSDUDDP RYLP HQWDomRGDXQLGDGHGHFDUJDQRV ORFDLVGHHP EDUTXHHGHVHP EDUTXHHHYHQWXDOP HQWHQRVWHUP LQDLVLQWHUP HGLiULRVGH WUDQVIHUrQFLDHQWUHGLIHUHQWHVP RGDLVGHWUDQVSRUWH x 1 HFHVVLGDGHHYHQWXDOP HQWHGHP RGLILFDo}HVQRVlayoutsGDVLQVWDODo}HVGRVORFDLVGH HP EDUTXHHGHVHP EDUTXHHGRVWHUP LQDLVLQWHUP HGLiULRV x $ XP HQWRGRYDORUGRIUHWHHP VLWXDo}HVHP TXHDWDUDGRGLVSRVLWLYRGHXQLWL]DomRp LQFRUSRUDGDQDSHVDJHP WRWDOGHWUDQVSRUWH x 7UDQVSRUWHGRGLVSRVLWLYRGHXQLWL]DomRYD]LRSDUDRORFDORQGHVHID]RFDUUHJDP HQWR GRP HVP R x ' HVSHVDVFRP UHSDURVUHSRVLomRHUHWRUQRGRVGLVSRVLWLYRVGHXQLWL]DomR x 7D[DVGHVREUHHVWDGLDdemurrageSHORXVRGRGLVSRVLWLYRGHXQLWL]DomRTXDQGRHVWH ILFDSRUXP SHUtRGRDOpP GRSUD]ROLYUHQDVGHSHQGrQFLDVGDHP SUHVDH[SRUWDGRUD ' HQWUHDVMXVWLILFDWLYDVWpFQLFDVHHFRQ{P LFDVDIDYRUGDXQLWL]DomRGHFDUJD WDOYH]DSULQFLSDOVHMDP RVJDQKRVGHSURGXWLYLGDGHSRUHTXLSDP HQWRKRUDQDVRSHUDo}HVGH FDUUHJDP HQWRHGHVFDUUHJDP HQWR6HJXQGRP DWpULDSXEOLFDGDQREROHWLP GD&DUWHLUDGH &RP pUFLR([WHULRU&DFH[HWUDQVFULWDQRFDGHUQRVHP DQDO0 DULQKD0 HUFDQWHHP 7RGRR 0 XQGRGRMRUQDO2 (VWDGRGH6mR3DXORQDHGLomRGHGHMDQHLURGH1 2 9 2 0 ,/Ç1 ,2 QRWUDQVERUGRFDLVQDYLRRVJDQKRVGHSURGXWLYLGDGHFRP FDUJDJHUDOVROWD QmRXQLWL]DGDVmRGHDWRQHODGDVSRUHTXLSDP HQWRKRUDHQTXDQWRTXHFRP FDUJDJHUDO SDOHWL]DGDVmRGHWRQHODGDVSRUHTXLSDP HQWRKRUDHFRP FDUJDJHUDOFRQWHLQHUL]DGDVmRGH WRQHODGDVSRUHTXLSDP HQWRKRUDHP WHUP LQDLVFRQYHQFLRQDLVHGHWRQHODGDVSRU HTXLSDP HQWRKRUDHP WHUP LQDLVHVSHFLDOL]DGRV(VWHVQ~P HURVMXQWDP HQWHFRP DH[SHULrQFLD GHHP SUHVDVTXHDGRWDUDP DXQLWL]DomRGHFDUJDLQGLFDP TXHHVWDWHQGHSURJUHVVLYDP HQWHD GHL[DUGHVHUXP LQVWUXP HQWRSUHIHUHQFLDOQRWUDQVSRUWHGHFDUJDJHUDOSDUDVHQRFRQVWLWXLU QRFRQWH[WREiVLFRHP TXHVHGHYHSURFHVVDURWUDQVSRUWHGHP HUFDGRULDVQRVFRP pUFLRV QDFLRQDOHLQWHUQDFLRQDO 35 2 %/(0 $ 6' (& 2 5 7((( 0 3$ & 2 7$ 0 (1 72 2 VSUREOHP DVGHFRUWHHHP SDFRWDP HQWRSRGHP VHUGLYLGLGRVJHQHULFDP HQWH HP problemas de corteRVTXDLVFRQVLVWHP HP FRUWDUXQLGDGHVP DLRUHVHP XQLGDGHVP HQRUHV HHP problemas de empacotamentoRVTXDLVFRQVLVWHP HP HP SDFRWDUXQLGDGHVP HQRUHV GHQWURGHXQLGDGHVP DLRUHV$ VXQLGDGHVP DLRUHVVmRDTXLGHQRP LQDGDVobjetosHDV XQLGDGHVP HQRUHVVmRDTXLGHQRP LQDGDVitens$ P ERVRVSUREOHP DVVHSURS}HP DRWLP L]DU FHUWRVREMHWLYRV([HP SORVGHDSOLFDo}HVGHSUREOHP DVGHFRUWHDSDUHFHP QRFRUWHGHEDUUDV GHDoRERELQDVGHSDSHOFDL[DVGHSDSHOmRFKDSDVP HWiOLFDVRXGHP DGHLUDURORVGHWHFLGR SODFDVGHYLGURHWF([HP SORVGHDSOLFDomRGRSUREOHP DGHHP SDFRWDP HQWRDSDUHFHP QR FDUUHJDP HQWRGHFDL[DVVREUHSDOHWHVRXGHQWURGHFRQWrLQHUHVHFDP LQK}HV (P ERUDQDSUiWLFDVHMDP GRLVSUREOHP DVP XLWRGLVWLQWRVGRSRQWRGHYLVWD P DWHP iWLFRQmRLP SRUWDVHRSDGUmRREWLGRSDUDXP GDGRFRQMXQWRGHXQLGDGHVpLQWHUSUHWDGR FRP RVHQGRXP SDGUmRGHFRUWHRXXP SDGUmRGHHP SDFRWDP HQWRRTXHLP SOLFDQDH[LVWrQFLD GHXP D³GXDOLGDGH´HQWUHRVSUREOHP DVGHFRUWHHRVSUREOHP DVGHHP SDFRWDP HQWRLVWRpQD GXDOLGDGHHQWUHFRUWDUP DWHULDOHP SDFRWDUHVSDoRHFRUWDUHVSDoRHP SDFRWDUP DWHULDO$ SDUWLU GRLQtFLRGRVDQRVDOpP GHVWDVGXDVFODVVHVGHSUREOHP DVRXWURVSUREOHP DVFRUUHODWRVRX LQWHJUDGRVFRP HVWUXWXUDOyJLFDVLP LODUSDVVDUDP DVHUWUDWDGRVFRP RSUREOHP DVGHFRUWHH HP SDFRWDP HQWR /LYURVUHODFLRQDGRVDRWHP DFRUWHHHP SDFRWDP HQWRSRGHP VHUHQFRQWUDGRVHP %URZ Q0 DUWHOORH7RWK' \FNKRIIH)LQNH' \FNKRIIet al $ UWLJRVHHGLo}HVHVSHFLDLVGHUHYLVWDVUHODFLRQDGRVDRWHP DFRUWHHHP SDFRWDP HQWRFRQWHQGR UHYLV}HVOHYDQWDP HQWRVWLSRORJLDVHP pWRGRVGHVROXomRSRGHP VHUHQFRQWUDGRVHP * ROGHQ + LQ[P DQ' RZ VODQG' \FNKRIIet al' \FNKRII + DHVVOHUH6Z HHQH\' RZ VODQGH' RZ VODQG0 RUDELWRH$ UHQDOHV5DP 6Z HHQH\H3DWHUQRVWHU&KHQJet al0 DUWHOORDE%LVFKRII H: lVFKHU&RIIP DQet al$ UHQDOHVet al+ LILE/RGLet al D: DQJH: lVFKHU2 OLYHLUDH: lVFKHU: lVFKHUet al : lVFKHUet alEDVHDGRVQDVLGpLDVRULJLQDLVGH' \FNKRII DSUHVHQWDP XP DQRYDWLSRORJLDSDUDRUJDQL]DUHFDWHJRUL]DUDOLWHUDWXUDGH3&(¶V2 VDXWRUHV GLVWLQJXHP FLQFRFULWpULRVSDUDGHILQLURVWLSRVrefinadosGH3&(¶V2 VFULWpULRVforma de alocação das unidadesHvariedade de itensGHILQHP RVWLSRVbásicosGH3&(¶V&RP UHODomRjforma de alocação das unidadesRVDXWRUHVGLVWLQJXHP HQWUHmaximização (do valor) das saídasHP TXHXP VXEFRQMXQWRGHWRGRVRVLWHQVGLVSRQtYHLVGHYHVHUVHOHFLRQDGR GHP RGRDVHUDORFDGRHP WRGRVRVREMHWRVHminimização (do valor) das entradasHP TXH XP VXEFRQMXQWRGHWRGRVRVREMHWRVGLVSRQtYHLVGHYHVHUVHOHFLRQDGRGHP RGRTXHWRGRVRV LWHQVVHMDP DORFDGRV(VWHVGRLVFULWpULRVMXQWDP HQWHFRP RFULWpULRvariedade de objetos GHILQHP RVWLSRVintermediáriosGH3&(¶VTXHHVWmRLOXVWUDGRVQDV)LJXUDVH UHVSHFWLYDP HQWHGHDFRUGRFRP RFULWpULRforma de alocação das unidades$ VVLJODV XWLOL]DGDVSDUDGHVLJQDURVWLSRVintermediáriosVmRH[SOLFLWDGDVQDVHomRVHJXLQWHQR FRQWH[WRGRVSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHV )LJXUD5HVXP RGRVWLSRVLQWHUP HGLiULRVGH3&(¶VP D[LP L]DomRGDVVDtGDV )RQWHDGDSWDGRGH: lVFKHUet al )LJXUD5HVXP RGRVWLSRVLQWHUP HGLiULRVGH3&(¶VP LQLP L]DomRGDVHQWUDGDV )RQWHDGDSWDGRGH: lVFKHUet al 1 RGHFRUUHUGRWH[WRHP P XLWDVRFDVL}HVpXWLOL]DGRRWHUP RtipoSDUDDJUXSDU XQLGDGHVLWHQVRXREMHWRVTXHSRVVXHP FDUDFWHUtVWLFDVFRP XQVFRP RSRUH[HP SORVXDV GLP HQV}HV1 DV)LJXUDVHXQLGDGHViguaisVHUHIHUHP jTXHODVTXHSHUWHQFHP DXP P HVP R H~QLFRWLSRHXQLGDGHVdiferentesVHUHIHUHP jTXHODVTXHSHUWHQFHP DWLSRVGLIHUHQWHV(P SDUWLFXODUXQLGDGHVpouco diferentesVHUHIHUHP jTXHODVTXHSHUWHQFHP DSRXFRVWLSRV GLIHUHQWHVP DVHP TXHKiP XLWDVXQLGDGHVLJXDLVGHFDGDWLSRHXQLGDGHVmuito diferentesVH UHIHUHP jTXHODVTXHSHUWHQFHP DP XLWRVWLSRVGLIHUHQWHVP DVHP TXHKiSRXFDVXQLGDGHV LJXDLVGHFDGDWLSR )LQDOP HQWHRVWLSRVrefinadosGH3&(¶VVmRGHILQLGRVDFUHVFHQWDQGRVHDRV WUrVFULWpULRVDQWHULRUHVRVFULWpULRVdimensãoHforma dos itenV2 V3&(¶VSRGHP WHU XP DGXDVRXWUrVGLP HQV}HVHWUDWDULWHQVFRP IRUP DVUHJXODUHVUHWkQJXORVFDL[DVFtUFXORV HVIHUDVFLOLQGURVHWFRXLUUHJXODUHVJHUDOP HQWHQmRFRQYH[DVHDVVLP pWULFDV3DUDRVFDVRV QmRFRQWHP SODGRVSHORVFLQFRFULWpULRVDQWHULRUHVDWLSRORJLDGH: lVFKHUet alRV GHILQHFRP RvariantesHLQFOXHP SRUH[HP SOR3&(¶VFRP GLP HQVmRP DLRUTXHWUrVREMHWRV QmRUHWDQJXODUHVHRXQmRKRP RJrQHRVFRP GHIHLWRVSRUH[HP SORSDGU}HVQmRRUWRJRQDLV HRXTXHFRP ELQHP LWHQVUHJXODUHVHLUUHJXODUHV 35 2 %/(0 $ 6' ( & $ 5 5 (* $ 0 (1 72 ' (& 2 1 7Ç,1 (5 (6 2 REMHWRGHHVWXGRGHVWHWUDEDOKRVmRRVproblemas de carregamento de contêineres TXH VmR FDVRV SDUWLFXODUHV GR SUREOHP D GH HP SDFRWDP HQWR (VWHV VmR UHIHUHQFLDGRVQDOLWHUDWXUDGHFRUWHHHP SDFRWDP HQWRFRP XP DJUDQGHGLYHUVLGDGHGHQRP HV $ OJXQVQRP HVHP LQJOrVP DLVFRP XP HQWHXWLOL]DGRVVmRcontainer loading problem container packing problemthree-dimensional cargo-loading problemthree-dimensional packing problemthree-dimensional knapsack packing problemthree-dimensional binpacking problemthree-dimensional strip packing problemsingle container loading problem multiple container loading problemthree-dimensional pallet loading problemmulti-pallet loading problemmulti-pallet packing problemthree-dimensional palletization problem three-dimensional cutting problemHWF 1 HVWHVSUREOHP DVJHQHULFDP HQWHFDL[DVUHWDQJXODUHVGHYHP VHUHP SDFRWDGDV RUWRJRQDOP HQWHGHQWURGHXP RXP DLVFRQWrLQHUHV1 RHQWDQWRDSyVHVWDRSHUDomR JHUDOP HQWHQHP WRGRVRVHVSDoRVGLVSRQtYHLVFRQVHJXHP VHUSUHHQFKLGRVJHUDQGRHVSDoRV RFLRVRVTXHVmRFRQVHTHQWHP HQWHWUDQVSRUWDGRVMXQWDP HQWHFRP DVFDL[DV6XUJHHQWmRD QHFHVVLGDGHGHSODQHMDURHP SDFRWDP HQWRGDVFDL[DVGHP RGRDXWLOL]DUGDP HOKRUP DQHLUDRV UHFXUVRVHVSDoRVRXFRQWrLQHUHVGLVSRQtYHLV&RP EDVHQDWLSRORJLDGH: lVFKHUet al pSRVVtYHOGLYLGLUHVWHVSUREOHP DVHQWUHTXDVHWRGRVRVTXDWRU]HWLSRVLQWHUP HGLiULRV GHSUREOHP DVDSUHVHQWDGRVQDV)LJXUDVHUHVVDOWDQGRVHTXHVmRSUREOHP DVFRP WUrV GLP HQV}HV' HDVIRUP DVGRVLWHQVVmRUHWDQJXODUHV5 7LSRVGHSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVP D[LP L]DomRGDVVDtGDV ' 5 ,,33Identical Item Packing Problem8 P VXEFRQMXQWRGHFDL[DViguaisGHYHVHU VHOHFLRQDGRSDUDVHUFDUUHJDGRHP XP únicoFRQWrLQHUGHP RGRDP D[LP L]DURYROXP HRX YDORUWRWDOGHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHU(VWHSUREOHP DIRLHVWXGDGRSRU H[HP SORSRU+ DQet al* HRUJH/LXH+ VLDXH/LQVet al ' 5 6/2 33Single Large Object Placement Problem8 P VXEFRQMXQWRGHFDL[DVpouco diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRHP XP únicoFRQWrLQHUGHP RGRD P D[LP L]DURYROXP HRXYDORUWRWDOGHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHU(VWH SUREOHP DIRLHVWXGDGRSRUH[HP SORSRU0 RUDELWRH$ UHQDOHV1 JRLet al %LVFKRIIH5DWFOLIID%LVFKRIIet al$ EGRXH$ UJKDYDQL; XHH /DL%RUWIHOGWH* HKULQJ&KLHQH: X* HKULQJH%RUWIHOGW 5DWFOLIIH%LVFKRII' DYLHVH%LVFKRII%RUWIHOGW(OH\+ LIL D%RUWIHOGWet al/LP et al&KLHQH' HQJ0 DFNet al0 RXUDH2 OLYHLUD%LVFKRII$ UDXMRH$ UP HQWDQR: DQJet al&KULVWHQVHQH5RXV¡HH+ XDQJH+ HE ' 5 0 ,/2 33Multiple Identical Large Object Placement Problem8 P VXEFRQMXQWRGH FDL[DVpouco diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRHP YiULRVFRQWrLQHUHViguais GHP RGRDP D[LP L]DURYROXP HRXYDORUJOREDOGHFDL[DVHP SDFRWDGDVGHQWURGRV FRQWrLQHUHV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU%RUWIHOGW ' 5 0 + /2 33 Multiple Heterogeneous Large Object Placement Problem 8 P VXEFRQMXQWRGHFDL[DVpouco diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRHP YiULRV FRQWrLQHUHVdiferentesGHP RGRDP D[LP L]DURYROXP HRXYDORUJOREDOGHFDL[DV HP SDFRWDGDVGHQWURGRVFRQWrLQHUHV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU(OH\ ' 5 6. 3Single Knapsack Problem8 P VXEFRQMXQWRGHFDL[DVmuito diferentesGHYHVHU VHOHFLRQDGRSDUDVHUFDUUHJDGRHP XP únicoFRQWrLQHUGHP RGRDP D[LP L]DURYROXP HRX YDORUWRWDOGHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHU(VWHSUREOHP DIRLHVWXGDGRSRU H[HP SORSRU* HRUJHH5RELQVRQ%LVFKRIIH0 DUULRWW* HKULQJet al + DHVVOHUH7DOERW* HKULQJH%RUWIHOGW3DGEHUJ%RUWIHOGWH * HKULQJ+ HH&KD3LVLQJHU&HFLOLR&HFLOLRH0 RUDELWR /LP et al0 RXUDH2 OLYHLUD< HXQJH7DQJ(JHEODGH3LVLQJHU H+ XDQJH+ HD ' 5 0 ,. 3Multiple Identical Knapsack Problem8 P VXEFRQMXQWRGHFDL[DVmuito diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRHP YiULRVFRQWrLQHUHViguaisGHP RGRD P D[LP L]DURYROXP HRXYDORUJOREDOGHFDL[DVHP SDFRWDGDVGHQWURGRVFRQWrLQHUHV(VWH SUREOHP DIRLHVWXGDGRSRUH[HP SORSRU5DLGOH. RG\GHN ' 5 0 + . 3Multiple Heterogeneous Knapsack Problem8 P VXEFRQMXQWRGHFDL[DV muito diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRHP YiULRVFRQWrLQHUHVdiferentesGH P RGRDP D[LP L]DURYROXP HRXYDORUJOREDOGHFDL[DVHP SDFRWDGDVGHQWURGRVFRQWrLQHUHV 1 mRIRUDP HQFRQWUDGRVWUDEDOKRVQDOLWHUDWXUDTXHWUDWDVVHP HVVHSUREOHP DHVSHFtILFR 7LSRVGHSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVP LQLP L]DomRGDVHQWUDGDV ' 5 666& 63Single Stock Size Cutting Stock Problem8 P VXEFRQMXQWRGHFRQWrLQHUHV iguaisGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVpouco diferentesGHP RGRD P LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDUWRGDVDV FDL[DV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU%LVFKRIIH5DWFOLIIE6FKHLWKDXHU et al%RUWIHOGW7HUQRet al(OH\H* HQGUHDXet al ' 5 0 66& 63Multiple Stock Size Cutting Stock Problem8 P VXEFRQMXQWRGHFRQWrLQHUHV pouco diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVpouco diferentesGH P RGRDP LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDU WRGDVDVFDL[DV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU%RUWIHOGWH(OH\ ' 5 5 & 63Residual Cutting Stock Problem8 P VXEFRQMXQWRGHFRQWrLQHUHVmuito diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVpouco diferentesGHP RGRD P LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDUWRGDVDV FDL[DV1 mRIRUDP HQFRQWUDGRVWUDEDOKRVQDOLWHUDWXUDTXHWUDWDVVHP HVVHSUREOHP DHVSHFtILFR ' 5 6%6%33Single Bin Size Bin Packing Problem8 P VXEFRQMXQWRGHFRQWrLQHUHV iguaisGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVmuito diferentesGHP RGRD P LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDUWRGDVDV FDL[DV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU0 DUWHOORet al/RGLet al E)DURHet al-LQet al0 L\D]DZ DH: DNDED\DVKL6LOYDH 6RP D6LOYDet alH%RVFKHWWL ' 5 0 %6%33Multiple Bin Size Bin Packing Problem8 P VXEFRQMXQWRGHFRQWrLQHUHV pouco diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVmuito diferentesGH P RGRDP LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDU WRGDVDVFDL[DV1 mRIRUDP HQFRQWUDGRVWUDEDOKRVQDOLWHUDWXUDTXHWUDWDVVHP HVVHSUREOHP D HVSHFtILFR ' 5 5 %33Residual Bin Packing Problem8 P VXEFRQMXQWRGHFRQWrLQHUHVmuito diferentesGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP FDL[DVmuito diferentesGHP RGRD P LQLP L]DURQ~P HURRXFXVWRJOREDOGHFRQWrLQHUHVQHFHVViULRVSDUDHP SDFRWDUWRGDVDV FDL[DV(VWHSUREOHP DIRLHVWXGDGRSRUH[HP SORSRU&KHQet al ' 5 2 ' 3Open Dimension Problem8 P únicoFRQWrLQHUFRP GXDVGLP HQV}HVIL[DVSRU H[HP SORDODUJXUDHDDOWXUDHXP DGLP HQVmRYDULiYHOSRUH[HP SORRFRP SULP HQWRGHYH VHUFDUUHJDGRFRP FDL[DVdiferentesGHP RGRDP LQLP L]DUDGLP HQVmRYDULiYHOR FRP SULP HQWRQHFHVViULDSDUDHP SDFRWDUWRGDVDVFDL[DV(VWHSUREOHP DIRLHVWXGDGRSRU H[HP SORSRU&RUFRUDQH: DLQZ ULJKW0 L\D]DZ DH: DNDED\DVKL/DLet al)DLQDH%RUWIHOGWH0 DFN 1 HVWHWUDEDOKRDOJXP DVGDVIRUP XODo}HVSURSRVWDVVmRSDVVtYHLVGHVHUHP XWLOL]DGDVFRP XP DRXWUDFODVVHGHSUREOHP DVGDOLWHUDWXUDGHFRUWHHHP SDFRWDP HQWR WDP EpP XP FDVRSDUWLFXODUGRSUREOHP DGHHP SDFRWDP HQWRTXHVmRRVSUREOHP DVGH FDUUHJDP HQWRGHSDOHWHVWULGLP HQVLRQDLV+ RGJVRQGLYLGHRSUREOHP DGHFDUUHJDU FDL[DVVREUHSDOHWHVHP GXDVYDULDQWHVR3UREOHP DGH&DUUHJDP HQWRGH3DOHWHVGR3URGXWRU Manufacturer´s Pallet Loading ProblemHR3UREOHP DGH&DUUHJDP HQWRGH3DOHWHVGR ' LVWULEXLGRUDistributor’s Pallet Loading Problem0 2 5$ /(6)$ 5$ * 2 2 /,9 (,5$ 52 &+ $ $ GLIHUHQoDHQWUHHOHVpTXHQRSULP HLURKiDSHQDVXP WLSRGHFDL[DLVWRpWRGDVDVFDL[DVVmRLJXDLVHQTXDQWRQRVHJXQGRKiP DLVGHXP WLSR $ P ERVRVSUREOHP DVSRGHP VHUUHVROYLGRVGHP DQHLUDELGLP HQVLRQDORXWULGLP HQVLRQDO HP ERUDDSULP HLUDVHMDDP DLVFRP XP HQWHHQFRQWUDGDQDSUiWLFD$ GLIHUHQoDHQWUHHODVpTXH QRFDVRELGLP HQVLRQDORSDGUmRGHHP SDFRWDP HQWRpFRQVWUXtGRHP FDP DGDVKRUL]RQWDLV VREUHRSDOHWHHQTXDQWRQRFDVRWULGLP HQVLRQDORSDGUmRGHHP SDFRWDP HQWRSRGHVHU JHQpULFR1 HVWH~OWLP RFDVRRVSUREOHP DVSRGHP VHUYLVWRVUHVSHFWLYDP HQWHFRP RVHQGR GRVWLSRV' 5 ,,33H' 5 6/2 330 2 5$ %,72 $ 5(1 $ /(6%,6&+ 2 )) 5$ 7&/,))D & 2 1 6,' (5 $ d ® (6 35 È 7,& $ 6 12 & $ 5 5 (* $ 0 (1 72 ' ( & 2 1 7Ç,1 (5 (6 2 VSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVFRP RWRGRVRVSUREOHP DVGH FRUWHHHP SDFRWDP HQWRGHYHP VDWLVID]HUGXDVFRQVLGHUDo}HVEiVLFDVLDVFDL[DVGHYHP VHU HP SDFRWDGDVFRP SOHWDP HQWHGHQWURGRVFRQWrLQHUHVLLDVFDL[DVHP SDFRWDGDVQmRGHYHP VH VREUHSRULVWRpQmRGHYHP RFXSDUXP P HVP ROXJDUGHQWURGRFRQWrLQHU2 VSULP HLURV WUDEDOKRVDWUDWDUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVWLQKDP FRP RP HWDFRQWHP SODU HVWDVGXDVFRQVLGHUDo}HV 1 RHQWDQWRFRP RDYDQoRGDVSHVTXLVDVRXWUDVFRQVLGHUDo}HVH[LJrQFLDV SUiWLFDVWDP EpP SDVVDUDP DWHUXP DSHORP DLRUDRWUDWDUSUREOHP DVGHFDUUHJDP HQWRGH FRQWrLQHUHV%LVFKRIIH5DWFOLIIDDSUHVHQWDP GR]HH[LJrQFLDVSUiWLFDVTXHSRGHP VHU OHYDGDVHP FRQVLGHUDomRTXDQGRVHGHVHMDP RGHODUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHV P DLVUHDOLVWDV$ 7DEHODDSUHVHQWDHVWDVGR]HFRQVLGHUDo}HVSUiWLFDVDFRP SDQKDGDVGHXP D EUHYHGHVFULomRHGHDOJXQVH[HP SORVGHWUDEDOKRVTXHWUDWDP HVWDVFRQVLGHUDo}HVLP SOtFLWDRX H[SOtFLWDP HQWH1 mRIRUDP HQFRQWUDGRVWUDEDOKRVTXHWUDWDVVHP SUREOHP DVGHFDUUHJDP HQWR GHFRQWrLQHUHVFRP FRQVLGHUDo}HVGHP DQXVHLRSULRULGDGHVHFRP SOH[LGDGHGRSDGUmRGH FDUUHJDP HQWR 7DEHOD&RQVLGHUDo}HVSUiWLFDVDSUHVHQWDGDVSRU%LVFKRIIH5DWFOLIID & RQVLGHUDomR ' HVFULomR 3UiWLFD $ OJXP DVFDL[DVGHYHP VHUFDUUHJDGDVGHQWURGRFRQWrLQHUFRP RULHQWDo}HVSUp 2 ULHQWDomR HVWDEHOHFLGDV 8 P Q~P HURP i[LP RGHFDL[DVSRGHVHUHP SLOKDGRXP DVVREUHDVRXWUDVRXP DLV JHQHULFDP HQWHDSUHVVmRWRWDOH[HUFLGDVREUHDIDFHVXSHULRUGHXP DGHWHUP LQDGD FDL[DQmRGHYHH[FHGHUXP OLP LWHP i[LP RSUpHVWDEHOHFLGRSDUDTXHQmRRFRUUDP (P SLOKDP HQWR DOWHUDo}HVQDVXDIRUP D([HP SORVDSDUHFHP HP 6FKHLWKDXHUet al* HKULQJH %RUWIHOGW5DWFOLIIH%LVFKRII%RUWIHOGWH* HKULQJ %LVFKRII* HQGUHDXet al/LQet al&KULVWHQVHQH5RXV¡H $ OJXP DVFDL[DVGHYLGRjVVXDVGLP HQV}HVDRVHXSHVRRXDRHTXLSDP HQWRTXH 0 DQXVHLR UHDOL]DRFDUUHJDP HQWRGHVFDUUHJDP HQWRGDFDUJDGHYHP HVWDUSRVLFLRQDGDVHP GHWHUP LQDGRVOXJDUHVGHQWURGRFRQWrLQHU $ OJXP DVFDL[DVGHYHP WHUVXDVIDFHVLQIHULRUHVVXSRUWDGDVSRUIDFHVVXSHULRUHVGH RXWUDVFDL[DVHRXVXDVIDFHVODWHUDLVDSRLDGDVQDVIDFHVODWHUDLVGHRXWUDVFDL[DV ([HP SORVDSDUHFHP HP * HKULQJet al%LVFKRIIH5DWFOLIID%LVFKRII et al6FKHLWKDXHUet al* HKULQJH%RUWIHOGW' DYLHVH (VWDELOLGDGH %LVFKRII7HUQRet al%RUWIHOGWH* HKULQJ(OH\ + HH&KD3LVLQJHU%RUWIHOGWet al6LOYDH6RP D6LOYD et al-LQet al0 DFNet al0 RXUDH2 OLYHLUD< HXQJH 7DQJ* HQGUHDXet al/LQet al$ UDXMRH$ UP HQWDQR &DL[DVFRP XP GHVWLQRFRP XP RXGHXP P HVP RWLSRGHYHP VHUSRVLFLRQDGDV $ JUXSDP HQWR SUy[LP DVGHQWURGRFRQWrLQHU([HP SORVDSDUHFHP HP %LVFKRIIH5DWFOLIID GHLWHQV 7HUQRet al(OH\,RUL &DL[DVDVHUHP HQWUHJXHVSDUDGLIHUHQWHVGHVWLQRVGHYHP VHUSRVLFLRQDGDVSUy[LP DV XP DVGDVRXWUDVGHQWURGRFRQWrLQHUHGHYHP VHUFDUUHJDGDVGHP RGRDFRQVLGHUDUR URWHLURDVHUSHUFRUULGRSHORFRQWrLQHUHDRUGHP HP TXHHODVVHUmRGHVFDUUHJDGDV 0 ~OWLSORV ([HP SORVDSDUHFHP HP %LVFKRIIH5DWFOLIID6FKHLWKDXHUet al/DLet ' HVWLQRV al7HUQRet al,RUL-LQet al0 RXUDH2 OLYHLUD $ UDXMR* HQGUHDXet al/LQet al&DP SRV&KULVWHQVHQ H5RXV¡H 6HSDUDomR &DL[DVTXHQmRSRGHP HVWDUHP FRQWDWRXP DVFRP DVRXWUDVGHYHP VHUSRVLFLRQDGDV GHLWHQV DIDVWDGDVGHQWURGRFRQWrLQHU([HP SORVDSDUHFHP HP (OH\ &DUUHJDP HQWR $ VFDL[DVFRQWHQGRWRGRVRVFRP SRQHQWHVTXH ID]HP SDUWHGHXP DP HVP DHQWLGDGH FRP SOHWRGH IXQFLRQDOSRUH[HP SORXP HTXLSDP HQWRGHYHP HVWDUSUHVHQWHVQRP HVP R JUXSRVGHLWHQV FDUUHJDP HQWR([HP SORVDSDUHFHP HP 7HUQRet al &DL[DVFRP SURGXWRVFRP GDWDGHHQWUHJDRXSUD]RGHYDOLGDGHSUy[LP RVSRU 3ULRULGDGHV H[HP SOR SRGHP WHU P DLRUHV SULRULGDGHV SDUD HVWDUHP QR FDUUHJDP HQWR HP GHWULP HQWRGHRXWUDVFDL[DVFRP P HQRUHVSULRULGDGHV &RP SOH[LGDGH &DL[DVSUHVHQWHVHP SDGU}HVGHFDUUHJDP HQWRFRP SOH[RVSRGHP GHP DQGDUHVIRUoRV GRSDGUmRGH P DLRUHVGHP DQXVHLRGHYLGRSRUH[HP SORjVOLP LWDo}HVGRHTXLSDP HQWRTXHUHDOL]D HP SDFRWDP HQWR RFDUUHJDP HQWRGHVFDUUHJDP HQWRGDFDUJD &DL[DVEDVWDQWHSHVDGDVGHYHP VHUFDUUHJDGDVGHQWURGRFRQWrLQHUVHP H[FHGHUR OLP LWHGHSHVRP i[LP RTXHRFRQWrLQHUSRGHVXSRUWDU([HP SORVDSDUHFHP HP /LP LWHGHSHVR 6FKHLWKDXHUet al* HKULQJH%RUWIHOGW7HUQRet al %RUWIHOGWH* HKULQJ,RUL* HQGUHDXet al 2 FHQWURGHJUDYLGDGHGHXP FRQWrLQHUFDUUHJDGRGHYHHVWDUORFDOL]DGRSUy[LP RGR ' LVWULEXLomRGHSHVRFHQWURJHRP pWULFRGRSODQRTXHGHILQHDEDVH([HP SORVDSDUHFHP HP * HKULQJet al GHQWURGRFRQWrLQHU* HKULQJH%RUWIHOGW' DYLHVH%LVFKRII%RUWIHOGWH* HKULQJ (OH\+ HH&KD & $ 3Ë78 /2 )2 5 0 8 /$ d ® (6(0 e72 ' 2 6' $ / ,7(5 $ 78 5 $ ,1 75 2 ' 8 d 2 1 HVWHFDStWXORSULP HLUDP HQWHpDSUHVHQWDGDXP DUHYLVmRGDVIRUP XODo}HV P DWHP iWLFDVGLVSRQtYHLVQDOLWHUDWXUDHTXHSRGHP VHUXWLOL]DGDVSDUDP RGHODUSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHV(P VHJXLGDpDSUHVHQWDGDXP DEUHYHGLVFXVVmRGHDOJXQV P pWRGRVGHVROXomRGLVSRQtYHLVQDOLWHUDWXUDSDUDVHUHVROYHUHVWHVSUREOHP DV )2 5 0 8 /$ d ® (60 $ 7(0 È 7,& $ 6 $ VHJXLUVmRUHYLVDGDVGLIHUHQWHVIRUP XODo}HVP DWHP iWLFDVWDP EpP FKDP DGDV LQGLVWLQWDP HQWHmodelos matemáticosQRGHFRUUHUGRWH[WRHQFRQWUDGDVQDOLWHUDWXUDTXH IRUDP SURSRVWDVSRUVHXVDXWRUHVSDUDP RGHODUGLUHWDP HQWHSUREOHP DVGHFDUUHJDP HQWRGH FRQWrLQHUHVRXTXHSRGHP VHUHVWHQGLGDVIDFLOP HQWHSDUDP RGHODUHVWHVSUREOHP DV6mR DSUHVHQWDGDVQDRUGHP FURQROyJLFDDVIRUP XODo}HVGH%HDVOH\7VDLet al &KHQet al+ DGMLFRQVWDQWLQRXH&KULVWRILGHVH%HDVOH\2 XWUDV IRUP XODo}HVTXHP RGHODP GLUHWDP HQWHRXTXHSRGHP VHUHVWHQGLGDVIDFLOP HQWHSDUDP RGHODU SUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVSRGHP VHUHQFRQWUDGDVHP 6FKHLWKDXHUH7HUQR 3DGEHUJH0 DUWLQVeLP SRUWDQWHGHVWDFDUa prioriTXHLDQRWDomR XWLOL]DGDQHVWHWH[WRSDUDFDGDIRUP XODomRQmRQHFHVVDULDP HQWHFRLQFLGHFRP DQRWDomR RULJLQDOXWLOL]DGDSHORVUHVSHFWLYRVDXWRUHVLLQDVIRUP XODo}HVGH%HDVOH\ + DGMLFRQVWDQWLQRXH&KULVWRILGHVH%HDVOH\VmRGHILQLGRVtiposSDUDDVFDL[DV P DVTXHSRUVLP SOLFLGDGHHVWDVVmRWUDWDGDVVLP SOHVP HQWHSRUFDL[DVLLLDVH[SUHVV}HV WDQWRQHVWHFDStWXORFRP RQRVHJXLQWHSRUVLP SOLFLGDGHVmRQXP HUDGDVVHTHQFLDOP HQWH &RP UHODomRDHVWH~OWLP RSRQWRFRP RP XLWDVH[SUHVV}HVVmRHYHQWXDOP HQWHUHSHWLGDVQDV GLIHUHQWHVIRUP XODo}HVDVH[SUHVV}HVTXHDSDUHFHP SHODSULP HLUDYH]VmRGHVWDFDGDVHP QHJULWRGDVGHP DLV,VWRpFDGDH[SUHVVmRQmRGHVWDFDGDSRVVXLSHORP HQRVXP DRXWUD H[SUHVVmRLGrQWLFDFRP XP DRXWUDQXP HUDomR $ OpP GLVVRGHP RGRDIDFLOLWDUDOHLWXUDGRVP RGHORVDRORQJRGRWH[WRD )LJXUDLOXVWUDXP FRQMXQWRGHSRQWRVGHUHIHUrQFLDTXHVmRFRP XQVDWRGDVDVIRUP XODo}HV DSUHVHQWDGDVQHVWHFDStWXORHQRVHJXLQWH )LJXUD3RQWRVGHUHIHUrQFLDSDUDFDL[DVHFRQWrLQHUHV )2 5 0 8 /$ d 2 ' (% ($ 6/(< %HDVOH\DSUHVHQWDXP P RGHORGHSURJUDP DomROLQHDULQWHLUDSDUDR SUREOHP DGHFRUWHQmRJXLOKRWLQDGRELGLP HQVLRQDOHP TXHSHoDVUHWDQJXODUHVGHGLIHUHQWHV GLP HQV}HVGHYHP VHUFRUWDGDVDSDUWLUGHXP ~QLFRUHWkQJXORJUDQGHFRP RREMHWLYRGH P D[LP L]DURYDORUWRWDOGDVSHoDVFRUWDGDV2 DXWRUGHVHQYROYHXP SURFHGLP HQWRH[DWRGH EXVFDHP iUYRUHSDUDUHVROYHURSUREOHP D2 DOJRULWP ROLP LWDRWDP DQKRGDEXVFDHP iUYRUH XWLOL]DQGRXP OLP LWDQWHVXSHULRUREWLGRFRP DUHOD[DomRODJUDQJLDQDGRP RGHOR2 SURFHGLP HQWRGHRWLP L]DomRGRVXEJUDGLHQWHpXWLOL]DGRSDUDRWLP L]DUROLP LWDQWHVXSHULRU REWLGRFRP DUHOD[DomRODJUDQJLDQDHWHVWHVGHUHGXomRGRSUREOHP DGHULYDGRVWDQWRGR SUREOHP DRULJLQDOTXDQWRGRSUREOHP DUHOD[DGRVmRXWLOL]DGRVSDUDUHGX]LURWDP DQKRGRV SUREOHP DV2 DXWRUDSUHVHQWDUHVXOWDGRVFRP SXWDFLRQDLVSDUDDVVROXo}HVyWLP DVGHGR]H SUREOHP DVWHVWHVGLIHUHQWHVFRP RP DLRUSUREOHP DUHVROYLGRWHQGRGH]WLSRVGHLWHQV GLVSRQtYHLV2 VtQGLFHVSDUkP HWURVHYDULiYHLVXWLOL]DGRVQHVWDIRUP XODomRVmRDSUHVHQWDGRVD VHJXLU ËQGLFHV i tQGLFHSDUDRVtiposGHFDL[DV ps tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Rx qt tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Ry r u tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Rz 3DUkP HWURV m Q~P HURWRWDOGHtiposGHFDL[DVGLVSRQtYHLV vi YDORUGDFDL[Di Pi Q~P HURP tQLP RGHUpSOLFDVGDFDL[Di TXHGHYHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHU Qi Q~P HURP i[LP RGHUpSOLFDVGDFDL[Di TXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHU li wi hi FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGDFDL[Di LW H FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGRFRQWrLQHU aipqrstu IXQomRELQiULDTXHpLJXDODVHDFDL[Di TXDQGRHP SDFRWDGDFRP VHXFDQWRLQIHULRU IURQWDOHVTXHUGRQDSRVLomRpqr QmRSHUP LWHTXHRXWUDFDL[DTXDOTXHURFXSHDSRVLomR s t u GHQWURGHODFDVRFRQWUiULRHODpLJXDOD 1 RWHTXHDIXQomRaipqrstu QmRpXP DYDULiYHOGHGHFLVmRGRP RGHORHSRGHVHU FRP SXWDGDa prioriLVWRpDQWHVGDUHVROXomRGRP RGHORGDVHJXLQWHP DQHLUD aipqrstu VH d p d s d p li d L ° d q d t d q w d W H ° i ® ° d r d u d r hi d H ° ¯FDVRFRQWUiULR 2 XVHMDVHaipqrstu VLJQLILFDTXHDSRVLomRs t u HVWiRFXSDGDSHODFDL[D i FRORFDGDFRP VHXFDQWRLQIHULRUIURQWDOHVTXHUGRQDSRVLomRpqr GRFRQWrLQHUYHMD )LJXUD&DVRFRQWUiULRVHaipqrstu VLJQLILFDTXHHVWDSRVLomRHVWiIRUDGDFDL[Di 9 DULiYHOGHGHFLVmR xipqr YDULiYHOELQiULDTXHpLJXDODVHDFDL[Di pHP SDFRWDGDFRP VHXFDQWRLQIHULRUIURQWDO HVTXHUGR QD SRVLomR pqr WDO TXH i m d p d L li d q d W wi H d r d H hi FDVRFRQWUiULRHODpLJXDOD )LJXUD/RFDOL]DomRGHXP DFDL[DGHQWURGRFRQWrLQHU 2 SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP RULHQWDomRIL[DGHQWURGHXP ~QLFR FRQWrLQHUSRGHVHUIRUP XODGRFRP RXP DH[WHQVmRGLUHWDGRP RGHORGHSURJUDP DomROLQHDU LQWHLUDSURSRVWRHP %HDVOH\SDUDRSUREOHP DGHFRUWHQmRJXLOKRWLQDGR ELGLP HQVLRQDO1 RWHTXHQHVWDIRUP XODomRKiUHVWULo}HVTXDQWRDRQ~P HURGHFDL[DVGHFDGD WLSRTXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHULVWRpRSUREOHP DprestritoGRSRQWRGH YLVWDGDGLVSRQLELOLGDGHGHcaixas 0 RGHOR m L li W wi H hi P D[ ¦ ¦ ¦ ¦ v x i ipqr s L t W u H i m i p q r 6XMHLWRD m L li W wi H hi ¦¦ ¦ ¦ a ipqrstu xipqr d i p q r L li W wi H hi Pi d ¦ ¦ ¦ xipqr d Qi p q r i m p L xipqr ^` q W r H 1 DIRUP XODomRDIXQomRREMHWLYRYLVDP D[LP L]DURYDORUWRWDOGH FDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHUVH vi li wi hi HQWmRFRUUHVSRQGHD P D[LP L]DURYROXP HWRWDOGHFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHKDMD VREUHSRVLomRHQWUHDVFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHRQ~P HURGH UpSOLFDVGHFDGDFDL[DGHQWURGRFRQWrLQHUHVWHMDDEDL[RRXDFLP DGRVYDORUHVHVWLSXODGRV )LQDOP HQWHDVUHVWULo}HVGHILQHP RGRP tQLRGDVYDULiYHLVGHGHFLVmR1 RWHTXHHVWD IRUP XODomR FRP R FRORFDGD DFLP D SRGH VHU XWLOL]DGD SDUD GHVFUHYHU SUREOHP DV GH FDUUHJDP HQWRGHFRQWrLQHUHVGRVWLSRV' 5 ,,336/2 336. 3 (VWDIRUP XODomRSRVVXL 2 m_L __W __H _YDULiYHLVH 2 _L __W __H _ UHVWULo}HV1 RWHTXHRP RGHORFUHVFHVXEVWDQFLDOP HQWHFRP RQ~P HURGHtiposGHFDL[DVH FRP RQ~P HURGHposiçõesHP UHODomRDRVHL[RVx y Hz )2 5 0 8 /$ d 2 ' (7 6$ ,ET AL 7VDLet alDSUHVHQWDP XP P RGHORGHSURJUDP DomROLQHDULQWHLUDP LVWD SDUDRSUREOHP DGHFDUUHJDP HQWRGHSDOHWHVGRGLVWULEXLGRUWULGLP HQVLRQDOHP TXHFDL[DV UHWDQJXODUHVGHGLIHUHQWHVGLP HQV}HVGHYHP VHUHP SDFRWDGDVVREUHXP ~QLFRSDOHWHFRP R REMHWLYRGHP D[LP L]DURYROXP HWRWDOGHFDL[DVHP SDFRWDGDVVREUHRSDOHWH2 VDXWRUHV DSUHVHQWDP UHVXOWDGRVFRP SXWDFLRQDLVFRP SHTXHQRVH[HP SORVQXP pULFRVDSHQDVSDUD YDOLGDURP RGHOR2 VtQGLFHVSDUkP HWURVHYDULiYHLVXWLOL]DGRVQHVWDIRUP XODomRVmR DSUHVHQWDGRVDVHJXLU ËQGLFHV i j k tQGLFHVSDUDDVFDL[DV 3DUkP HWURV M Q~P HURVXILFLHQWHP HQWHJUDQGH m Q~P HURWRWDOGHFDL[DVGLVSRQtYHLV vk YROXP HGDFDL[Dk li wi hi FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGDFDL[Di LW H FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGRFRQWrLQHU X o Y o Z o SRVLomRGRFDQWRLQIHULRUIURQWDOHVTXHUGRGRFRQWrLQHUQRHVSDoRGH FRRUGHQDGDVFDUWHVLDQDVUHVSHFWLYDP HQWHHP UHODomRDRVHL[RVx y Hz YHMD)LJXUD QRWHTXHHVWHVYDORUHVGHYHP VHUVXILFLHQWHP HQWHJUDQGHVGHP RGRTXHDVFDL[DVQmR HP SDFRWDGDVGHQWURGRFRQWrLQHUGHGLP HQV}HVLW H FDLEDP GHQWURGRFRQWrLQHU ILFWtFLRGHGLP HQV}HVX o Y o Z o 9 DULiYHLVGHGHFLVmR pk YDULiYHOELQiULDTXHpLJXDODVHDFDL[Dk pHP SDFRWDGDGHQWURGRFRQWrLQHUWDOTXH k m FDVRFRQWUiULRHODpLJXDOD xi yi zi YDULiYHLVUHDLVTXHLQGLFDP DSRVLomRGRFDQWRLQIHULRUIURQWDOHVTXHUGRGDFDL[D i UHVSHFWLYDP HQWHHP UHODomRDRVHL[RVx y Hz WDOTXHi m uij>@uij>@uij>@ YDULiYHLV ELQiULDV XWLOL]DGDV QDV UHVWULo}HV GLVMXQWLYDV WDO TXH i m Hj i i m )LJXUD/RFDOL]DomRGRFRQWrLQHUQRHVSDoRGHFRRUGHQDGDVFDUWHVLDQDV 2 SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP RULHQWDomRIL[DGHQWURGHXP ~QLFR FRQWrLQHUpIRUP XODGRSRU7VDLet alFRP RDVHJXLU1 RWHTXHQHVWDIRUP XODomRQmRKi UHVWULo}HVTXDQWRDRQ~P HURGHFDL[DVTXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHULVWRp RSUREOHP DpirrestritoGRSRQWRGHYLVWDGDGLVSRQLELOLGDGHGHcaixas 0 RGHOR m P D[ ¦ vk pk i m j i i m k 6XMHLWRD x j xi d l j M uij>@ uij>@ xi x j d li M uij>@ uij>@ y j yi d w j M uij>@ uij>@ yi y j d wi M > uij>@ uij>@@ z j zi d h j M > uij>@ uij>@@ i m i m j i i m j i i m i m j i i m i m j i i m i m j i i m zi z j d hi M > uij>@ uij>@@ i m d uij>@ uij>@ uij>@ d j i i m xk t X o pk k m yk t Y o pk k m zk t Z o pk k m xk d X o L lk k m yk d Y o W wk k m zk d Z o H hk k m pk ^` k m xk yk zk t k m i m uij>@uij>@uij>@ ^` j i i m 1 DIRUP XODomRDIXQomRREMHWLYRYLVDP D[LP L]DURYROXP HWRWDOGH FDL[DV HP SDFRWDGDV GHQWUR GR FRQWrLQHU $ V UHVWULo}HV LP SHGHP TXH KDMD VREUHSRVLomRHQWUHDVFDL[DVGHQWURGRFRQWrLQHU$ UHVWULomRLP SHGHTXHP DLVGRTXH XP DGHQWUHDVUHVWULo}HVWHQKDHIHLWRGHYLGRDRYDORUVXILFLHQWHP HQWHJUDQGHGRODGR GLUHLWRGDVUHVWULo}HV$ VUHVWULo}HVLP SHGHP TXHDVFDL[DVVHMDP HP SDFRWDGDV DOpP GDVGLP HQV}HVGRFRQWrLQHU)LQDOP HQWHDVUHVWULo}HVGHILQHP RGRP tQLRGDV YDULiYHLVGHGHFLVmR1 RWHTXHHVWDIRUP XODomRFRP RFRORFDGDDFLP DSRGHVHUXWLOL]DGDSDUD GHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVGRVWLSRV' 5 ,,336/2 336. 3 (VWD IRUP XODomR SRVVXL 2 m m m YDULiYHLV H 2 m m UHVWULo}HV1 RWHTXHRP RGHORFUHVFHVXEVWDQFLDOP HQWHFRP RQ~P HURGH caixasDVHUHP FDUUHJDGDV 1 RWHDLQGDTXHFRQIRUP HREVHUYDGRHP 5RFKDGHP RGRDWRUQDUHVWH P RGHORP DLVHFRQ{P LFRpSRVVtYHOUHHVFUHYHUDVUHVWULo}HVHGHVGHTXH X o Y o Z o ! FRP RDVHJXLUQRWHTXHRVtQGLFHVFRP RVTXDLVDVUHVWULo}HVYDULDP VmRRVP HVP RVGHILQLGRVDQWHULRUP HQWHHHVWmRDTXLRP LWLGRVSRUVLP SOLFLGDGH x j xi d l j p j M uij>@ uij>@ xi x j d li pi M uij>@ uij>@ y j yi d w j p j M uij>@ uij>@ yi y j d wi pi M > uij>@ uij>@@ z j zi d h j p j M > uij>@ uij>@@ zi z j d hi pi M > uij>@ uij>@@ xk d >X o L lk @pk yk d >Y o W wk @pk zk d >Z o H hk @pk 1 RWHTXHRVQ~P HURVGHYDULiYHLVHUHVWULo}HVGRP RGHORQmRVmRDOWHUDGRV P DVGLIHUHQWHGRP RGHORDQWHULRUDVUHVWULo}HVDFLP DSDVVDP DVHUYHULILFDGDVDSHQDVTXDQGR XP DFDL[DpHP SDFRWDGDGHQWURGRFRQWrLQHULVWRpVHpk &DVRFRQWUiULRHVWDVUHVWULo}HV QmRWrP HIHLWR )2 5 0 8 /$ d 2 ' (& + (1 ET AL &KHQet alDSUHVHQWDP XP P RGHORGHSURJUDP DomROLQHDULQWHLUDP LVWD SDUDRSUREOHP DGHFDUUHJDP HQWRGHP ~OWLSORVFRQWrLQHUHVHP TXHXP VXEFRQMXQWRGH FRQWrLQHUHVGHGLIHUHQWHVGLP HQV}HVGHYHVHUVHOHFLRQDGRSDUDVHUFDUUHJDGRFRP WRGDVDV FDL[DVUHWDQJXODUHVGLVSRQtYHLVFRP RREMHWLYRGHP LQLP L]DURYROXP HWRWDOQmRXWLOL]DGRGH WRGRVRVFRQWrLQHUHVVHOHFLRQDGRV2 VDXWRUHVDSUHVHQWDP UHVXOWDGRVFRP SXWDFLRQDLVFRP SHTXHQRVH[HP SORVQXP pULFRVDSHQDVSDUDYDOLGDURP RGHOR2 VtQGLFHVSDUkP HWURVH YDULiYHLVXWLOL]DGRVQHVWDIRUP XODomRVmRDSUHVHQWDGRVDVHJXLU ËQGLFHV ij tQGLFHVSDUDDVFDL[DV k tQGLFHSDUDRVFRQWrLQHUHV 3DUkP HWURV M Q~P HURVXILFLHQWHP HQWHJUDQGH m Q~P HURWRWDOGHFDL[DVGLVSRQtYHLV n Q~P HURWRWDOGHFRQWrLQHUHVGLVSRQtYHLV li wi hi FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGDFDL[Di Lk Wk H k FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGRFRQWrLQHUk 9 DULiYHLVGHGHFLVmR nk YDULiYHOELQiULDTXHpLJXDODVHRFRQWrLQHUk pVHOHFLRQDGRWDOTXHk n FDVR FRQWUiULRHODpLJXDOD sik YDULiYHOELQiULDTXHpLJXDODVHDFDL[Di pHP SDFRWDGDGHQWURGRFRQWrLQHUk WDOTXH i m Hk n FDVRFRQWUiULRHODpLJXDOD xi yi zi YDULiYHLVUHDLVTXHLQGLFDP DSRVLomRGRFDQWRLQIHULRUIURQWDOHVTXHUGRGDFDL[D i UHVSHFWLYDP HQWHHP UHODomRDRVHL[RVx y Hz WDOTXHi m lxi lyi lzi YDULiYHLVELQiULDVTXHLQGLFDP VHRFRP SULP HQWRGDFDL[Di pSDUDOHORDRHL[R x y RXz WDOTXHi m 3RUH[HP SORlxi pLJXDODVHRFRP SULP HQWRGDFDL[Di p SDUDOHORDRHL[Rx FDVRFRQWUiULRHODpLJXDOD wxi wyi wzi YDULiYHLVELQiULDVTXHLQGLFDP VHDODUJXUDGDFDL[Di pSDUDOHODDRHL[Rx y RXz WDOTXHi m 3RUH[HP SORwxi pLJXDODVHDODUJXUDGDFDL[Di pSDUDOHOD DRHL[Rx FDVRFRQWUiULRHODpLJXDOD hxi hyi hzi YDULiYHLVELQiULDVTXHLQGLFDP VHDDOWXUDGDFDL[Di pSDUDOHODDRHL[Rx y RXz WDOTXHi m 3RUH[HP SORhxi pLJXDODVHDDOWXUDGDFDL[Di pSDUDOHODDR HL[Rx FDVRFRQWUiULRHODpLJXDOD aij bij cij dij eij f ij YDULiYHLVELQiULDVTXHLQGLFDP DSRVLomRUHODWLYDGDVFDL[DVXP DVjV RXWUDV3RUH[HP SORaij pLJXDODVHDFDL[Di HVWiSRVLFLRQDGDjHVTXHUGDGDFDL[Dj WDO TXHij m FDVRFRQWUiULRHODpLJXDODYHMD)LJXUD$ QDORJDP HQWHDVGHP DLV YDULiYHLVLQGLFDP VHDFDL[Di HVWiSRVLFLRQDGDUHVSHFWLYDP HQWHjGLUHLWDjIUHQWHDR IXQGRDEDL[RRXDFLP DGDFDL[Dj )LJXUD/RFDOL]DomRUHODWLYDGHGXDVFDL[DVGHQWURGHXP FRQWrLQHU 2 SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP P ~OWLSODVRULHQWDo}HVGHQWURGH P ~OWLSORVFRQWrLQHUHVpIRUP XODGRSRU&KHQet alFRP RDVHJXLU1 RWHTXHQHVWD IRUP XODomRKiUHVWULo}HVTXDQWRDRQ~P HURGHFRQWrLQHUHVTXHSRGHP VHUHP SDFRWDGRVLVWRp RSUREOHP DprestritoGRSRQWRGHYLVWDGDGLVSRQLELOLGDGHGHcontêineres 0 RGHOR n m P LQ ¦ Lk Wk H k nk ¦ li wi hi xi li lxi wi wxi hi hxi d x j aij M ij mi j x j l j lx j w j wx j h j hx j d xi bij M ij mi j yi li lyi wi wyi hi hyi d y j cij M ij mi j y j l j ly j w j wy j h j hy j d yi dij M ij mi j zi li lzi wi wzi hi hzi d z j eij M ij mi j z j l j lz j w j wz j h j hz j d zi fij M ij mi j k i 6XMHLWRD aij bij cij dij eij fij t sik s jk ij mi j k n n ¦s i m k n xi li lxi wi wxi hi hxi d Lk sik M i mk n yi li lyi wi wyi hi hyi d Wk sik M i mk n zi li lzi wi wzi hi hzi d H k sik M i mk n nk ^` k n sik ^` i mk n xi yi zi t i m lxi lyi lzi wxi wyi wzi hxi hyi hzi ^` i m aij bij cij dij eij fij ^` ij m ik k m ¦s ik d M nk i 1 DIRUP XODomRDIXQomRREMHWLYRYLVDP LQLP L]DURYROXP HWRWDO QmRXWLOL]DGRGHWRGRVRVFRQWrLQHUHVVHOHFLRQDGRV$ VUHVWULo}HVLP SHGHP TXHKDMD VREUHSRVLomRHQWUHDVFDL[DVGHQWURGRVFRQWrLQHUHV$ VUHVWULo}HVLP SHGHP TXHDV UHVWULo}HVWHQKDP HIHLWRFDVRRSDUGHFDL[DVYHULILFDGRHVWHMDHP SDFRWDGRGHQWUR GHFRQWrLQHUHVGLIHUHQWHVGHYLGRDRYDORUVXILFLHQWHP HQWHJUDQGHGRODGRGLUHLWRGDV UHVWULo}HV$ VUHVWULo}HVLP SHGHP TXHXP DP HVP DFDL[DVHMDHP SDFRWDGDGHQWURGH P DLVGRTXHXP FRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHDVFDL[DVVHMDP HP SDFRWDGDV GHQWURGHXP FRQWrLQHUFDVRHVWHQmRWHQKDVLGRVHOHFLRQDGR$ VUHVWULo}HV LP SHGHP TXHDVFDL[DVVHMDP HP SDFRWDGDVDOpP GDVGLP HQV}HVGRVFRQWrLQHUHV)LQDOP HQWH DVUHVWULo}HVGHILQHP RGRP tQLRGDVYDULiYHLVGHGHFLVmR1 RWHTXHHVWDIRUP XODomR FRP RFRORFDGDDFLP DSRGHVHUXWLOL]DGDSDUDGHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGH FRQWrLQHUHVGRVWLSRV' 5 666& 630 66& 635 & 636%6%330 %6%335 %33 1 RWHDLQGDTXHDVYDULiYHLVELQiULDVlxi lyi lzi wxi wyi wzi hxi hyi H hzi VmRGHSHQGHQWHVHHVWmRUHODFLRQDGDVHQWUHVLFRP RDVHJXLU lxi lyi lzi wxi wyi wzi hxi hyi hzi lxi wxi hxi lyi wyi hyi lzi wzi hzi 8 WLOL]DQGRDVUHODo}HVpSRVVtYHOHOLP LQDUGDIRUP XODomRDV YDULiYHLVlyi wxi wzi hxi Hhyi UHVXOWDQGRHP XP DUHGXomRVLJQLILFDWLYDGRWDP DQKRGR P RGHOR$ VUHVWULo}HVDIHWDGDVSRGHP VHUUHHVFULWDVFRP RDVHJXLUQRWHTXHRVtQGLFHVFRP RVTXDLVDVUHVWULo}HVYDULDP VmRRVP HVP RVGHILQLGRVDQWHULRUP HQWHHHVWmRDTXLRP LWLGRV SRUVLP SOLFLGDGH xi li lxi wi lzi wyi hzi hi lxi lzi wyi hzi d x j aij M x j l j lx j w j lz j wy j hz j h j lx j lz j wy j hx j d xi bij M yi li lxi lzi wi wyi hi lxi lzi wyi d y j cij M y j l j lx j lz j w j wy j h j lx j lz j wy j d yi dij M zi li lzi wi lzi hzi hi hzi d z j eij M z j l j lz j w j lz j hz j h j hz j d zi fij M xi li lxi wi lzi wyi hzi hi lxi lzi wyi hzi d Lk sik M yi li lxi lzi wi wyi hi lxi lzi wyi d Wk sik M zi li lzi wi lzi hzi hi hzi d H k sik M (VWDIRUP XODomRFRP UHVWULo}HVUHYLVDGDVSRVVXLm n m n YDULiYHLV H n m m m m n m n UHVWULo}HV 1 RWH TXH R P RGHOR FUHVFH VXEVWDQFLDOP HQWHFRP RQ~P HURGHcaixasDVHUHP FDUUHJDGDVHFRP RQ~P HURGHcontêineres GLVSRQtYHLV &KHQet alDLQGDGLVFXWHP FRP RP RGLILFDUDIRUP XODomRSDUD WUDWDURXWURVSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHV8 P DSRVVLELOLGDGHFRQVLVWHHP GHILQLURVSDUkP HWURVX o Y o Z o HDYDULiYHOGHGHFLVmRpi VLP LODUP HQWHjIRUP XODomRGH 7VDLet alVXEVWLWXLUDIXQomRREMHWLYRSHODIXQomRREMHWLYRH[FOXLUDV YDULiYHLVGHGHFLVmRnk Hsik DOWHUDURODGRGLUHLWRGDVUHVWULo}HVSDUDH[FOXLUDV UHVWULo}HVHDFUHVFHQWDUDVUHVWULo}HVHDOWHUDURODGR GLUHLWRGDVUHVWULo}HVHUHVSHFWLYDP HQWHSDUDX o LY o W HZ o H HDOWHUDUDVUHVWULo}HVSDUDLQFOXLUDQRYDYDULiYHOGHGHFLVmRpi &RP HVWDVP RGLILFDo}HV pSRVVtYHOIRUP XODURSUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP P ~OWLSODVRULHQWDo}HVGHQWUR GHXP ~QLFRFRQWrLQHUFRP RXP FDVRSDUWLFXODUGDIRUP XODomRGH&KHQet al m P D[ ¦ pi xi li lxi wi wxi hi hxi d x j aij M ij mi j x j l j lx j w j wx j h j hx j d xi bij M ij mi j yi li lyi wi wyi hi hyi d y j cij M ij mi j y j l j ly j w j wy j h j hy j d yi dij M ij mi j zi li lzi wi wzi hi hzi d z j eij M ij mi j z j l j lz j w j wz j h j hz j d zi f ij M ij mi j aij bij cij dij eij f ij t ij mi j xi t X o pi i m yi t Y o pi i m zi t Z o pi i m xi li lxi wi wxi hi hxi d X o L i m yi li lyi wi wyi hi hyi d Y o W i m zi li lzi wi wzi hi hzi d Z o H i m xi yi zi t i m pi lxi lyi lzi wxi wyi wzi hxi hyi hzi ^` i m aij bij cij dij eij fij ^` ij m i 6XMHLWRD 1 RWHTXHHVWDIRUP XODomRFRP RFRORFDGDDFLP DSRGHVHUXWLOL]DGDSDUD GHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVGRVWLSRV' 5 ,,336/2 336. 3 8 P DRXWUDSRVVLELOLGDGHFRQVLVWHHP GHILQLUL FRP RVHQGRXP DYDULiYHOGH GHFLVmRUHDOVXEVWLWXLUDIXQomRREMHWLYRSHODIXQomRREMHWLYRH[FOXLUDVUHVWULo}HV HHDFUHVFHQWDUDUHVWULomR&RP HVWDVP RGLILFDo}HVpSRVVtYHOIRUP XODUR SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP P ~OWLSODVRULHQWDo}HVGHQWURGHXP ~QLFRFRQWrLQHU GHP RGRDP LQLP L]DURFRP SULP HQWRQHFHVViULRSDUDHP SDFRWDUWRGDVDVFDL[DVFRP RXP RXWURFDVRSDUWLFXODUGDIRUP XODomRGH&KHQet al P LQL xi li lxi wi wxi hi hxi d x j aij M ij mi j x j l j lx j w j wx j h j hx j d xi bij M ij mi j yi li lyi wi wyi hi hyi d y j cij M ij mi j y j l j ly j w j wy j h j hy j d yi dij M ij mi j zi li lzi wi wzi hi hzi d z j eij M ij mi j z j l j lz j w j wz j h j hz j d zi fij M ij mi j aij bij cij dij eij f ij t ij mi j xi li lxi wi wxi hi hxi d X o L i m yi li lyi wi wyi hi hyi d Y o W i m zi li lzi wi wzi hi hzi d Z o H i m L t xi yi zi t i m lxi lyi lzi wxi wyi wzi hxi hyi hzi ^` i m aij bij cij dij eij f ij ^` ij m 6XMHLWRD 1 RWHTXHHVWDIRUP XODomRFRP RFRORFDGDDFLP DSRGHVHUXWLOL]DGDSDUD GHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVGRWLSR' 5 2 ' 3 )2 5 0 8 /$ d 2 ' (+ $ ' -,& 2 1 67$ 1 7,1 2 8 (& + ,672 ),' (6 + DGMLFRQVWDQWLQRX H &KULVWRILGHV DSUHVHQWDP XP P RGHOR GH SURJUDP DomROLQHDULQWHLUDSDUDRSUREOHP DGHFRUWHQmRJXLOKRWLQDGRELGLP HQVLRQDOHP TXHSHoDVUHWDQJXODUHVGHGLIHUHQWHVGLP HQV}HVGHYHP VHUFRUWDGDVDSDUWLUGHXP ~QLFR UHWkQJXORJUDQGHFRP RREMHWLYRGHP D[LP L]DURYDORUWRWDOGDVSHoDVFRUWDGDV2 VDXWRUHV GHVHQYROYHP XP SURFHGLP HQWRH[DWRGHEXVFDHP iUYRUHSDUDUHVROYHURSUREOHP D2 DOJRULWP ROLP LWDRWDP DQKRGDEXVFDHP iUYRUHXWLOL]DQGRXP OLP LWDQWHVXSHULRUREWLGRFRP D UHOD[DomRODJUDQJLDQDGRP RGHOR2 SURFHGLP HQWRGHRWLP L]DomRGRVXEJUDGLHQWHpXWLOL]DGR SDUDRWLP L]DUROLP LWDQWHVXSHULRUREWLGRFRP DUHOD[DomRODJUDQJLDQDHWHVWHVGHUHGXomRGR SUREOHP DGHULYDGRVWDQWRGRSUREOHP DRULJLQDOTXDQWRGRSUREOHP DUHOD[DGRVmRXWLOL]DGRV SDUDUHGX]LURWDP DQKRGRVSUREOHP DV2 VDXWRUHVDSUHVHQWDP UHVXOWDGRVFRP SXWDFLRQDLVSDUD DVVROXo}HVyWLP DVGHVHWHSUREOHP DVWHVWHVGLIHUHQWHVHSDUDDVP HOKRUHVVROXo}HVLQWHLUDV IDFWtYHLVGHFLQFRSUREOHP DVWHVWHVGLIHUHQWHVFRP RP DLRUSUREOHP DUHVROYLGRWHQGRTXLQ]H WLSRVGHLWHQVGLVSRQtYHLV2 VtQGLFHVSDUkP HWURVHYDULiYHLVXWLOL]DGRVQHVWDIRUP XODomRVmR DSUHVHQWDGRVDVHJXLU ËQGLFHV ij tQGLFHVSDUDRVtiposGHFDL[DV ps tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Rx qt tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Ry r u tQGLFHVSDUDDVSRVLo}HVHP UHODomRDRHL[Rz 3DUkP HWURV m Q~P HURWRWDOGHtiposGHFDL[DVGLVSRQtYHLV vi YDORUGDFDL[Di Qi Q~P HURP i[LP RGHUpSOLFDVGDFDL[Di TXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHU li wi hi FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGDFDL[Di LW H FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGRFRQWrLQHU 9 DULiYHLVGHGHFLVmR xijp YDULiYHOELQiULDTXHpLJXDODVHDj pVLP DUpSOLFDGDFDL[Di pHP SDFRWDGDFRP VHX FDQWRLQIHULRUIURQWDOHVTXHUGRQDSRVLomRp HP UHODomRDRHL[Rx WDOTXH j Qi H p L li FDVRFRQWUiULRHODpLJXDOD yijq YDULiYHOELQiULDTXHpLJXDODVHDj pVLP DUpSOLFDGDFDL[Di pHP SDFRWDGDFRP VHX FDQWRLQIHULRUIURQWDOHVTXHUGRQDSRVLomRq HP UHODomRDRHL[Ry WDOTXH j Qi H q W wi FDVRFRQWUiULRHODpLJXDOD zijr YDULiYHOELQiULDTXHpLJXDODVHDj pVLP DUpSOLFDGDFDL[Di pHP SDFRWDGDFRP VHX FDQWRLQIHULRUIURQWDOHVTXHUGRQDSRVLomRr HP UHODomRDRHL[Rz WDOTXH j Qi H r H hi FDVRFRQWUiULRHODpLJXDOD t u QmRHVWiRFXSDGDSRUQHQKXP D k stu YDULiYHOELQiULDTXHpLJXDODVHDSRVLomRs FDL[DWDOTXHs L t W Hu H FDVRFRQWUiULRHODpLJXDOD 2 SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP RULHQWDomRIL[DGHQWURGHXP ~QLFR FRQWrLQHUSRGHVHUIRUP XODGRFRP RXP DH[WHQVmRGLUHWDGRP RGHORGHSURJUDP DomROLQHDU LQWHLUDSURSRVWRHP + DGMLFRQVWDQWLQRXH&KULVWRILGHVSDUDRSUREOHP DGHFRUWH QmRJXLOKRWLQDGRELGLP HQVLRQDO1 RWHTXHQHVWDIRUP XODomRKiUHVWULo}HVTXDQWRDRQ~P HUR GHFDL[DVGHFDGDWLSRTXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHULVWRpRSUREOHP Dp restritoGRSRQWRGHYLVWDGDGLVSRQLELOLGDGHGHcaixas 0 RGHOR m Qi L li P D[ ¦ vi ¦ ¦ xijp i j p 6XMHLWRD i mj Qi p li q wi r hi ¦ ¦ ¦ s p t q u r k stu d xijp yijq zijr li wi hi p L li q W wi r H hi L li ¦x ijp d i mj Qi i mj Qi p L li W wi ¦x ¦ p q ijp m Qi ¦ wi hi ¦ i m m zijr r P LQs L li W H xijp ¦ ¦ j p P D[s li Qi P LQt W wi ¦ Qi ¦k W H s P LQ^li `L stu L H t P LQ^wi `W stu L W u P LQ^hi `H stu t u i L H yijq ¦ j q P D[t wi ¦ li wi ¦ i ¦ yijq ¦ li hi ¦ i H hi P LQu H hi ¦ j r P D[u hi ¦k s u i L W zijr ¦ ¦k s t i i mj Qi xijp yijq zijr ^` p L li q W wi r H hi s L t W k stu ^` u H 1 DIRUP XODomRDIXQomRREMHWLYRYLVDP D[LP L]DURYDORUWRWDO GHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHUVHvi li wi hi HQWmRFRUUHVSRQGHD P D[LP L]DURYROXP HWRWDOGHFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHKDMD VREUHSRVLomRHQWUHDVFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHXP D FDL[DVHMDHP SDFRWDGDP DLVGRTXHXP DYH]GHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHWRGDVDVFDL[DVFXMDVRP DGDViUHDVwi hi H[FHGDDiUHDW H VHMDP HP SDFRWDGDVFRP VHXFDQWRLQIHULRUIURQWDOHVTXHUGRQDP HVP DSRVLomRp HP UHODomRDRHL[Rx 6LP LODUP HQWH DVUHVWULo}HVLP SHGHP TXHWRGDVDVFDL[DVFXMDVRP DGDViUHDVli hi H[FHGDDiUHD L H VHMDP HP SDFRWDGDVFRP VHXFDQWRLQIHULRUIURQWDOHVTXHUGRQDP HVP DSRVLomRq HP UHODomRDRHL[Ry YHMD)LJXUDHDVUHVWULo}HVLP SHGHP TXHWRGDVDVFDL[DVFXMD VRP DGDViUHDVli wi H[FHGDDiUHDL W VHMDP HP SDFRWDGDVFRP VHXFDQWRLQIHULRUIURQWDO HVTXHUGRQDP HVP DSRVLomRr HP UHODomRDRHL[Rz )LQDOP HQWHDVUHVWULo}HV GHILQHP RGRP tQLRGDVYDULiYHLVGHGHFLVmR1 RWHTXHHVWDIRUP XODomRFRP RFRORFDGDDFLP D SRGHVHUXWLOL]DGDSDUDGHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVGRVWLSRV' 5 ,,336/2 336. 3 )LJXUD3ODQRL H QDSRVLomRt HP UHODomRDRHL[Ry (VWD IRUP XODomR SRVVXL m ¦ m i Qi _li _ _wi _ _hi _ L W H YDULiYHLV H m ¦ i Qi ¦ i Qi _li __wi __hi _ L W H UHVWULo}HV 1 RWH TXH R P RGHOR FUHVFH VXEVWDQFLDOP HQWHFRP RQ~P HURGHtiposGHFDL[DVFRP RQ~P HURGHcaixasGLVSRQtYHLVGH FDGDWLSRHFRP RQ~P HURGHposiçõesHP UHODomRDRVHL[RVx y Hz 6HJXQGR $ P DUDO H /HFKWIRUG SDUD R FDVR ELGLP HQVLRQDO HVWD IRUP XODomRQHP VHP SUHpYiOLGDXP DYH]TXHKiVROXo}HVLQWHLUDVLQIDFWtYHLVTXHVmR VDWLVIHLWDVSHORP RGHOR(VWDREVHUYDomRWDP EpP VHHVWHQGHSDUDRFDVRWULGLP HQVLRQDO$ LQGD VHJXQGRRVDXWRUHVXP DIRUP XODomRYiOLGDSRGHVHUREWLGDHOLP LQDQGRVHDVYDULiYHLVk stu H VXEVWLWXLQGRVHDVUHVWULo}HVHSHODVUHVWULo}HVTXH LP SHGHP TXHKDMDVREUHSRVLomRHQWUHDVFDL[DVGHQWURGRFRQWrLQHU2 SUREOHP DGHYHULDVHU HQWmRIRUP XODGRFRP R m Qi L li P D[ ¦ vi ¦ ¦ xijp i j p 6XMHLWRD L li ¦x ijp d i mj Qi i mj Qi p L li W wi ¦x ¦ p q ijp H hi yijq ¦ zijr r i mj Qi k ml Qk xijp yijq zijr xkls yklt zklu d i z j RXp z q p L li s L q W wi t W r H hi u H i mj Qi xijp yijq zijr ^` p L li q W wi r H hi )2 5 0 8 /$ d 2 ' (% ($ 6/(< %HDVOH\DSUHVHQWDXP P RGHORGHSURJUDP DomRQmROLQHDULQWHLUDP LVWD SDUDRSUREOHP DGHFRUWHQmRJXLOKRWLQDGRELGLP HQVLRQDOHP TXHSHoDVUHWDQJXODUHVGH GLIHUHQWHVGLP HQV}HVGHYHP VHUFRUWDGDVDSDUWLUGHXP ~QLFRUHWkQJXORJUDQGHFRP R REMHWLYRGHP D[LP L]DURYDORUWRWDOGDVSHoDVFRUWDGDV2 DXWRUGHVHQYROYHXP DKHXUtVWLFD SRSXODFLRQDODOJRULWP RJHQpWLFREDVHDGDQRP RGHORSDUDUHVROYHURSUREOHP D$ JHUDomR GRVLQGLYtGXRVpIHLWDFRP EDVHQDVYDULiYHLVGHGHFLVmRGRP RGHORHDHYROXomRGD SRSXODomRpREWLGDDWUDYpVGHRSHUDGRUHVGHFUX]DP HQWRHP XWDomR6ROXo}HVLQIDFWtYHLVVmR SHQDOL]DGDVSRUXP WHUP RQHJDWLYRQDIXQomRGHDSWLGmRHP RYLP HQWRVGHP HOKRULDVLP SOHV VmRHP SUHJDGRVGHP RGRDREWHUIDFWLELOLGDGH2 DXWRUDSUHVHQWDUHVXOWDGRVFRP SXWDFLRQDLV SDUDDVVROXo}HVyWLP DVGHSUREOHP DVWHVWHVGDOLWHUDWXUDHJHUDGRVDSDUWLUGHGDGRVDOHDWyULRV HP XP EDL[RWHP SRFRP SXWDFLRQDO2 VtQGLFHVSDUkP HWURVHYDULiYHLVXWLOL]DGRVQHVWD IRUP XODomRVmRDSUHVHQWDGRVDVHJXLU ËQGLFHV ij tQGLFHVSDUDRVtiposGHFDL[DV pq tQGLFHVSDUDDVFDL[DV 3DUkP HWURV m Q~P HURWRWDOGHtiposGHFDL[DVGLVSRQtYHLV vi YDORUGDFDL[Di Pi Q~P HURP tQLP RGHUpSOLFDVGDFDL[Di TXHGHYHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHU Qi Q~P HURP i[LP RGHUpSOLFDVGDFDL[Di TXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHU li wi hi FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGDFDL[Di LW H FRP SULP HQWRODUJXUDHDOWXUDUHVSHFWLYDP HQWHGRFRQWrLQHU 9 DULiYHLVGHGHFLVmR rip YDULiYHOELQiULDTXHpLJXDODVHDp pVLP DUpSOLFDGDFDL[Di pHP SDFRWDGDGHQWURGR FRQWrLQHUWDOTXHi m Hp Qi FDVRFRQWUiULRHODpLJXDOD xip yip zip YDULiYHLVUHDLVTXHLQGLFDP DSRVLomRGRFHQWURGDp pVLP DUpSOLFDGDFDL[Di UHVSHFWLYDP HQWHHP UHODomRDRVHL[RVx y Hz WDOTXHi m H p Qi YHMD )LJXUD )LJXUD/RFDOL]DomRUHODWLYDGHGXDVFDL[DVGHQWURGHXP FRQWrLQHU 2 SUREOHP DGHFDUUHJDP HQWRGHFDL[DVFRP RULHQWDomRIL[DGHQWURGHXP ~QLFR FRQWrLQHUSRGHVHUIRUP XODGRFRP RXP DH[WHQVmRGLUHWDGRP RGHORGHSURJUDP DomRQmR OLQHDULQWHLUDP LVWDSURSRVWRHP %HDVOH\SDUDRSUREOHP DGHFRUWHQmR JXLOKRWLQDGRELGLP HQVLRQDO1 RWHTXHQHVWDIRUP XODomRKiUHVWULo}HVTXDQWRDRQ~P HURGH FDL[DVGHFDGDWLSRTXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHULVWRpRSUREOHP Dp restritoGRSRQWRGHYLVWDGDGLVSRQLELOLGDGHGHcaixas 0 RGHOR m Qi P D[ ¦ ¦ vi rip i p 6XMHLWRD P D[>_xip x jq _D ij _yip y jq _Eij _zip z jq _Jij @rip rjq t D ij li l j ° FRP ®Eij wi w j ° ¯Jij hi h j i mj m p Qi q Q j i z j RXp z q i m rip Pi ! p Pi li d xip d L li i mp Qi wi d yip d W wi i mp Qi hi d zip d H hi i mp Qi rip ^` i mp Qi 1 DIRUP XODomRDIXQomRREMHWLYRYLVDP D[LP L]DURYDORU WRWDOGHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHUVHvi li wi hi HQWmRFRUUHVSRQGHD P D[LP L]DURYROXP HWRWDOGHFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXH KDMDVREUHSRVLomRHQWUHDVFDL[DVGHQWURGRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHR Q~P HURGHUpSOLFDVGHFDGDFDL[DGHQWURGRFRQWrLQHUHVWHMDDEDL[RGRYDORUHVWLSXODGR )LQDOP HQWHDVUHVWULo}HVGHILQHP RGRP tQLRGDVYDULiYHLVGHGHFLVmRHP SDUWLFXODUDVUHVWULo}HVWDP EpP LP SHGHP TXHDVFDL[DVVHMDP HP SDFRWDGDVDOpP GDVGLP HQV}HVGRFRQWrLQHU1 RWHTXHHVWDIRUP XODomRFRP RFRORFDGDDFLP DSRGHVHU XWLOL]DGDSDUDGHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVGRVWLSRV' 5 ,,336/2 336. 3 m m (VWDIRUP XODomRSRVVXL¦ i Qi YDULiYHLVH2 ¦ i Qi UHVWULo}HV1 RWHTXH RP RGHORFUHVFHVXEVWDQFLDOP HQWHFRP RQ~P HURGHtiposGHFDL[DVHFRP RQ~P HURGHcaixas GLVSRQtYHLVGHFDGDWLSR 0 e72 ' 2 6' (62 /8 d 2 2 VSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVFRP RFDVRVSDUWLFXODUHVGR SUREOHP DGHHP SDFRWDP HQWRVmR1 3FRP SOHWRVTXDQGRWUDWDGRVFRP RSUREOHP DVGHGHFLVmR H1 3GLItFHLVTXDQGRWUDWDGRVFRP RSUREOHP DVGHRWLP L]DomRVHQGRP XLWRGLItFHLVGHVHUHP UHVROYLGRVQDSUiWLFD' 2 : 6/$ 1 ' ' 2 : 6/$ 1 ' $ SHQDVSUREOHP DVGHWDP DQKR EHP P RGHUDGRVmRFDSD]HVGHVHUUHVROYLGRVRWLP DP HQWHGHQWURGHXP OLP LWHGHWHP SR UD]RiYHORTXHMXVWLILFDRGHVHQYROYLP HQWRGHGLYHUVRVP pWRGRVKHXUtVWLFRVSDUDVHUHVROYHU HVWHV SUREOHP DV $ OJRULWP RV GH DSUR[LP DomR EXVFD HP iUYRUHJUDIR WpFQLFDV GH GHFRP SRVLomRHUHOD[DomRP HWDKHXUtVWLFDVHQWUHRXWUDVHVWmRHQWUHDVDERUGDJHQVP DLV FRP XP HQWHHVWXGDGDV 3LVLQJHUFODVVLILFDDVDERUGDJHQVKHXUtVWLFDVGHDFRUGRFRP RP pWRGR XWLOL]DGRSDUDFRQVWUXLURSDGUmRGHFDUUHJDP HQWRVHQGRSRVVtYHOGLVWLQJXLUDOJRULWP RVTXH XWLOL]DP 3DUHGHV9 LUWXDLV&DP DGDV9 HUWLFDLVRX+ RUL]RQWDLV3LOKDVGH&DL[DV&RUWHV * XLOKRWLQDGRVH&XEyLGHV Paredes VirtuaisSRVVLELOLWDP FRQVWUXLUFDP DGDVYHUWLFDLVRXKRUL]RQWDLVDR ORQJRGHXP DGDVGLP HQV}HVGRFRQWrLQHU1 RFDVRGDVcamadas verticaisDVSDUHGHVYLUWXDLV VmRFRQVWUXtGDVDSDUWLUGHXP DSDUHGHODWHUDOGRFRQWrLQHUSURJUHGLQGRHP GLUHomRjRXWUD SDUHGHODWHUDORSRVWDGRP HVP RYHMD)LJXUD(VWHSURFHGLP HQWRGHFRQVWUXomRGRSDGUmR GHFDUUHJDP HQWRSRGHVHUHQFRQWUDGRSRUH[HP SORHP * HRUJHH5RELQVRQ%LVFKRIIH 0 DUULRWW* HKULQJet al' RZ VODQG%LVFKRIIH5DWFOLIID' DYLHV H%LVFKRII7HUQRet al%RUWIHOGWH* HKULQJ* HKULQJH%RUWIHOGW 3LVLQJHU/LP et al&HFLOLRH0 RUDELWR0 RXUDH2 OLYHLUD %LVFKRIIH%RUWIHOGWH0 DFN1 RFDVRGDVcamadas horizontaisDV SDUHGHVYLUWXDLVVmRFRQVWUXtGDVDSDUWLUGRSLVRGRFRQWrLQHUSURJUHGLQGRHP GLUHomRDRWHWR GRP HVP RYHMD)LJXUD(VWHSURFHGLP HQWRGHFRQVWUXomRGRSDGUmRGHFDUUHJDP HQWR SRGHVHUHQFRQWUDGRSRUH[HP SORHP + DQet al%LVFKRIIet al0 RUDELWRH $ UHQDOHV5DWFOLIIH%LVFKRIIH/LP H=KDQJ )LJXUD([HP SORVGHFDL[DVVHQGRFDUUHJDGDVHP FDP DGDVYHUWLFDLVHKRUL]RQWDLV Pilhas de CaixasSRVVLELOLWDP FRQVWUXLUSLOKDVGHFDL[DVLQGHSHQGHQWHVXP DV GDVRXWUDVTXHGHYHP GHSRLVVHUDUUDQMDGDVVREUHRSLVRGRFRQWrLQHU1 RWHQD)LJXUDXP SDGUmR GH FDUUHJDP HQWR FRQVWUXtGR SDUFLDOP HQWH FRP GXDV SLOKDV GH FDL[DV (VWH SURFHGLP HQWRGHFRQVWUXomRGRSDGUmRGHFDUUHJDP HQWRSRGHVHUHQFRQWUDGRSRUH[HP SOR HP * LOP RUHH* RP RU\+ DHVVOHUH7DOERW* HKULQJH%RUWIHOGWH 0 RUDELWRH$ UHQDOHV )LJXUD([HP SORGHFDL[DVVHQGRFDUUHJDGDVHP SLOKDV Cortes GuilhotinadosSRVVLELOLWDP ³GHVFRQVWUXLU´RSDGUmRGHFDUUHJDP HQWR DWUDYpVGHXP DVHTrQFLDGHFRUWHVJXLOKRWLQDGRVLVWRpFRUWHVTXHTXDQGRUHDOL]DGRVGHXP D IDFHDWpDRXWUDIDFHRSRVWDGHXP DP HVP DFDL[DSURGX]HP GXDVQRYDVFDL[DVP HQRUHVH DGMDFHQWHV1 HVWHFDVRREYLDP HQWHDFRQVWUXomRGRSDGUmRGHFDUUHJDP HQWRVHGiQDRUGHP LQYHUVDHP TXHRVFRUWHVVmRUHDOL]DGRVLVWRpDWUDYpVGHXP DVHTrQFLDGH³HP SDFRWDP HQWRV JXLOKRWLQDGRV´1 RWHQD)LJXUDTXHRSDGUmRGHFDUUHJDP HQWRGDHVTXHUGDSRGHVHU GHVFRQVWUXtGRSRUFRUWHVJXLOKRWLQDGRVHQTXDQWRQRSDGUmRGHFDUUHJDP HQWRGDGLUHLWDLVVR QmRpSRVVtYHO(VWHSURFHGLP HQWRGHFRQVWUXomRGRSDGUmRGHFDUUHJDP HQWRSRGHVHU HQFRQWUDGRSRUH[HP SORHP 0 RUDELWRH$ UHQDOHVH+ DVDP RQWU )LJXUD([HP SORVGHFDL[DVIRUP DQGRXP SDGUmRJXLOKRWLQDGRHQmRJXLOKRWLQDGR CubóidesSRVVLELOLWDP FRQVWUXLUEORFRVIRUP DGRVSRUFDL[DVGHXP P HVP RWLSR HFRP XP DP HVP DRULHQWDomRTXHGHYHP GHSRLVVHUDUUDQMDGRVRUWRJRQDOP HQWHGHQWURGR FRQWrLQHU1 RWHQD)LJXUDXP SDGUmRGHFDUUHJDP HQWRFRQVWUXtGRSDUFLDOP HQWHFRP WUrV FXEyLGHVIRUP DGRVSRUXP P HVP RWLSRGHFDL[DP DVFRP RULHQWDo}HVGLIHUHQWHV(VWH SURFHGLP HQWRGHFRQVWUXomRGRSDGUmRGHFDUUHJDP HQWRSRGHVHUHQFRQWUDGRSRUH[HP SOR HP (OH\%RUWIHOGWet al0 DFNet al$ UD~MR$ UDXMRH $ UP HQWDQRH+ XDQJH+ HDE )LJXUD([HP SORGHFDL[DVVHQGRFDUUHJDGDVHP FXEyLGHV 0 HWDKHXUtVWLFDVGHQWUHDVP DLVFRP XP HQWHXWLOL]DGDVSDUDUHVROYHUSUREOHP DV GHFDUUHJDP HQWRGHFRQWrLQHUHVSRGHP VHUHQFRQWUDGDVSRUH[HP SORHP $ OJRULWP R * HQpWLFR&RUFRUDQH: DLQZ ULJKW* HKULQJH%RUWIHOGW%RUWIHOGWH * HKULQJ+ HH&KD3LP SDZ DWH&KDL\DUDWDQD< HXQJH7DQJ /LQet alSimulated Annealing-LQet al0 DFNet al%XVFD7DEX /RGLet alE%RUWIHOGWet al,RUL0 DFNet al* HQGUHDXet al* 5$ 630 ~OWLSORV,QtFLRV/DLet al0 RXUDH2 OLYHLUDH$ UDXMRH $ UP HQWDQR %XVFDHP È UYRUH* UDIRHWpFQLFDVGHGHFRP SRVLomRHUHOD[DomRHQWUHRXWUDV XWLOL]DGDVSDUDUHVROYHUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVSRGHP VHUHQFRQWUDGDV SRUH[HP SORHP 0 RUDELWRH$ UHQDOHV0 DUWHOORet al(OH\ 3LVLQJHU,RUL%UXQHWWDH* UHJRLUH/LP et al%RUWIHOGWH0 DFN &KULVWHQVHQH5RXV¡HH+ XDQJH+ HDE & $ 3Ë78 /2 0 2 ' (/$ * (0 & 2 0 & 2 1 6,' (5 $ d ® (6$ ' ,& ,2 1 $ ,6 ,1 75 2 ' 8 d 2 1 HVWH FDStWXOR VmR DSUHVHQWDGDV H[WHQV}HV GR P RGHOR GH SURJUDP DomR P DWHP iWLFDSURSRVWRSRU%HDVOH\YHMDVHomRGHP RGRDDERUGDUVLWXDo}HV FRP XP HQWHHQFRQWUDGDVQDSUiWLFDGRFDUUHJDP HQWRGHFRQWrLQHUHV7RP DQGRFRP REDVHDV FRQVLGHUDo}HVSUiWLFDVSURSRVWDVSRU%LVFKRIIH5DWFOLIIDYHMDVHomRVmR DSUHVHQWDGDVIRUP XODo}HVDERUGDQGRFRQVLGHUDo}HVGHP ~OWLSODVRULHQWDo}HVOLP LWHGHSHVR GRFRQWrLQHUHVWDELOLGDGHGRFDUUHJDP HQWRUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRHFDUJD IUDFLRQDGDHP P ~OWLSORVGHVWLQRV$ VVHo}HVHWUDWDP UHVSHFWLYDP HQWHGHVWDV WUrV~OWLP DVFRQVLGHUDo}HVHWrP DSUHWHQVmRGHHVWDUHQWUHDVSULQFLSDLVFRQWULEXLo}HVGHVWH WUDEDOKR 0 $ 1 ,38 /$ 1 ' 2 $ )2 5 0 8 /$ d 2 ' (% ($ 6/(< $ VSRVVtYHLVSRVLo}HVDRORQJRGRFRP SULP HQWRL GDODUJXUDW HGDDOWXUD H GRFRQWrLQHURQGHFDGDFDL[DSRGHVHUFRORFDGDSRGHP VHUGHILQLGDVSRUP HLRGRV FRQMXQWRV X ^p _ d p d L P LQli HLQWHLURi m` Y ^q _ d q d W P LQwi HLQWHLURi m` Z ^r _ d r d H P LQhi HLQWHLURi m` i i i + HU]H&KULVWRILGHVH: KLWORFNREVHUYDUDP TXHHP XP GDGR SDGUmRGHHP SDFRWDP HQWRRXGHFRUWHFDGDFDL[DHP SDFRWDGDSRGHVHUP RYLGDSDUDEDL[R HRXSDUDIUHQWHHRXSDUDHVTXHUGDDWpTXHVXDVIDFHVLQIHULRUODWHUDOGDIUHQWHHODWHUDO HVTXHUGDILTXHP DGMDFHQWHVjVGHP DLVFDL[DVRXDRSUySULRFRQWrLQHU(VWHVSDGU}HV FKDP DGRVpadrões normaisRXcombinações cônicasSHUP LWHP VHP SHUGDGHJHQHUDOLGDGH UHGX]LURVFRQMXQWRVX Y HZ SDUD ¦ m X ^p _p Y ^q _q ¦ i i Z ^r _r ¦ i i m m H li d p d L P LQli d Hi d bi HLQWHLURi m` H wi d q d W P LQwi d Hi d bi HLQWHLURi m` H hi d r d H P LQhi d Hi d bi HLQWHLURi m` i i i i i $ )LJXUDLOXVWUDXP H[HP SORQXP pULFRFRP RVFRQMXQWRV X H Y DSUHVHQWDGRVSDUDRFDVRQmRJXLOKRWLQDGRELGLP HQVLRQDOHVFROKLGRDTXLSRUIDFLOLGDGHGH YLVXDOL]DomRSRUH[HP SORRFRUWHGHXP DSODFD&RQVLGHUDVHXP DSODFDFRP GLP HQV}HV LW HTXDWURWLSRVGHLWHQVFRP GLP HQV}HV lw l w lw Hl w ¬ HVTXHUGDHVWmRRVFRQMXQWRVUHVXOWDQWHVGLVSRVWRVVHJXQGR HHjGLUHLWDHVWmRRVFRQMXQWRVUHVXOWDQWHVGLVSRVWRVVHJXQGR H1 RFDVRjHVTXHUGDKiSRVVtYHLVSRVLo}HVSDUDVHDUUDQMDUDVSHoDVQDSODFD HQTXDQWRQRFDVRjGLUHLWDHVWHQ~P HURFDLSDUDXP DUHGXomRGHP DLVGH )LJXUD([HP SORQXP pULFRFRP RVFRQMXQWRVX HY )RQWHDGDSWDGRGH0 RUDELWR 6HMDP DLQGDRVFRQMXQWRVGHILQLGRVFRP RDVHJXLU Xi ^p X _ d p d L li ` i m Yi ^q Y _ d q d W wi ` i m Zi ^r Z _ d r d H hi ` i m &RP EDVHQHVWDQRWDomRGHFRQMXQWRVDIRUP XODomRSRGHVHUUHHVFULWD FRQIRUP HDEDL[R m P D[ ¦ ¦ ¦ ¦ v x i ipqr s X t Y u Z i m i m p X i q Yi r Z i i p X i qYi r Zi 6XMHLWRD m ¦¦ ¦¦a ipqrstu xipqr d i p X i qYi r Z i ¦¦¦x ipqr d bi p X i qYi r Zi xipqr ^` 1 RWHTXHSRUVLP SOLFLGDGHDVUHVWULo}HVFRQWHP SODP DSHQDVRQ~P HUR P i[LP RGHUpSOLFDVGDFDL[Di TXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHUDTXLGHILQLGR FRP Rbi DRLQYpVGHDSUHVHQWDURVQ~P HURVP tQLP RHP i[LP R $ OpP GLVVRSDUDHFRQRP L]DUP HP yULDFRP SXWDFLRQDODRFRP SLODURP RGHOR HP * $ 0 6DH[SUHVVmRSRGHVHUUHHVFULWDFRQIRUP HDEDL[RGHP RGRD FRQVLGHUDUDIXQomRaipqrstu LP SOLFLWDP HQWHHFRP LVVRQmRSUHFLVDUGHWHUP LQDUa prioriRV YDORUHVGHVWDIXQomR m ¦ ¦ ¦ ¦ xipqr d s X t Y u Z i ^ p X i _s li d p ds`^qYi _t wi dq dt `^r Zi _u hi dr du ` %HDVOH\DLQGDGLVFXWHFRP RHVWHQGHUVXDIRUP XODomRSDUDWUDWDULR FRUWHGHSHoDVDSDUWLUGHP ~OWLSORVUHWkQJXORVLLRFRUWHGHSHoDVDSDUWLUGHUHWkQJXORVFRP DSUHVHQoDGHGHIHLWRVLLLRFRUWHGHSHoDVDSDUWLUGHUHWkQJXORVFRP RXDVSHoDVRXRV UHWkQJXORVRXDP ERVVHQGRQmRUHWDQJXODUHV$ VLGpLDVDSUHVHQWDGDVHP LHLLSRGHP VHU XWLOL]DGDVSDUDIRUP XODUSUREOHP DVHFDUUHJDP HQWRGHP ~OWLSORVFRQWrLQHUHVFRP GLP HQV}HV LJXDLVRXGLIHUHQWHV 3RUVLP SOLFLGDGHFRQVLGHUHGRLVFRQWrLQHUHVSRVLFLRQDGRVXP DRODGRGRRXWUR HP SRVLo}HVpeSRVVtYHOGHILQLUXP ³VXSHUFRQWrLQHU´IRUP DGRSHODXQLmRGHVWHVGRLV FRQWrLQHUHVYHMD)LJXUD )LJXUD6XSHUFRQWrLQHUIRUP DGRSHODXQLmRGHGRLVFRQWrLQHUHV eSRVVtYHOUHGHILQLUDYDULiYHOGHGHFLVmR xipqr GHP RGRDLP SHGLUTXHDV FDL[DVVHMDP HP SDFRWDGDVDRORQJRGDVMXQo}HVGRVFRQWrLQHUHV$ VVLP xipqr pLJXDODVHD FDL[Di pHP SDFRWDGDQDSRVLomRpqr WDOTXHi m L li d p d L SDUDR FRQWrLQHUSRVLFLRQDGRjHVTXHUGDGHWRGRVRVGHP DLVHSDUDRVFRQWrLQHUHVLQWHUP HGLiULRVRX L L li d p d L L SDUDRFRQWrLQHUSRVLFLRQDGRjGLUHLWDGHWRGRVRVGHP DLV d q d W wi H d r d H hi 6HMDDLQGD D RFRQMXQWRGHWRGRVRVSRQWRVTXHHVWmRQRVREVWiFXORV ³GHIHLWRV´SUHVHQWHVGHQWURGRVFRQWrLQHUHVeSRVVtYHOUHHVFUHYHUDVUHVWULo}HVGH P RGRDLP SHGLUTXHDVFDL[DVVHMDP HP SDFRWDGDVDRORQJRGHVWHVREVWiFXORV³GHIHLWRV´DV UHVWULo}HVWDP EpP SRGHP VHUUHHVFULWDVGHP DQHLUDDQiORJD m ¦¦ ¦¦a ipqrstu i p X i qYi r Zi xipqr s t u D & 2 1 6,' (5 $ 1 ' 2 0 Ò /7,3/$ 62 5 ,(1 7$ d ® (6' $ 6& $ ,; $ 6 $ VP ~OWLSODVorientaçõesGDVFDL[DVWUDWDP VLWXDo}HVHP TXHRSHVVRDO HQFDUUHJDGRGHID]HURFDUUHJDP HQWRGDVFDL[DVGHQWURGHXP FRQWrLQHUVHGHSDUDSRU H[HP SORFRP LQVWUXo}HVGRWLSR³HVWHODGRSDUDFLP D´HVFULWDVQDVHP EDODJHQV(VWHpXP FDVRLQWHUP HGLiULRTXHGHVFUHYHDSRVVLELOLGDGHTXHXP DGHWHUP LQDGDFDL[DWHP GHVHU URWDFLRQDGDHP WRUQRGRHL[RGDVXDEDVHHL[Rz SRGHQGRVHUFRORFDGDSRUWDQWRFRP XP D GHQWUHGXDVRULHQWDo}HVSRVVtYHLV$ OpP GHVWHFDVRLQWHUP HGLiULRSRGHKDYHURXWURVGRLV FDVRVH[WUHP RV(P XP H[WUHP RXP DGHWHUP LQDGDFDL[DWHP DSRVVLELOLGDGHGHVHU URWDFLRQDGDHP WRUQRGHWRGRVRVHL[RVHL[RVx y Hz SRGHQGRVHUFRORFDGDSRUWDQWR FRP XP DGHQWUHVHLVRULHQWDo}HVSRVVtYHLV(P RXWURH[WUHP RXP DGHWHUP LQDGDFDL[DQmR WHP DSRVVLELOLGDGHGHVHUURWDFLRQDGDHP WRUQRGHQHQKXP GRVHL[RVGHYHQGRVHUFRORFDGD SRUWDQWRFRP XP D~QLFDRULHQWDomRIL[D$ )LJXUDLOXVWUDWRGDVDVVHLVSRVVtYHLV RULHQWDo}HVFRP TXHXP DFDL[DSRGHVHFRORFDGDGHQWURGHXP FRQWrLQHUFDVRQmRKDMD QHQKXP DOLP LWDomRTXDQWRjRULHQWDomR1 RWHTXHDSULP HLUDHDWHUFHLUDRULHQWDo}HV GHVFUHYHP RFDVRHP TXHXP DFDL[DGHYHWHURULHQWDomRYHUWLFDOIL[D )LJXUD2 ULHQWDo}HVTXHXP DFDL[DSRGHWHUFRP URWDo}HVHP WRUQRGHWRGRVRVHL[RV $ IRUP XODomRFRQWHP SODDSHQDVRFDVRHP TXHDVFDL[DVGHYHP VHUFRORFDGDVGHQWURGHXP FRQWrLQHUFRP XP D~QLFDRULHQWDomRIL[D1 RHQWDQWRHVWD IRUP XODomR SRGH VHU IDFLOP HQWH HVWHQGLGD SDUD SHUP LWLU TXH DV FDL[DV SRVVDP VHU URWDFLRQDGDVHSRUWDQWRFRORFDGDVGHQWURGRFRQWrLQHUFRP P DLVGHXP DRULHQWDomR,VWR SRGHVHUWUDWDGRGHGXDVP DQHLUDV 8 P DP DQHLUDFRQVLVWHHP FRQVLGHUDUXP WLSRGHFDL[DFRP XP DRULHQWDomR GLIHUHQWHFRP RVHQGRXP DFDL[DGLIHUHQWH$ VVLP SRUH[HP SORSDUDRFDVRHP TXHKiVHLV SRVVtYHLVRULHQWDo}HVRQ~P HURGHWLSRVGHFDL[DVSDVVDDVHUm DRLQYpVGHDSHQDVm HD IRUP XODomRSRGHVHUUHHVFULWDFRQIRUP HDEDL[R m P D[ ¦ ¦ ¦ ¦ v x xipqr d s X t Y u Z d bj j m i ipqr i p X i qYi r Zi 6XMHLWRD m ¦¦ ¦¦a ipqrstu i p X i qYi r Zi j ¦ ¦¦¦x ipqr i j p X i qYi r Zi i m xipqr ^` p X i q Yi r Z i 1 RWHTXHQDVH[SUHVV}HVHRtQGLFH i YDULDDWp m HQTXDQWRQDH[SUHVVmRRtQGLFHj YDULDDWpm SRLVDFDL[Di VySRGHVHUFRORFDGDFRP XP DGHQWUHDVVHLVRULHQWDo}HVSRVVtYHLV1 RP DLVRSDSHOGDVH[SUHVV}HVGDIRUP XODomR pLGrQWLFRUHVSHFWLYDP HQWHDRSDSHOGDVH[SUHVV}HVGDIRUP XODomR 8 P DRXWUDP DQHLUDP DLVJHQpULFDFRQVLVWHHP GHILQLUXP tQGLFHg SDUDDV SRVVtYHLVRULHQWDo}HVFRP TXHDFDL[Di SRGHVHUFRORFDGDGHQWURGHXP FRQWrLQHU(VWDV SRVVtYHLVRULHQWDo}HVSRGHP VHUGHILQLGDVSRUP HLRGRFRQMXQWRRi ^`LVWRpRi pXP VXEFRQMXQWRGH^`FRP Ri z $ VVLP UHGHILQLQGRVHDYDULiYHOxigpqr D IRUP XODomRSRGHVHUUHHVFULWDFRQIRUP HDEDL[R m P D[ ¦ ¦ ¦ ¦ ¦ v x i igpqr s X t Y u Z i m i g Ri p X i qYi r Z i 6XMHLWRD m ¦¦ ¦ ¦¦a igpqrstu xigpqr d i g Ri p X i qYi r Zi ¦ ¦¦¦x igpqr d bi g Ri p X i qYi r Zi xigpqr ^` i mg Ri p X i q Yi r Z i 1 RWHTXHRSDSHOGDVH[SUHVV}HVGDIRUP XODomRpLGrQWLFR UHVSHFWLYDP HQWHDRSDSHOGDVH[SUHVV}HVGDIRUP XODomR & 2 1 6,' (5 $ 1 ' 2 / ,0 ,7(' (3(62 ' 2 & 2 1 7Ç,1 (5 2 limite de pesoGRFRQWrLQHUWUDWDVLWXDo}HVSRUH[HP SORHP TXHRFRQWrLQHU QmRHVWiSURMHWDGRSDUDVXSRUWDUXP FDUUHJDP HQWRFRP SHVRWRWDOP DLRUTXHXP OLP LWH P i[LP RSHUP LWLGR8 P DP DQHLUDGHWUDWDUHVWDVLWXDomRFRQVLVWHHP GHILQLUXP SDUkP HWURPi SDUDRSHVRGDFDL[Di HXP SDUkP HWURPP D[ SDUDRSHVRP i[LP RTXHSRGHVHUFDUUHJDGR GHQWURGRFRQWrLQHU$ VVLP DUHVWULomRGHOLP LWHGHSHVRGHQWURGRFRQWrLQHUSRGHVHU IRUP XODGDFRP RXP DUHVWULomRGRWLSRP RFKLOD m ¦ ¦ ¦ ¦ P x i ipqr d PP D[ i p X i qYi r Z i 2 XVHMDRSHVRWRWDOGHFDL[DVFDUUHJDGDVGHQWURGRFRQWrLQHUQmRGHYHH[FHGHU ROLP LWHGHSHVRVXSRUWDGRSHORP HVP R & 2 1 6,' (5 $ 1 ' 2 ( 67$ %,/,' $ ' (' 2 & $ 5 5 (* $ 0 (1 72 $ estabilidadeGRFDUUHJDP HQWRSRGHVHUGLYLGLGDHP GXDVFRP SRQHQWHVD HVWDELOLGDGHYHUWLFDOHDHVWDELOLGDGHKRUL]RQWDO$ HVWDELOLGDGHverticalHVWiUHODFLRQDGDj FDSDFLGDGHGDVFDL[DVHP XP FDUUHJDP HQWRGHUHVLVWLUHP jDWXDomRGDDFHOHUDomRGD JUDYLGDGHVREUHVHXVFRUSRVLVWRpGHQmRVHGHVORFDUHP HP UHODomRDRHL[R z (VWD FRP SRQHQWHGDHVWDELOLGDGHpWDP EpP FKDP DGDGHHVWDELOLGDGHestáticaXP DYH]TXHWUDWDR FDUUHJDP HQWRHP VLWXDo}HVHP TXHRFRQWrLQHURXFDP LQKmRHVWiSDUDGR$ HVWDELOLGDGH horizontalSRUVXDYH]HVWiUHODFLRQDGDjFDSDFLGDGHGDVFDL[DVHP XP FDUUHJDP HQWRGH UHVLVWLUHP jDWXDomRGDLQpUFLDGRVVHXVSUySULRVFRUSRVLVWRpGHQmRVHGHVORFDUHP HP UHODomRDRVHL[RVx Hy (VWDFRP SRQHQWHGDHVWDELOLGDGHpWDP EpP FKDP DGDGHHVWDELOLGDGH dinâmicaXP DYH]TXHWUDWDRFDUUHJDP HQWRHP VLWXDo}HVHP TXHRFRQWrLQHURXFDP LQKmR HVWiVHQGRGHVORFDGRKRUL]RQWDOP HQWHHILFDLQHYLWDYHOP HQWHVXMHLWRDYDULDo}HVQD YHORFLGDGHDFHOHUDomRGRGHVORFDP HQWR (VWDVGXDVFRP SRQHQWHVVmRWUDWDGDVVHSDUDGDP HQWH (VWDELOLGDGHYHUWLFDO $ HVWDELOLGDGHYHUWLFDOFRP RWUDWDGDHVWDELOLGDGHHP UHODomRDRHL[Rz VH UHIHUHSRUWDQWRDRVXSRUWHGDIDFHLQIHULRUGHFDGDFDL[D$ VVLP GHP RGRD³P DSHDU´R FRQMXQWRGHSRQWRVTXHXP DGHWHUP LQDGDFDL[DSRGH³RIHUHFHU´SDUDVXSRUWDUFDL[DV FRORFDGDVLP HGLDWDP HQWHVREUHVXDIDFHVXSHULRUVHMDDIXQomRcipqrst r hi GHILQLGDFRP R cipqrst r hi IXQomRELQiULDTXHpLJXDODVHDFDL[Di TXDQGRHP SDFRWDGDFRP VHXFDQWR LQIHULRUIURQWDOHVTXHUGRQDSRVLomRpqr FRQWpP RSRQWRGHILQLGRSHODSRVLomR s t r hi QDVXDIDFHsuperiorFDVRFRQWUiULRHODpLJXDOD $ ULJRURtQGLFHr hi pUHGXQGDQWHP DVIRLDTXLP DQWLGRSRUFRQYHQLrQFLDGH QRWDomR1 RWHTXHDIXQomRcipqrst r hi DVVLP FRP RDIXQomRaipqrstu YHMDVHomRQmRp XP DYDULiYHOGHGHFLVmRGRP RGHORHWDP EpP SRGHVHUFRP SXWDGDa prioriLVWRpDQWHVGD UHVROXomRGRP RGHORGDVHJXLQWHP DQHLUD cipqrst r hi VH d p d s d p li d L ° d q d t d q w d W H ° i ® d r d H h i ° ° ¯FDVRFRQWUiULR 1 RWHDLQGDTXHcipqrst r hi pGHILQLGDDQDORJDP HQWHjaipqrstu FRP DGLIHUHQoDGH TXHDSULP HLUD³P DSHLD´VRP HQWHRFRQMXQWRGHSRQWRVGDIDFHVXSHULRUGDFDL[Di QDSRVLomR pqr HD~OWLP D³P DSHLD´RFRQMXQWRGHSRQWRVFRQWLGRVGHQWURGDFDL[Di QDSRVLomR pqr H[FHWXDQGRVHRVSRQWRVFRQWLGRVQDVIDFHVVXSHULRUODWHUDOGRIXQGRHODWHUDOGLUHLWD GDP HVP D $ )LJXUDLOXVWUDRP DSHDP HQWRGHVVHFRQMXQWRGHSRQWRVSDUDGXDVFDL[DV FRORFDGDVGHQWURGHXP FRQWrLQHUHP TXHDIDFHLQIHULRUGDFDL[D j HVWiSDUFLDOP HQWH VXSRUWDGDSHODIDFHVXSHULRUGDFDL[Di (VWHP DSHDP HQWRVLJQLILFDGHWHUP LQDUSDUDDFDL[Di FRORFDGDQDSRVLomRpqr WRGRVRVSRVVtYHLVSRQWRVs t r hi TXHHVWDFDL[DSRGH ³RIHUHFHU´SDUDVXSRUWHGHRXWUDFDL[D j TXDOTXHUFRORFDGDQDSRVLomRp q r FRP r r hi LVWRpFRP DVFDL[DVHP FRQWDWR )LJXUD0 DSHDP HQWRGRFRQMXQWRGHSRQWRVGDIDFHVXSHULRUGDFDL[Di HVWDELOLGDGHYHUWLFDO±HP UHODomRDRHL[Rz $ OpP GLVVRSRGHVHUGHILQLGRXP SDUkP HWURD >@FKDP DGRGHSDUkP HWUR GHHVWDELOLGDGHHP UHODomRDRHL[Rz RXSDUkP HWURGHHVWDELOLGDGHYHUWLFDO(VWHSDUkP HWURp FRP XP QDOLWHUDWXUDGHFDUUHJDP HQWRGHFRQWrLQHUHV(/(< HLQGLFDRSHUFHQWXDOGH HVWDELOLGDGHYHUWLFDOTXHVHGHVHMDSDUDWRGDVDVFDL[DV(P XP H[WUHP RD LQGLFDTXHDV IDFHVLQIHULRUHVGHWRGDVDVFDL[DVGHYHP HVWDU VXSRUWDGDVSHODVIDFHVVXSHULRUHVGH XP DRXP DLVFDL[DVFRORFDGDVLP HGLDWDP HQWHDEDL[RGHODVHQRRXWURH[WUHP RD LQGLFD TXHQmRKiH[LJrQFLDVTXDQWRjHVWDELOLGDGHGDVFDL[DVHP UHODomRDRHL[Rz SRUH[HP SORDV FDL[DVSRGHP HVWDUDSHQDVSDUFLDOP HQWHVXSRUWDGDVRXP HVP R³IOXWXDQGR´GHQWURGR FRQWrLQHU &RQVLGHUDQGRVHRVFRQMXQWRVX Y HZ GHILQLGRVFRQIRUP HH UHVSHFWLYDP HQWHDUHVWULomRGHHVWDELOLGDGHHP UHODomRDRHL[Rz SRGHVHUIRUP XODGD FRP R ¦ ¦¦ ¦ ¦ ^i m _r hi t` p X i q Yi ^s X _p d s d p l j `^t Y _q dt d q w j ` cipq r h str xipq r h t D l j w j x jp q r i i j m p X j q Y j r Z j ^` 2 XVHMDXP DIUDomRP tQLP DD GRVSRQWRVGDIDFHLQIHULRUGDFDL[D j GHYH HVWDUVXSRUWDGDSHORVSRQWRV³P DSHDGRV´GDVIDFHVVXSHULRUHVGHFDL[DVi TXDLVTXHUTXH HVWHMDP FRORFDGDVLP HGLDWDP HQWHDEDL[RGDFDL[Dj HP FRQWDWRFRP HVWDYHMD)LJXUD 1 RWHHP TXHr Z j ^`DRLQYpVGHr Z j SRUTXHXP DFDL[DFRORFDGDVREUHRSLVR GRFRQWrLQHULVWRpr VHP SUHWHP HVWDELOLGDGHHP UHODomRDRHL[Rz 6LP LODUP HQWHDRTXHIRLIHLWRFRP DH[SUHVVmRDH[SUHVVmR WDP EpP SRGHVHUUHHVFULWDFRQIRUP HDEDL[RGHP RGRDFRQVLGHUDUDIXQomR cipqrst r hi LP SOLFLWDP HQWHHFRP LVVRQmRSUHFLVDUGHWHUP LQDUa prioriRVYDORUHVGHVWDIXQomR P LQp li p l j P LQq wi q w j ¦ ¦ ¦ ^i m_r hi t`^p X i _p li d pd p l j `^qYi _q wi dqdq w j ` ¦ ¦ s P D[p p t P D[q q xipq r h t D l j w j x jp q r i j m p X j q Y j r Z j ^` 4 XHSRGHVHUUHHVFULWDFRP R ¦ ¦ ¦ />ij@ : ij>@ xipq r h t D l j w j x jp q r i ^i m _r hi t `^ p X i _p li d p d p l j `^q Yi _q wi d q d q w j ` >@ °/ij P LQp li p l j P D[pp FRP ® >@ P LQq wi q w j P D[qq °̄: ij j m p X j q Y j r Z j ^` 1 RHQWDQWRDVIRUP XODo}HVHQmRVmRVHP SUHYiOLGDVTXDQGR VHFRQVLGHUDP RVFRQMXQWRV X Y H Z GHILQLGRVFRQIRUP HH UHVSHFWLYDP HQWHSDGU}HVQRUP DLVSRLVFRP DXWLOL]DomRGHVWHVSRGHRFRUUHUDIRUP DomRGH ³EXUDFRV´QDIDFHVXSHULRUGDFDL[Di SDVVDQGRHVWDDQmRP DLVFRQWULEXLUFRP WRGRVRV SRQWRVs t r hi TXHHODFRQWULEXtDDQWHULRUP HQWHXWLOL]DQGRHYHMD )LJXUDSDUDXP P DLRUHVFODUHFLP HQWRVREUHRWHUP R³EXUDFRV´' HP RGRDFRQWRUQDUHVWD GLILFXOGDGHXP DIRUP XODomRDOWHUQDWLYDGDVUHVWULo}HVGHHVWDELOLGDGHHP UHODomRDRHL[Rz RXpSURSRVWD ¦ ¦ ¦ >@ />@ ij : ij xipq r h t D l j w j x jp q r i ^i m _r hi t `^ p X i _p li d p d p l j `^q Yi _q wi d q d q w j ` >@ °/ij P LQp li p l j P D[pp FRP ® >@ P LQq wi q w j P D[qq °̄: ij j m p X j q Y j r Z j ^` 2 XVHMDXP DIUDomRP tQLP DD GDiUHDGDIDFHLQIHULRUGDFDL[Dj GHYHHVWDU VXSRUWDGDSHODViUHDVGDVIDFHVVXSHULRUHVGHFDL[DVi TXDLVTXHUTXHWHQKDP DVSURMHo}HV GHVWDViUHDVFRP XQVHP UHODomRjFDL[Dj HTXHHVWHMDP FRORFDGDVLP HGLDWDP HQWHDEDL[RGD FDL[Dj HP FRQWDWRFRP HVWDYHMD)LJXUD1 RWHTXHDUHVWULomRDRFRQWUiULRGDV UHVWULo}HVRXpYiOLGDP HVP RTXDQGRKiDIRUP DomRGH³EXUDFRV´QDIDFH VXSHULRUGDFDL[Di LVWRppYiOLGDSDUDX Y HZ GHILQLGRVFRQIRUP HH )LJXUDÈ UHDGHFRQWDWRHQWUHGXDVFDL[DVQRSODQRxy HVWDELOLGDGHYHUWLFDO±HP UHODomRDRHL[Rz (VWDELOLGDGHKRUL]RQWDO $ HVWDELOLGDGHKRUL]RQWDOFRP RWUDWDGDHVWDELOLGDGHHP UHODomRDRVHL[RVx H y VHUHIHUHSRUWDQWRDRDSRLRGDVIDFHVODWHUDOGLUHLWDHODWHUDOGRIXQGRGHFDGDFDL[D UHVSHFWLYDP HQWH$ VUHVWULo}HVGHHVWDELOLGDGHKRUL]RQWDOVmRGHGX]LGDVGHP DQHLUDDQiORJDjV UHVWULo}HVGHHVWDELOLGDGHYHUWLFDOHSRUVLP SOLFLGDGHDVVXDVGXDVVXEFRP SRQHQWHVVmR DSUHVHQWDGDVHP SDUDOHOR $ VVLP GHP RGRD³P DSHDU´RFRQMXQWRGHSRQWRVTXHXP DGHWHUP LQDGDFDL[D SRGH³RIHUHFHU´SDUDDSRLDUFDL[DVFRORFDGDVLP HGLDWDP HQWHjGLUHLWDGDVXDIDFHODWHUDO GLUHLWDVHMDDIXQomRdipqr p li tu GHILQLGDFRP R dipqr p li tu IXQomRELQiULDTXHpLJXDODVHDFDL[Di TXDQGRHP SDFRWDGDFRP VHXFDQWR LQIHULRUIURQWDOHVTXHUGRQDSRVLomRpqr FRQWpP RSRQWRGHILQLGRSHODSRVLomR p li t u QDVXDIDFHlateral direitaFDVRFRQWUiULRHODpLJXDOD 6LP LODUP HQWHGHP RGRD³P DSHDU´RFRQMXQWRGHSRQWRVTXHXP DGHWHUP LQDGD FDL[DSRGH³RIHUHFHU´SDUDDSRLDUFDL[DVFRORFDGDVLP HGLDWDP HQWHDRIXQGRGDVXDIDFHODWHUDO GRIXQGRVHMDDIXQomReipqrs q wi u GHILQLGDFRP R eipqrs q wi u IXQomRELQiULDTXHpLJXDODVHDFDL[Di TXDQGRHP SDFRWDGDFRP VHXFDQWR LQIHULRUIURQWDOHVTXHUGRQDSRVLomR pqr FRQWpP RSRQWRGHILQLGRSHODSRVLomR sq wi u QDVXDIDFHlateral do fundoFDVRFRQWUiULRHODpLJXDOD 1 RWHTXHDVIXQo}HVdipqr p li tu Heipqrs q wi u DVVLP FRP RDIXQomRcipqrst r hi GD HVWDELOLGDGHHP UHODomRDRHL[Rz QmRVmRYDULiYHLVGHGHFLVmRGRP RGHORHWDP EpP SRGHP VHUFRP SXWDGDVa prioriLVWRpDQWHVGDUHVROXomRGRP RGHORGDVHJXLQWHP DQHLUD dipqr p li tu VH d p d L li ° d q d t d q w d W H ° i eipqrs q wi u ® d r d u d r h i d H ° ° ¯FDVRFRQWUiULR VH d p d s d p li d L ° d q d W w H ° i ® d r d u d r hi d H ° ° ¯FDVRFRQWUiULR $ ULJRURVtQGLFHVp li Hq wi VmRUHGXQGDQWHVP DVIRUDP DTXLP DQWLGRV SRU FRQYHQLrQFLD GH QRWDomR 1 RWH DLQGD TXH dipqr p li tu H eipqrs q wi u VmR GHILQLGDV DQDORJDP HQWHjcipqrst r hi FRP DGLIHUHQoDGHTXHDVSULP HLUDV³P DSHLDP ´RVFRQMXQWRVGH SRQWRVGDVIDFHVODWHUDOGLUHLWDHODWHUDOGRIXQGRUHVSHFWLYDP HQWHGDFDL[Di QDSRVLomR pqr HD~OWLP D³P DSHLD´RFRQMXQWRGHSRQWRVGDIDFHVXSHULRUGDFDL[Di QDSRVLomR pqr $ )LJXUDLOXVWUDRP DSHDP HQWRGHVVHVFRQMXQWRVGHSRQWRVSDUDGXDVFDL[DV FRORFDGDVGHQWURGHXP FRQWrLQHU1 RFDVRGDHVTXHUGDDIDFHODWHUDOHVTXHUGDGDFDL[Dj HVWiSDUFLDOP HQWHDSRLDGDSHODIDFHODWHUDOGLUHLWDGDFDL[Di HHVWHP DSHDP HQWRVLJQLILFD t u GHWHUP LQDUSDUDDFDL[Di FRORFDGDQDSRVLomRpqr WRGRVRVSRVVtYHLVSRQWRVp li TXHHVWDFDL[DSRGH³RIHUHFHU´SDUDDSRLRGHRXWUDFDL[D j TXDOTXHUFRORFDGDQDSRVLomR p q r FRP p p li LVWRpFRP DVFDL[DVHP FRQWDWR1 RFDVRGDGLUHLWDDIDFHODWHUDO GDIUHQWHGDFDL[Dj HVWiSDUFLDOP HQWHDSRLDGDSHODIDFHODWHUDOGRIXQGRGDFDL[Di HHVWH P DSHDP HQWRVLJQLILFDGHWHUP LQDUSDUDDFDL[Di FRORFDGDQDSRVLomRpqr WRGRVRV SRVVtYHLVSRQWRVsq wi u TXHHVWDFDL[DSRGH³RIHUHFHU´SDUDDSRLRGHRXWUDFDL[D j TXDOTXHUFRORFDGDQDSRVLomRp q r FRP q q wi LVWRpFRP DVFDL[DVHP FRQWDWR )LJXUD0 DSHDP HQWRGRVFRQMXQWRVGHSRQWRVGDVIDFHVODWHUDOGLUHLWDHODWHUDOGRIXQGRGDFDL[Di HVWDELOLGDGHKRUL]RQWDO±HP UHODomRDRVHL[RVx Hy $ OpP GLVVRDVVLP FRP RRSDUkP HWURD QRFDVRGDHVWDELOLGDGHYHUWLFDO SRGHP VHUGHILQLGRVGRLVSDUkP HWURVEJ >@FKDP DGRVGHSDUkP HWURVGHHVWDELOLGDGHHP UHODomRDRVHL[RVx Hy UHVSHFWLYDP HQWHRXSDUkP HWURVGHHVWDELOLGDGHKRUL]RQWDO1 RFDVR GDHVWDELOLGDGHHP UHODomRDRHL[Rx E LQGLFDTXHDVIDFHVODWHUDLVHVTXHUGDVGHWRGDVDV FDL[DVGHYHP HVWDU DSRLDGDVSHODVIDFHVODWHUDLVGLUHLWDVGHXP DRXP DLVFDL[DV FRORFDGDVLP HGLDWDP HQWHjHVTXHUGDGHODVHE LQGLFDTXHQmRKiH[LJrQFLDVTXDQWRj HVWDELOLGDGHGDVFDL[DVHP UHODomRDRHL[R x 6LP LODUP HQWHQRFDVRGDHVWDELOLGDGHHP UHODomRDRHL[Ry J LQGLFDTXHDVIDFHVODWHUDLVGDIUHQWHGHWRGDVDVFDL[DVGHYHP HVWDU DSRLDGDVSHODVIDFHVODWHUDLVGRIXQGRGHXP DRXP DLVFDL[DVFRORFDGDVLP HGLDWDP HQWH jIUHQWHGHODVHJ LQGLFDTXHQmRKiH[LJrQFLDVTXDQWRjHVWDELOLGDGHGDVFDL[DVHP UHODomRDRHL[Ry &RQVLGHUDQGRVHRVFRQMXQWRVX Y HZ GHILQLGRVFRQIRUP HH UHVSHFWLYDP HQWHDVUHVWULo}HVGHHVWDELOLGDGHHP UHODomRDRVHL[RV x H y UHVSHFWLYDP HQWHSRGHP VHUIRUP XODGDVFRP R ¦ ¦¦ ¦ ¦ ^i m _p li t ` q Yi r Zi ^t Y _q dt d q w j `^u Z _r du d r h j ` di p l qrp tu xi p l qr t Ew j h j x jp q r i i j m p X j ^`q Y j r Z j ¦ ¦¦ ¦ ¦ ^i m _q wi t ` p X i r Zi ^s X _p d s d p l j `^u Z _r du d r h j ` eip q w rsq u xip q w r t Jl j h j x jp q r i i j m p X j q Y j ^`r Z j 2 XVHMDXP DIUDomRP tQLP DE GRVSRQWRVGDIDFHODWHUDOHVTXHUGDGDFDL[Dj GHYHHVWDUDSRLDGDSHORVSRQWRV³P DSHDGRV´GDVIDFHVODWHUDLVGLUHLWDVGHFDL[DV i TXDLVTXHUTXHHVWHMDP FRORFDGDVLP HGLDWDP HQWHjHVTXHUGDGDFDL[Dj HP FRQWDWRFRP HVWD YHMD)LJXUD1 RWHHP TXH p X j ^`DRLQYpVGH p X j SRUTXHXP DFDL[D FRORFDGDjGLUHLWDGDSDUHGHHVTXHUGDGRFRQWrLQHULVWRpp VHP SUHWHP HVWDELOLGDGHHP UHODomRDRHL[Rx 6LP LODUP HQWHXP DIUDomRP tQLP DJGRVSRQWRVGDIDFHODWHUDOGDIUHQWHGD FDL[Dj GHYHHVWDUDSRLDGDSHORVSRQWRV³P DSHDGRV´GDVIDFHVODWHUDLVGRIXQGRGHFDL[DVi TXDLVTXHUTXHHVWHMDP FRORFDGDVLP HGLDWDP HQWHjIUHQWHGDFDL[D j HP FRQWDWRFRP HVWD YHMD)LJXUD1 RWHWDP EpP HP TXHq Y j ^`DRLQYpVGHq Y j SRUTXHXP D FDL[DFRORFDGDDRIXQGRGDSDUHGHGDIUHQWHGRFRQWrLQHULVWRp q VHP SUHWHP HVWDELOLGDGHHP UHODomRDRHL[Ry 6LP LODUP HQWHDRTXHIRLIHLWRFRP DH[SUHVVmRDVH[SUHVV}HVH WDP EpP SRGHP VHUUHHVFULWDVFRQIRUP HDEDL[RGHP RGRDFRQVLGHUDUDVIXQo}HV dipqr p li tu Heipqrs q wi u LP SOLFLWDP HQWHHFRP LVVRQmRSUHFLVDUGHWHUP LQDUa prioriRVYDORUHV GHVWDVIXQo}HV P LQq wi q w j P LQr hi r h j ¦ ¦ ¦ ^i m_p li t`^qYi _q wi dqdq w j `^r Zi _r hi dr dr h j ` ¦ ¦ t P D[q q u P D[r r xi p l qr t E w j h j x jp q r i j m p X j ^`q Y j r Z j P LQp li p l j P LQr hi r h j ¦ ¦ ¦ ^i m_q wi t`^ p X i _p li d pd p l j `^r Z i _r hi dr dr h j ` ¦ ¦ s P D[p p u P D[r r xip q w r t Jl j h j x jp q r i j m p X j q Y j ^`r Z j 4 XHSRGHP VHUUHHVFULWDVFRP R ¦ ¦ ¦ : ij>@ + >ij@ xi p l qr t Ew j h j x jp q r i ^i m _p li t `^q Yi _q wi d q d q w j `^r Zi _r hi d r d r h j ` >@ P LQq wi q w j P D[qq °: ij FRP ® >@ °̄+ ij P LQr hi r h j P D[r r j m p X j ^`q Y j r Z j ¦ ¦ ¦ ^i m_q wi t `^p X i _p li d p d p l j `^r Z i _r hi d r d r h j ` />ij@ + >ij@ xip q w r t Jl j h j x jp q r >@ °/ij P LQp li p l j P D[pp FRP ® >@ + P L Q r h r h P D[ r r °̄ ij i j i j m p X j q Y j ^`r Z j 1 RHQWDQWRDVIRUP XODo}HVHSDUDDHVWDELOLGDGHHP UHODomR DRHL[Rx QmRVmRVHP SUHYiOLGDVTXDQGRVHFRQVLGHUDP RVFRQMXQWRVX Y HZ GHILQLGRV FRQIRUP HHUHVSHFWLYDP HQWHSDGU}HVQRUP DLVSRLVFRP DXWLOL]DomR GHVWHVSRGHRFRUUHUDIRUP DomRGH³EXUDFRV´QDIDFHODWHUDOGLUHLWDGDFDL[Di SDVVDQGRHVWDD QmRP DLVFRQWULEXLUFRP RVSRQWRVp li t u TXHHODFRQWULEXtDDQWHULRUP HQWHXWLOL]DQGR H6LP LODUP HQWHDVIRUP XODo}HVHSDUDDHVWDELOLGDGH HP UHODomRDRHL[Ry QmRVmRVHP SUHYiOLGDVTXDQGRVHFRQVLGHUDP RVFRQMXQWRVX Y HZ GHILQLGRVFRQIRUP HHUHVSHFWLYDP HQWHSDGU}HVQRUP DLVSRLVFRP D XWLOL]DomRGHVWHVSRGHRFRUUHUDIRUP DomRGH³EXUDFRV´QDIDFHODWHUDOGRIXQGRGDFDL[Di SDVVDQGRHVWDDQmRP DLVFRQWULEXLUFRP RVSRQWRV sq wi u TXHHODFRQWULEXtD DQWHULRUP HQWHXWLOL]DQGRH' HP RGRDFRQWRUQDUHVWDGLILFXOGDGH IRUP XODo}HVDOWHUQDWLYDVGDVUHVWULo}HVGHHVWDELOLGDGHHP UHODomRDRHL[Rx RX HGDVUHVWULo}HVGHHVWDELOLGDGHHP UHODomRDRHL[R y RXVmR SURSRVWDV ¦ ¦ ¦ : ij>@ + >@ ij xi p l qr t Ew j h j x jp q r i ^i m _p li t`^q Yi _q wi d q d q w j `^r Zi _r hi d r d r h j ` >@ P LQq wi q w j P D[qq °: ij FRP ® >@ + P L Q r h r h P D[ r r °̄ ij i j j m p X j ^`q Y j r Z j ¦ ¦ ¦ ^i m _q wi t`^ p X i _p li d p d p l j `^r Zi _r hi d r d r h j ` >@ °/ij P LQp li p l j P D[pp FRP ® >@ P LQr hi r h j P D[r r °̄+ ij >@ />@ ij + ij xip q w r t Jl j h j x jp q r i j m p X j q Y j ^`r Z j 2 XVHMDXP DIUDomRP tQLP DE GDiUHDGDIDFHODWHUDOHVTXHUGDGDFDL[D j GHYHHVWDUDSRLDGDSHODViUHDVGDVIDFHVODWHUDLVGLUHLWDVGHFDL[DVi TXDLVTXHUTXHWHQKDP DV SURMHo}HVGHVWDViUHDVFRP XQVHP UHODomRjFDL[Dj HTXHHVWHMDP FRORFDGDVLP HGLDWDP HQWH jHVTXHUGDGDFDL[Dj HP FRQWDWRFRP HVWDYHMD)LJXUD1 RWHTXHDUHVWULomRSDUD DHVWDELOLGDGHHP UHODomRDRHL[Rx DRFRQWUiULRGDVUHVWULo}HVRXpYiOLGD P HVP RTXDQGRKiDIRUP DomRGH³EXUDFRV´QDIDFHODWHUDOGLUHLWDGDFDL[Di LVWRppYiOLGD SDUDX Y HZ GHILQLGRVFRQIRUP HH6LP LODUP HQWHXP DIUDomRP tQLP D JGDiUHDGDIDFHODWHUDOGDIUHQWHGDFDL[Dj GHYHHVWDUDSRLDGDSHODViUHDVGDVIDFHVODWHUDLV GRIXQGRGHFDL[DVi TXDLVTXHUTXHWHQKDP DVSURMHo}HVGHVWDViUHDVFRP XQVHP UHODomRj FDL[Dj HTXHHVWHMDP FRORFDGDVLP HGLDWDP HQWHjIUHQWHGDFDL[Dj HP FRQWDWRFRP HVWD YHMD)LJXUD1 RWHWDP EpP TXHDUHVWULomRSDUDDHVWDELOLGDGHHP UHODomRDRHL[R y DRFRQWUiULRGDVUHVWULo}HVRXpYiOLGDP HVP RTXDQGRKiDIRUP DomRGH ³EXUDFRV´QDIDFHODWHUDOGRIXQGRGDFDL[Di LVWRppYiOLGDSDUDX Y HZ GHILQLGRV FRQIRUP HH )LJXUDÈ UHDVGHFRQWDWRHQWUHGXDVFDL[DVQRVSODQRVyz Hxz HVWDELOLGDGHKRUL]RQWDO±HP UHODomRDRVHL[RVx Hy 1 RWHTXHQRFDVRGDHVWDELOLGDGHYHUWLFDOQmRKiH[LJrQFLDGHTXHDVIDFHV VXSHULRUHVGDVFDL[DVHVWHMDP HP FRQWDWRFRP DVIDFHVLQIHULRUHVGHRXWUDVFDL[DVRXFRP R WHWRGRFRQWrLQHU,VWRSRUTXHQHVWDFRP SRQHQWHGDHVWDELOLGDGHLP SRUWDTXHDSHQDVDVIDFHV LQIHULRUHVGDVFDL[DVHVWHMDP VXSRUWDGDVLVWRpHP FRQWDWRFRP RXWUDVFDL[DVRXFRP RSLVR GRFRQWrLQHU' HVVDP DQHLUDDVIDFHVVXSHULRUHVGDVFDL[DVTXHHVWmRDFLP DGHWRGDVDVRXWUDV HP XP SDGUmRGHHP SDFRWDP HQWRSRGHP HVWDU³GHVFREHUWDV´RTXHQmRLP SOLFDHP XP FDUUHJDP HQWRYHUWLFDOP HQWHLQVWiYHO1 RHQWDQWRQRFDVRGDHVWDELOLGDGHKRUL]RQWDOFRP Rp DTXLGHGX]LGDGHP DQHLUDDQiORJDDRFDVRGDHVWDELOLGDGHYHUWLFDOLVWRSRGHLP SOLFDUHP XP FDUUHJDP HQWRKRUL]RQWDOP HQWHLQVWiYHO,VWRSRUTXHQDVVXDVGXDVVXEFRP SRQHQWHVDVIDFHV ODWHUDLVGLUHLWDVGDVFDL[DVTXHHVWmRjGLUHLWDGHWRGDVDVRXWUDVHDVIDFHVODWHUDLVGRIXQGR GDVFDL[DVTXHHVWmRDRIXQGRGHWRGDVDVRXWUDVSRGHP HVWDU³GHVFREHUWDV´RTXHQmR LP SHGLULDTXHHVWDVFDL[DVVHGHVORFDVVHP SDUDDGLUHLWDHSDUDRIXQGRUHVSHFWLYDP HQWHH QmRHVWDULDP SRUWDQWRFRP HVWDELOLGDGHKRUL]RQWDOJDUDQWLGD 1 RHQWDQWRKiSHORP HQRVGXDVUD]}HVSDUDVHDFUHGLWDUTXHDVUHVWULo}HVGH HVWDELOLGDGHKRUL]RQWDOFRP RP RGHODGDVDFLP DFRQWLQXDP YiOLGDVSDUDGHVFUHYHUVLWXDo}HV SUiWLFDV8 P DUD]mRVHUHIHUHjSRVVLELOLGDGHGHRSHVVRDOHQFDUUHJDGRGHID]HUR FDUUHJDP HQWRGDVFDL[DVGHQWURGHXP FRQWrLQHUSRGHUFRORFDUHVSXP DVRXFDOoRVGHP DGHLUD SDUDLP SHGLUTXHHVWDV³~OWLP DV´FDL[DVVHGHVORTXHP QDKRUL]RQWDORTXHpXP DSUiWLFD FRP XP SRUH[HP SORQRFDUUHJDP HQWRGHFDP LQK}HVHP WUDQVSRUWDGRUDV$ RXWUDUD]mRp TXHH[LJLQGRTXHDP EDVDVIDFHVODWHUDOGLUHLWDHODWHUDOHVTXHUGDQRFDVRGDHVWDELOLGDGHHP UHODomRDRHL[R x HDP EDVDVIDFHVODWHUDOGRIXQGRHODWHUDOGDIUHQWHQRFDVRGD HVWDELOLGDGHHP UHODomRDRHL[Ry HVWHMDP HP FRQWDWRFRP RXWUDVFDL[DVOLP LWDEDVWDQWHRV SRVVtYHLVSDGU}HVGHHP SDFRWDP HQWR 3RUILP FRQYpP REVHUYDUTXHWRGDVDVGHILQLo}HVDSUHVHQWDGDVSDUDWUDWDUWDQWR DHVWDELOLGDGHYHUWLFDOTXDQWRDHVWDELOLGDGHKRUL]RQWDOVmRVLP SOLVWDVHSRUWDQWRIiFHLVGH VHUHP P RGHODGDV & 2 1 6,' (5 $ 1 ' 2 5 (6,67Ç1 & ,$ ' $ 6& $ ,; $ 6$ 2 ( 0 3,/+ $ 0 (1 72 $ UHVLVWrQFLDGDVFDL[DVDRempilhamentoWUDWDVLWXDo}HVHP TXHRSHVVRDO HQFDUUHJDGRGHID]HURFDUUHJDP HQWRGDVFDL[DVGHQWURGHXP FRQWrLQHUVHGHSDUDSRU H[HP SORFRP LQVWUXo}HVGRWLSR³HP SLOKDP HQWRP i[LP R[FDL[DV´HVFULWDVQDVHP EDODJHQV ,VWRpQmRpSHUP LWLGRHP SLOKDUVREUHXP DGHWHUP LQDGDFDL[DP DLVGRTXHXP Q~P HUR P i[LP RHVWLSXODGRGHFDL[DVQmRDSHQDVLP HGLDWDP HQWHDFLP DRXGHXP DRXWUDP DQHLUDD SUHVVmRWRWDOH[HUFLGDVREUHXP DGHWHUP LQDGDFDL[DQmRGHYHH[FHGHUXP OLP LWHP i[LP R SHUP LWLGRVRERULVFRGHRFRUUHUHP DOWHUDo}HVQDIRUP DGDHP EDODJHP SURWHWRUDH FRQVHTHQWHSRVVtYHODYDULDGRVSURGXWRVGHQWURGHOD 3DUDLP SHGLUTXHSRVVDRFRUUHUDIRUP DomRGH³EXUDFRV´QRSDGUmRGH HP SDFRWDP HQWRDGP LWHVHDTXL GHHVWDELOLGDGHHP UHODomRDRHL[Rz LVWRpD R TXHpFRP XP QDOLWHUDWXUDGHFDUUHJDP HQWRGHFRQWrLQHUHV5$ 7&/,))%,6&+ 2 )) %,6&+ 2 ))1 RWHTXHRWHUP R³EXUDFRV´WHP DTXLXP VLJQLILFDGRGLIHUHQWHTXHR XWLOL]DGRQRFRQWH[WRGDHVWDELOLGDGHGRFDUUHJDP HQWR$ TXL³EXUDFRV´VHUHIHUHjHVSDoRV YD]LRVUHVXOWDQWHVGDDXVrQFLDGHcaixasQRSDGUmRGHHP SDFRWDP HQWRHQTXDQWRQD HVWDELOLGDGHGRFDUUHJDP HQWRRWHUP RVHUHIHUHjHVSDoRVYD]LRVUHVXOWDQWHVGDDXVrQFLDGH pontosHP DOJXP DIDFHGDVFDL[DVGHYLGRjXWLOL]DomRGRVSDGU}HVQRUP DLVFRP ELQDo}HV F{QLFDV $ VVLP VHMD Pj RSHVRGHFDL[DV j TXDLVTXHUH Vi DSUHVVmRP i[LP D DGP LVVtYHOTXHSRGHVHUVXSRUWDGDHP TXDOTXHUSRQWRs t u GDIDFHVXSHULRUGDFDL[Di FRP u r hi $ )LJXUDLOXVWUDFDL[DVTXDLVTXHUFRORFDGDVDFLP DGHXP DFDL[DP DLRU WRP DGDFRP RUHIHUrQFLDHTXHH[HUFHP SUHVVmRVREUHSRQWRVGDIDFHVXSHULRUGHVWDFDL[D 1 RWHTXHRVSRQWRVs t u WRP DGRVFRP RUHIHUrQFLDQHVWHP RP HQWRVmRRVLQGLFDGRVSHOD OLQKD,$ GP LWHVHDTXLTXHTXDOTXHUSRQWRGDIDFHVXSHULRUGDFDL[Di VXSRUWDDP HVP D SUHVVmRDGP LVVtYHOVi HTXHDSUHVVmRH[HUFLGDSRUFDL[DV j TXDLVTXHUpXQLIRUP HP HQWH GLVWULEXtGDVREUHDiUHDl j w j GDVXDIDFHLQIHULRU )LJXUD&RQMXQWRGHFDL[DVHP SLOKDGDVVREUHXP DFDL[DGHUHIHUrQFLD &RQVLGHUDQGRVHRVFRQMXQWRV X Y H Z GHILQLGRVWDQWRFRQIRUP H HTXDQWRFRQIRUP HHVHP SHUGDGHJHQHUDOLGDGHDUHVWULomRGH HP SLOKDP HQWRSRGHVHUIRUP XODGDFRP R § Pj ¨ ¨ j ^p X j _p l j d p d p li `^q Y j _q w j dq dq wi `^r Z j _r hi dr d H h j `©l j w j i m p X i q Yi r Z i m ¦ ¦ ¦ ¦ · x d Vi xipqr xipqr M ¸ ¸ jp q r ¹ 2 XVHMDDSUHVVmRP i[LP DDGP LVVtYHOTXHSRGHVHUVXSRUWDGDSRUFDGDSRQWR GDIDFHVXSHULRUGDFDL[Di FRORFDGDQDSRVLomRpqr QmRSRGHVHUH[FHGLGDSHODSUHVVmR WRWDOH[HUFLGDSRUFDL[DVj TXDLVTXHUFRORFDGDVDFLP DGDFDL[Di $ ULJRURVtQGLFHVs t u VHULDP UHGXQGDQWHVHIRUDP DTXLRP LWLGRVSRUFRQYHQLrQFLDGHQRWDomR 1 RHQWDQWRDIRUP XODomRSRVVXLXP DVSHFWRQHJDWLYRTXHpDSUHVHQoD GHXP Q~P HURM VXILFLHQWHP HQWHJUDQGHGRODGRGLUHLWRGDH[SUHVVmR$ SUHVHQoDGHVWH Q~P HURSRGHGLILFXOWDUDUHVROXomRGRP RGHORTXDQGRDUHOD[DomROLQHDUGHVWHpXWLOL]DGD' H P RGRDFRQWRUQDUHVWDGLILFXOGDGHXP DIRUP XODomRDOWHUQDWLYDGDUHVWULomRGHHP SLOKDP HQWR t u WRP DGRVFRP RUHIHUrQFLDQHVWHP RP HQWRVmRRV pSURSRVWD1 RWHTXHRVSRQWRVs LQGLFDGRVSHODOLQKD,,YHMD)LJXUD § Pj ¨ ¨ ^p X j _s l j d p ds`^q Y j _t w j dq dt `^r Z j _u dr d H h j `©l j w j m ¦ j ¦ ¦ ¦ · x d ¸ ¸ jp q r ¹ m ¦ ¦ ¦ ¦ Vi xipqr i ^p X i _s li d p ds`^qYi _t wi dq dt `^r Zi _u hi dr du ` s X t Y u Z 2 XVHMDFDVRKDMDDOJXP DFDL[Di RFXSDQGRDSRVLomRs t u HQWmRDSUHVVmR P i[LP DDGP LVVtYHOTXHSRGHVHUVXSRUWDGDSRUFDGDSRQWRGDIDFHVXSHULRUGDFDL[Di QmR SRGHVHUH[FHGLGDSHODSUHVVmRWRWDOH[HUFLGDSRUFDL[DV j TXDLVTXHUFRORFDGDVDFLP DGD FDL[Di 1 RWHTXHDOJXP DUHVWULomRGHQmRVREUHSRVLomRGHYHVHUXWLOL]DGDFRQMXQWDP HQWHSDUD LP SHGLUTXHP DLVGRTXHXP DFDL[Di RFXSHDSRVLomRs t u &RQYpP REVHUYDUTXHWDQWRDUHVWULomRTXDQWRDUHVWULomRHP ERUD WUDWHP GRHP SLOKDP HQWRGHFDL[DVXP DVVREUHDVRXWUDVQmRH[LJHP TXHRSDGUmRGH HP SDFRWDP HQWRVHMDFRQVWUXtGRHP SLOKDVGHFDL[DVYHMD)LJXUD,VWRpRSDGUmRDVHU FRQVWUXtGRSRGHVHUJHQpULFRP DVDOJXP DUHVWULomRGHHVWDELOLGDGHHP UHODomRDRHL[Rz FRP D GHYHVHUXWLOL]DGDFRQMXQWDP HQWHSDUDLP SHGLUTXHSRVVDRFRUUHUDIRUP DomRGH ³EXUDFRV´QRSDGUmRGHHP SDFRWDP HQWR 8 P FDVRSDUWLFXODUGHUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRpDFKDP DGD fragilidadeTXHWUDWDVLWXDo}HVHP TXHRSHVVRDOHQFDUUHJDGRGHID]HURFDUUHJDP HQWRGDV FDL[DVGHQWURGHXP FRQWrLQHUVHGHSDUDFRP LQVWUXo}HVGRWLSR³IUiJLO´HVFULWDVQDV HP EDODJHQV1 HVWHFDVRQHQKXP DFDL[DGHYHVHUFRORFDGDDFLP DGDFDL[DGHUHIHUrQFLDSRLV DIDFHVXSHULRUGHVWDQmRSRGHVRIUHUQHQKXP DSUHVVmR3DUDWUDWDUHVWHFDVRXP D SRVVLELOLGDGHVHULDFRQVLGHUDUVi SDUDFDGDFDL[DIUiJLOi QRODGRGLUHLWRGDVUHVWULo}HV H8 P DRXWUDSRVVLELOLGDGHVHULDHVFUHYHUUHVWULo}HVOyJLFDVSDUD]HUDUWRGDVDV YDULiYHLVTXHSHUP LWLVVHP RFDUUHJDP HQWRGHFDL[DVDFLP DGDFDL[DIUiJLO 1 RYDP HQWHFRQYpP REVHUYDUTXHWRGDVDVGHILQLo}HVDSUHVHQWDGDVSDUDWUDWDUD UHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRVmRVLP SOLVWDVHSRUWDQWRIiFHLVGHVHUHP P RGHODGDV & 2 1 6,' (5 $ 1 ' 2 & $ 5 * $ )5 $ & ,2 1 $ ' $ (0 0 Ò /7,3/2 6' (67,1 2 6 $ FDUJDIUDFLRQDGDHP múltiplos destinosWUDWDVLWXDo}HVHP TXHXP FRQWrLQHU RXFDP LQKmRFRP RpP DLVFRP XP QDSUiWLFDHVWiFDUUHJDGRFRP FDL[DVFRP SURGXWRV HQFRP HQGDGRVSRUGLIHUHQWHVFOLHQWHVGHVWLQRVTXHHVWmRHVSDOKDGRVSRUXP DUHJLmR2 FDP LQKmRGHYHHQWmRSHUFRUUHUXP URWHLURGHHQWUHJDVDLQGRGHXP GHSyVLWRRQGHHOHp FDUUHJDGRHSDVVDQGRSHORVGLIHUHQWHVGHVWLQRV(P FDGDGHVWLQRDVFDL[DVFRP SURGXWRV HQFRP HQGDGRVSRUDTXHOHFOLHQWHGHYHP VHUGHVFDUUHJDGDV$ SyVUHDOL]DUWRGDVDVHQWUHJDVR FDP LQKmRSRGHUHWRUQDUYD]LRSDUDRGHSyVLWR$ TXHVWmRTXHVXUJHpFRP RSODQHMDUR FDUUHJDP HQWRGRFDP LQKmRGHP RGRDFRQVLGHUDUQDP HGLGDGRSRVVtYHODRUGHP HP TXHDV FDL[DVGHYHP VHUGHVFDUUHJDGDVSDUDHYLWDUGHVSHUGtFLRVGHWHP SRGHVFDUUHJDQGRH UHFDUUHJDQGRDVFDL[DVGRVGHVWLQRVUHP DQHVFHQWHV$ )LJXUDLOXVWUDXP FDP LQKmRTXH SDUWHFDUUHJDGRGHXP GHSyVLWRHpGHVFDUUHJDGRDRORQJRGHFLQFRGHVWLQRVUHWRUQDQGR YD]LRSDUDRGHSyVLWRGHSDUWLGDLVWRpRURWHLURGHSyVLWRGHSyVLWR )LJXUD&DP LQKmRVHQGRGHVFDUUHJDGRDRORQJRGHFLQFRGHVWLQRV 1 RWHTXHHVWHSUREOHP DLQYHUVDP HQWHSRGHVHUYLVWRFRP RRSUREOHP DGHXP FDP LQKmRGHFROHWDTXHVDLGRGHSyVLWRYD]LRHHP FDGDGHVWLQRGRVHXURWHLURDVFDL[DVVmR FDUUHJDGDVGHQWURGRFDP LQKmRVHP GHVFDUUHJDUDVFDL[DVMiFDUUHJDGDVGRVGHVWLQRV DQWHULRUHVGRURWHLUR1 RWHTXHRURWHLURGHFROHWDpRLQYHUVRGRURWHLURGHHQWUHJDLVWRpR URWHLURGHSyVLWRGHSyVLWRQD)LJXUD 3DUDWUDWDUHVWDVFRQVLGHUDo}HVVmRDSUHVHQWDGRVGRLVSURFHGLP HQWRVKHXUtVWLFRV TXHHQYROYHP IRUP XODo}HV3DUDHVWHVGRLVSURFHGLP HQWRVDGP LWHVHTXHRFRQWrLQHUWHP XP FRP SULP HQWRL VXILFLHQWHP HQWHJUDQGHSDUDHP SDFRWDUWRGDVDVFDL[DVGHWRGRVRVGHVWLQRV 1 RWHTXHRSUREOHP DGHFDUUHJDP HQWRGHFRQWrLQHUHVFRP RGHVFULWRQHVWDVHomRWUDWDVHGR WLSR' 5 2 ' 3 3URFHGLP HQWR 6HMDXP URWHLURFRP n GHVWLQRVTXHXP FRQWrLQHUGHYHSHUFRUUHU(P FDGD GHVWLQR k k n WHP VH mk WLSRVGHFDL[DVSDUDVHUHP FDUUHJDGDVFDGDWLSR i i mk FRP bi FDL[DVGHGLP HQV}HVli wi hi &RQYpP QRWDUTXHk VHUHIHUHDR FRQMXQWR GH FDL[DV TXH VmR FDUUHJDGDV SULP HLUR H GHVFDUUHJDGDV SRU ~OWLP R n VHUHIHUHDRFRQMXQWRGHFDL[DVTXHVmRFDUUHJDGDVSRU~OWLP RH &RQVHTHQWHP HQWHk GHVFDUUHJDGDVSULP HLUR eSRVVtYHOUHGHILQLUDVSRVVtYHLVSRVLo}HVHDRORQJRGR FRP SULP HQWRL GDODUJXUDW HGDDOWXUDH GRFRQWrLQHURQGHFDGDFDL[DSRGHVHU FRORFDGDDJRUDSDUDFDGDGHVWLQRk SRUP HLRGRVFRQMXQWRV Xk ^p _ d p d L P LQli HLQWHLURi mk ` k n Yk ^q _ d q d W P LQwi HLQWHLURi mk ` k n Zk ^r _ d r d H P LQhi HLQWHLURi mk ` k n i i i 4 XHSRGHP VHUUHGX]LGRVVHP SHUGDGHJHQHUDOLGDGHDRVpadrões normaisRX combinações cônicas Xk Yk Zk ^p _p ¦ mk H li d p d L P LQli d Hi d bi HLQWHLURi mk ` k n i m ^q _q ¦ i Hi wi d q d W P LQwi d Hi d bi HLQWHLURi mk ` k n i m ^r _r ¦ i Hi hi d r d H P LQhi d Hi d bi HLQWHLURi mk ` k n i i i k k 6HMDP DLQGDRVFRQMXQWRVGHILQLGRVFRP RDVHJXLU X ik ^p X k _ d p d L li ` i mk k n Yik ^q Yk _ d q d W wi ` i mk k n Z ik ^r Z k _ d r d H hi ` i mk k n e SRVVtYHO GHILQLU D YDULiYHO GH GHFLVmR UHDO L k k n SDUD R FRP SULP HQWRP tQLP RQHFHVViULRSDUDHP SDFRWDUWRGDVDVFDL[DVGRGHVWLQRk $ VVLP FRP EDVHQDIRUP XODomRpSRVVtYHOUHHVFUHYHUXP DQRYDIRUP XODomRGHQWURGHXP SURFHGLP HQWRUHFXUVLYRSDUDFDGDGHVWLQRk 3DUDk n UHVROYDDIRUP XODomR P LQ L k s X k t Yk u Z k i m p li xipqr d L k i m p X ik q Yik r Z ik L k t 6XMHLWRD m ¦¦ ¦¦ aipqrstu xipqr d i p X ik qYik r Zik ¦ ¦¦ xipqr bi p X ik qYik r Zik i m xipqr ^` p X ik q Yik r Z ik 5HWRUQHL L L n 6HL L L n d L HQWmRDVROXomRpIDFWtYHO 1 D IRUP XODomR D IXQomR REMHWLYR YLVD P LQLP L]DU R FRP SULP HQWRWRWDOQHFHVViULRL k SDUDHP SDFRWDUWRGDVDVFDL[DVGRGHVWLQRk $ VUHVWULo}HV LP SHGHP TXHKDMDVREUHSRVLomRHQWUHDVFDL[DVGRGHVWLQRk GHQWURGRFRQWrLQHU$ V UHVWULo}HVLP SHGHP TXHRQ~P HURGHUpSOLFDVGHFDGDFDL[DVHMDGLIHUHQWHGRYDORUbi UHTXHULGRSHORGHVWLQRFOLHQWHk $ VUHVWULo}HVLP SHGHP TXHDVFDL[DVGRGHVWLQRk VHMDP HP SDFRWDGDVDOpP GRFRP SULP HQWRP tQLP RQHFHVViULRL k )LQDOP HQWHDVUHVWULo}HV GHILQHP RGRP tQLRGDVYDULiYHLVGHGHFLVmR 1 RWHTXHQHVWHFDVRRSRVLFLRQDP HQWRUHODWLYRHQWUHDVFDL[DVGRVGLIHUHQWHV GHVWLQRVILFDOLP LWDGRSHODP DLRURUGHQDGDp li REWLGDFRP DVFDL[DVHP SDFRWDGDVGHFDGD GHVWLQR1 RWHWDP EpP TXHHVWHSURFHGLP HQWRUHDOL]DXP DRWLP L]DomRindependenteSDUDDV FDL[DVGHFDGDGHVWLQRk HDVROXomRILQDOREWLGDpXP DFRP SRVLomRGHn VROXo}HV ORFDOP HQWHyWLP DV&RQYpP DLQGDREVHUYDUTXHQHVWDIRUP XODomRFRQVLGHUDo}HVGHP ~OWLSODV RULHQWDo}HVGDVFDL[DVOLP LWHGHSHVRGRFRQWrLQHUFDP LQKmRHVWDELOLGDGHGRFDUUHJDP HQWR HUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRWDP EpP SRGHP VHUIDFLOP HQWHLQFRUSRUDGDV $ )LJXUDLOXVWUDXP DSRVVtYHOGLVSRVLomRXWLOL]DQGRHVWHSURFHGLP HQWRGH FDL[DVGHWUrVGHVWLQRVGLIHUHQWHV2 EVHUYHTXHpFULDGDXP DHVSpFLHGH³FRUWLQDGLYLVyULD´ LP DJLQiULDHQWUHDVFDL[DVGHGRLVGHVWLQRVFRQVHFXWLYRVGHQWURGRFDP LQKmR' HIDWRD FULDomRGHVXEGLYLV}HVFRP SDUWLP HQWRVpXP DSUiWLFDFRP XP QRFDUUHJDP HQWRGH FDP LQK}HVHP WUDQVSRUWDGRUDV )LJXUD([HP SORGHHP SDFRWDP HQWRGDVFDL[DVFRP R3URFHGLP HQWR 3URFHGLP HQWR 6HMDXP URWHLURFRP n GHVWLQRVTXHXP FRQWrLQHUGHYHSHUFRUUHU(P FDGD GHVWLQR k k n WHP VH m WLSRVGHFDL[DVSDUDVHUHP FDUUHJDGDVFDGDWLSRi i m FRP bik FDL[DVGHGLP HQV}HVli wi hi 1 RYDP HQWHFRQYpP QRWDUTXHk VH UHIHUHDRFRQMXQWRGHFDL[DVTXHVmRFDUUHJDGDVSULP HLURHGHVFDUUHJDGDVSRU~OWLP R n VHUHIHUHDRFRQMXQWRGHFDL[DVTXHVmRFDUUHJDGDVSRU~OWLP RH &RQVHTHQWHP HQWHk GHVFDUUHJDGDVSULP HLUR eSRVVtYHOGHILQLUDYDULiYHOGHGHFLVmRUHDOL SDUDRFRP SULP HQWRP tQLP R QHFHVViULRSDUDHP SDFRWDUWRGDVDVFDL[DVGHWRGRVRVn GHVWLQRV$ VVLP FRP EDVHQD IRUP XODomR p SRVVtYHO UHHVFUHYHU XP D QRYD IRUP XODomR GHQWUR GH XP SURFHGLP HQWRUHFXUVLYRSDUDWRGRVRVn GHVWLQRV )DoDk HUHVROYDDIRUP XODomR P LQL s X t Y u Z i m 6XMHLWRD m ¦¦ ¦¦a ipqrstu xipqr d i p X i qYi r Z i k ¦ ¦¦x ¦b p X i qYi r Z i k ipqr ik i m p li xipqr d L p X i q Yi r Z i L t i m xipqr ^` )L[HDVYDULiYHLVxipqr )DoDk p X i q Yi r Z i k HUHVROYDRP RGHORDFLP DHP k FRP DVYDULiYHLVxipqr DFLP DIL[DGDV 5HWRUQHR~OWLP RL REWLGR 6HL d L HQWmRDVROXomRpIDFWtYHO DVVRFLDGDVjVFDL[DVGHVWHGHVWLQR 5HSLWDHVWHSURFHGLP HQWRSDUDWRGRVRVn GHVWLQRV 1 D IRUP XODomR D IXQomR REMHWLYR YLVD P LQLP L]DU R FRP SULP HQWRWRWDOQHFHVViULRL SDUDHP SDFRWDUWRGDVDVFDL[DVGHWRGRVRVn GHVWLQRV$ V UHVWULo}HVLP SHGHP TXHKDMDVREUHSRVLomRHQWUHDVFDL[DVGRVGLIHUHQWHVGHVWLQRVGHQWUR GRFRQWrLQHU$ VUHVWULo}HVLP SHGHP TXHRQ~P HURGHUpSOLFDVGHFDGDFDL[DVHMD GLIHUHQWHGRYDORUbik UHTXHULGRSHORGHVWLQRFOLHQWHk QRWHTXHFRP RDVFDL[DVGRV GHVWLQRVSUHFHGHQWHVHVWmRIL[DGDVpSUHFLVRVRP DUHVWDVTXDQWLGDGHVDWpRGHVWLQRP DLV DWXDO$ VUHVWULo}HVLP SHGHP TXHDVFDL[DVGHWRGRVRVn GHVWLQRVVHMDP HP SDFRWDGDV DOpP GRFRP SULP HQWRP tQLP RQHFHVViULRL )LQDOP HQWHDVUHVWULo}HVGHILQHP R GRP tQLRGDVYDULiYHLVGHGHFLVmR 1 RWH TXH QHVWH FDVR GLIHUHQWHP HQWH GR SURFHGLP HQWR DQWHULRU R SRVLFLRQDP HQWRUHODWLYRHQWUHDVFDL[DVGRVGLIHUHQWHVGHVWLQRVQmRILFDOLP LWDGRSHODP DLRU RUGHQDGD p li REWLGDFRP DVFDL[DVHP SDFRWDGDVGHFDGDGHVWLQRSRLVpSRVVtYHOSRU H[HP SORTXHDVFDL[DVGHXP GHVWLQRSRVWHULRUVHMDP FRORFDGDVHP FRQWDWRFRP DVFDL[DVGH GHVWLQRVDQWHULRUHVQRURWHLURGRFDP LQKmR1 RWHWDP EpP TXHHVWHSURFHGLP HQWRUHDOL]DXP D RWLP L]DomRcegaSDUDDVFDL[DVGHFDGDGHVWLQRk XP DYH]TXHDVFDL[DVGHXP GHVWLQRXP D YH]IL[DGDVQmRSRGHP P DLVVHUUHDUUDQMDGDVRTXHSRGHLP SOLFDUQD³SHUGD´GDVROXomR yWLP DJOREDOTXDQGRVHFRQVLGHUDGHXP DVyYH]DRWLP L]DomRGHWRGDVDVFDL[DVGHWRGRVRV n GHVWLQRV&RQYpP DLQGDREVHUYDUTXHQHVWDIRUP XODomRFRQVLGHUDo}HVGHP ~OWLSODV RULHQWDo}HVGDVFDL[DVOLP LWHGHSHVRGRFRQWrLQHUFDP LQKmRHVWDELOLGDGHGRFDUUHJDP HQWR HUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWRWDP EpP SRGHP VHUIDFLOP HQWHLQFRUSRUDGDV $ )LJXUDLOXVWUDXP DSRVVtYHOGLVSRVLomRXWLOL]DQGRHVWHSURFHGLP HQWRGH FDL[DV GH WUrV GHVWLQRV GLIHUHQWHV 2 EVHUYH TXH R DVSHFWR FULDGR SHOR SDGUmR GH HP SDFRWDP HQWROHP EUDRGRMRJRHOHWU{QLFR³7HWULV´GHVHQYROYLGRQRVDQRVHFXMR REMHWLYRpHQFDL[DUSHoDVGHGLYHUVRVIRUP DWRVTXHGHVFHP GRWRSRGHXP DWHOD4 XDQGRXP D OLQKDpFRP SOHWDGDHVWDGHVDSDUHFHHSRQWRVH[WUDVVmRGDGRVDRMRJDGRU2 MRJRWHUP LQD TXDQGRDVOLQKDVLQFRP SOHWDVVHHP SLOKDP DWpRWRSRGDWHOD )LJXUD([HP SORGHHP SDFRWDP HQWRGDVFDL[DVFRP R3URFHGLP HQWR & $ 3Ë78 /2 5 (68 /7$ ' 2 6& 2 0 38 7$ & ,2 1 $ ,6(' ,6& 8 66 2 ,1 75 2 ' 8 d 2 1 HVWHFDStWXORVmRDSUHVHQWDGRVRVUHVXOWDGRVREWLGRVFRP RVH[SHULP HQWRV FRP SXWDFLRQDLV UHDOL]DGRV $ OJXQV GRV P RGHORV DSUHVHQWDGRV QR FDStWXOR IRUDP LP SOHP HQWDGRVQDOLQJXDJHP GHP RGHODJHP * $ 0 6YHUVmRHRsolver&3/(; YHUVmR FRP SDUkP HWURVdefaultIRLXWLOL]DGRSDUDUHVROYrORV7RGRVRVH[SHULP HQWRVIRUDP UHDOL]DGRVHP XP P LFURFRP SXWDGRU3&3HQWLXP ' * + ]* %2 VP RGHORVIRUDP WHVWDGRVFRP H[HP SORVJHUDGRVDOHDWRULDP HQWHHFRP H[HP SORVGDOLWHUDWXUD 5 (68 /7$ ' 2 6' (( ; (0 3/2 6* (5 $ ' 2 6$ /($ 72 5 ,$ 0 (1 7( (VWD VHomR DSUHVHQWD RV UHVXOWDGRV REWLGRV FRP H[HP SORV JHUDGRV DOHDWRULDP HQWH3ULP HLUDP HQWHVmRDSUHVHQWDGRVRVUHVXOWDGRVGHH[HP SORVWHVWDGRVFRP P RGHORVFRQVLGHUDQGR0 DSHQDVDQmRVREUHSRVLomRGDVFDL[DV0 DQmRVREUHSRVLomRGDV FDL[DVHDHVWDELOLGDGHYHUWLFDOGRFDUUHJDP HQWR0 DQmRVREUHSRVLomRGDVFDL[DVD HVWDELOLGDGHYHUWLFDOGRFDUUHJDP HQWRHDUHVLVWrQFLDGDVFDL[DVDRHP SLOKDP HQWR(P VHJXLGDVmRDSUHVHQWDGRVUHVXOWDGRVGHH[HP SORVWHVWDGRVFRP P RGHORVFRQVLGHUDQGR0 D FDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRV3URFHGLP HQWRHDQmRVREUHSRVLomRGDVFDL[DV 0 DFDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRV3URFHGLP HQWRDQmRVREUHSRVLomRGDVFDL[DV HDHVWDELOLGDGHYHUWLFDOGRFDUUHJDP HQWR0 DFDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRV 3URFHGLP HQWRHDQmRVREUHSRVLomRGDVFDL[DV0 DFDUJDIUDFLRQDGDHP P ~OWLSORV GHVWLQRV3URFHGLP HQWRDQmRVREUHSRVLomRGDVFDL[DVHDHVWDELOLGDGHYHUWLFDOGR FDUUHJDP HQWR (VWHVP RGHORVVmRFRP SRVWRVSRUYiULDVGDVH[SUHVV}HVDSUHVHQWDGDVQR FDStWXOR$ VVLP GHP RGRDHYLWDUP DLRUHVFRQIXV}HVQRGHFRUUHUGHVWHFDStWXORD7DEHOD DSUHVHQWDHVWHVP RGHORVDVH[SUHVV}HVTXHRVFRP S}HP HRVWLSRVGHSUREOHP DVGH FDUUHJDP HQWRGHFRQWrLQHUHVTXHHOHVGHVFUHYHP 7DEHOD0 RGHORVXWLOL]DGRVQRVH[SHULP HQWRVFRP SXWDFLRQDLV 7LSRGH3UREOHP D 0 RGHOR ([SUHVV}HV 0 ' 5 ,,336/2 336. 3 0 0 0 0 ' 5 2 ' 3 0 0 2 VH[HP SORVJHUDGRVDOHDWRULDP HQWHIRUDP GLYLGLGRVGHDFRUGRFRP DV VHJXLQWHVFDUDFWHUtVWLFDV x 4 XDWURTXDQWLGDGHVGLIHUHQWHVGHWLSRVGHFDL[DVm QHVWHFDVRDVFDL[DVSRGHP VHU URWDFLRQDGDVHP WRUQRGHWRGRVRVHL[RVm HQHVWHVWUrV~OWLP RVFDVRVDV FDL[DVGHYHP WHUXP D~QLFDRULHQWDomRIL[D x ' XDVP DQHLUDVGLIHUHQWHVGHJHUDUDVGLP HQV}HVGDVFDL[DV$ mm H GLP HQV}HVGDVFDL[DVXQLIRUP HP HQWHVRUWHDGDVHQWUH H GDVGLP HQV}HVGR FRQWrLQHU RX VHMD li >LL@ wi >W W @ H hi >H H @% mm HGLP HQV}HVGDVFDL[DVXQLIRUP HP HQWH VRUWHDGDVHQWUH H GDVGLP HQV}HVGRFRQWrLQHURXVHMDli >LL@ wi >W W @H hi >H H @3RUVLP SOLFLGDGHHP WRGRVRV H[HP SORVIRUDP FRQVLGHUDGRVFRQWrLQHUHVF~ELFRVLVWRpFRP GLP HQV}HVL W H (P SDUWLFXODUSDUDRFDVRFRP m RVP RGHORVIRUDP DGHTXDGDP HQWH P RGLILFDGRVSDUDSHUP LWLUDURWDomRGDVFDL[DVHP WRUQRGHWRGRVRVHL[RVYHMDVHomR 8 P DP RWLYDomRSDUDDUHDOL]DomRGHH[SHULP HQWRVFRP H[HP SORVGRVJUXSRV$ H% pTXH HOHV SRGHP VHU YLVWRV FRP R SUREOHP DV GH FDUUHJDP HQWR GH SDOHWHV GR SURGXWRU WULGLP HQVLRQDLVHP TXHDVFDL[DVQmRSUHFLVDP VHUDUUDQMDGDVHP FDP DGDVKRUL]RQWDLVVREUHR SDOHWHYHMDVHomR $ 7DEHODDSUHVHQWDDVGLP HQV}HVL W H GRVFRQWrLQHUHVYDULDQGRGH DWp$ SULP HLUDFROXQDGHVWDFDDVGLIHUHQWHVTXDQWLGDGHVGHWLSRVGHFDL[DVHD VHJXQGDHWHUFHLUDFROXQDVGHVWDFDP UHVSHFWLYDP HQWHDVP DQHLUDV$ mH% mGHJHUDUDV GLP HQV}HVGDVFDL[DV2 VJUXSRV$ mHQYROYHP H[HP SORVHP JHUDOP DLVIiFHLVTXDQGR FRP SDUDGRVFRP RVJUXSRV% mSRLVFRP RDVGLP HQV}HVGDVFDL[DVJHUDGDVVmRHP P pGLD P DLRUHVRQ~P HURGHSDGU}HVQRUP DLVFRP ELQDo}HVF{QLFDVpHP P pGLDEHP P HQRU1 R FDVRGRVJUXSRV% mIRUDP UHDOL]DGRVWHVWHVDSHQDVDWpGLP HQV}HVL W H LJXDLVD SRLVHP JHUDOSDUDYDORUHVP DLRUHVDP HP yULDSULQFLSDOGRFRP SXWDGRUXWLOL]DGRIRL LQVXILFLHQWHSDUDRDSOLFDWLYR* $ 0 6FRP SLODURVP RGHORV$ VVLP SDUDFDGDXP GRVYDORUHV GDVGLP HQV}HV L W H GRVFRQWrLQHUHVIRUDP JHUDGRVH[HP SORVWRWDOL]DQGR H[HP SORVSDUDVHUHP WHVWDGRVFRP RVP RGHORV0 0 H0 7DEHOD' LP HQV}HVL W H GRVFRQWrLQHUHVSDUDRVJUXSRVGHH[HP SORVJHUDGRVDOHDWRULDP HQWH $ m % m m H H H H H H H H 2 YDORUvi GDFDL[Di IRLGHILQLGRFRP RVHQGRDIUDomRGHYROXP HRFXSDGD SHODFDL[Di QRFRQWrLQHULVWRpvi >li wi hi L W H @SDUDWRGRi m 2 Q~P HUR P i[LP Rbi GHUpSOLFDVGDFDL[Di TXHSRGHP VHUHP SDFRWDGDVGHQWURGRFRQWrLQHUIRLJHUDGR GHGXDVP DQHLUDVGLIHUHQWHV3DUDRVH[HP SORVFRP m H RQ~P HUR bi IRL XQLIRUP HP HQWHVRUWHDGRQRLQWHUYDOR>¬ «L li » «W wi » «H hi » ¼¬ ¼¬ ¼@SDUDWRGRi m 1 RWH TXHGHVWDP DQHLUDRSUREOHP DpUHVWULWRGRSRQWRGHYLVWDGHGLVSRQLELOLGDGHGHFDL[DVQD OLWHUDWXUD GH FRUWH H HP SDFRWDP HQWR R SUREOHP D p FKDP DGR restrito VH bi ¬ «L W H li wi hi ¼ »SDUDDOJXP i 3DUDRVH[HP SORVFRP m RQ~P HURbi IRL GHILQLGRFRP R bi « ¬L W H li wi hi » ¼SDUDWRGR i m RTXHLP SOLFDTXHR SUREOHP DpLUUHVWULWRGRSRQWRGHYLVWDGHGLVSRQLELOLGDGHGHFDL[DV 2 SHVRPi GDFDL[Di IRLGHILQLGRFRP RVHQGRRSUySULRYROXP HGDFDL[Di XP DYH]TXHSRUVLP SOLFLGDGHIRLFRQVLGHUDGRTXHWRGDVDVFDL[DVSRVVXHP DP HVP D GHQVLGDGHLVWRpPi li wi hi SDUDWRGRi m $ SUHVVmRP i[LP DDGP LVVtYHOVi TXHD FDL[Di SRGHVXSRUWDUHP TXDOTXHUSRQWRGDVXDIDFHVXSHULRUIRLGHILQLGDGHGXDVP DQHLUDV GLIHUHQWHV3DUDRVH[HP SORVFRP m H DSUHVVmRP i[LP DDGP LVVtYHO Vi IRL XQLIRUP HP HQWHVRUWHDGDQRLQWHUYDOR>hi @SDUDWRGRi m &RP RQHVWHVFDVRVDV FDL[DVGHYHP WHUXP D~QLFDRULHQWDomRIL[DHRSHVRGHFDGDFDL[DSRGHVHUGHILQLGRFRP R VHQGRRVHXSUySULRYROXP HHQWmRDSUHVVmRP i[LP DDGP LVVtYHOSRGHVHUGHILQLGDFRP R VHQGRSURSRUFLRQDOjDOWXUDGDFDL[D$ FRQVWDQWHP XOWLSOLFDQGRRYDORUGDDOWXUDGDFDL[Dp RYDORUP DLVFRP XP XWLOL]DGRQDOLWHUDWXUD5$ 7&/,))%,6&+ 2 ))1 RWHTXHSDUDR FDVRHP TXHRYDORUVRUWHDGRSDUDVi pLVWRLQGLFDTXHDIDFHVXSHULRUGDFDL[DpIUiJLOLVWR pQHQKXP DRXWUDFDL[DSRGHVHUFRORFDGDHQFLP DGHOD3DUDRVH[HP SORVFRP m D SUHVVmRP i[LP DDGP LVVtYHOVi IRLGHILQLGDVLP LODUP HQWHP DVDJRUDGHSHQGHQGRGHVREUH TXDOGDVVXDVIDFHVDFDL[DHVWiDSRLDGD>hi @SDUDRFDVRHP TXHDFDL[DHVWiDSRLDGD VREUHli wi >wi @SDUDRFDVRHP TXHDFDL[DHVWiDSRLDGDVREUHli hi H>li @SDUDR FDVRHP TXHDFDL[DHVWiDSRLDGDVREUHwi hi SDUDWRGRi m 2 YDORUD GRSDUkP HWURGHHVWDELOLGDGHHP UHODomRDRHL[Rz IRLGHILQLGR FRP RVHQGRLVWRpDVIDFHVLQIHULRUHVGHWRGDVDVFDL[DVGHYHP HVWDU VXSRUWDGDVSHODV IDFHVVXSHULRUHVGHXP DRXP DLVFDL[DVFRORFDGDVLP HGLDWDP HQWHDEDL[RGHODVRXSHORSLVR GRFRQWrLQHU1 RWHTXHQRFDVRGRVP RGHORVFRP SRVWRVSHODH[SUHVVmRD p FRQGLomRQHFHVViULDSDUDHYLWDUTXHSRVVDRFRUUHUDIRUP DomRGH³EXUDFRV´QRSDGUmRGH HP SDFRWDP HQWRYHMDVHomR 3DUDLOXVWUDURWDP DQKRGRVP RGHORVJHUDGRVFRP RVJUXSRV$ mH% mD7DEHOD DSUHVHQWDRVWDP DQKRVP tQLP RP pGLRHP i[LP RGRVFRQMXQWRVX Y HZ HRVQ~P HURV P tQLP RP pGLRHP i[LP RGHUHVWULo}HVHYDULiYHLVELQiULDVSDUDFDGDXP GRVRLWRJUXSRV FRQVLGHUDQGR XP FRQWrLQHU FRP GLP HQV}HV L W H LJXDLV D (VWHV Q~P HURV FRUUHVSRQGHP DRVYDORUHVUHSRUWDGRVSHOR&3/(; DSyVRSUpSURFHVVDP HQWR 7DEHOD1 ~P HURGHHOHP HQWRVGRVSDGU}HVQRUP DLVHQ~P HURGHUHVWULo}HVHYDULiYHLVGRVP RGHORVFRP L W H LJXDLVD 1 R5HV 1 R3DGU1 RUP DLV R (VW 1 9 DU X Y Z 0 RGHOR0 0 RGHOR0 0 RGHOR0 min. $ med. max. min. $ med. max. min. $ med. max. min. $ med. max. min. % med. max. min. % med. max. min. % med. max. min. % med. max. &RP RSRGHVHUREVHUYDGRQD7DEHODRQ~P HURGHYDULiYHLVHUHVWULo}HV FUHVFHVLJQLILFDWLYDP HQWHjP HGLGDTXHm FUHVFHFRP SDUHSRUH[HP SOR$ H$ Hj P HGLGDTXHRWDP DQKRGDVFDL[DVGLP LQXLFRP SDUHSRUH[HP SOR$ H% 1 RWHTXHP HVP R SDUDSUREOHP DVFRP L W H SHTXHQRVLVWRpLJXDLVDRVP RGHORVSRGHP HQYROYHU RUGHP GHP LOKDUHVGHYDULiYHLVHUHVWULo}HV (P WRGRVRVH[SHULP HQWRVRWHP SRFRP SXWDFLRQDOSDUDUHVROYHUFDGDP RGHOR IRLOLP LWDGRHP KRUDVHJXQGRVHRVgapsGHRWLP DOLGDGHIRUDP FDOFXODGRVFRP R gap P HOKRUOLP LWDQWHREWLGRP HOKRUYDORUREWLGR P HOKRUOLP LWDQWHREWLGR $ VVLP TXDWURVLWXDo}HVVmRSRVVtYHLVGHRFRUUHUTXDQWRjTXDOLGDGHGDVROXomR REWLGDSHORDSOLFDWLYR* $ 0 6&3/(; LVROXomRyWLP DFRP gapLJXDOD]HURLLVROXomR LQWHLUDFRP gapP DLRUTXH]HURHFRP ROLP LWHGHWHP SRH[FHGLGRSHOR&3/(; LLLVHP VROXomRVHP gapHFRP ROLP LWHGHWHP SRH[FHGLGRSHOR&3/(; LYLQVXILFLrQFLDGH P HP yULDGRFRP SXWDGRUSDUDFRP SLODURP RGHORSHOR* $ 0 6VHP gapHVHP LQIRUP DomR UHOHYDQWHVREUHRWHP SR(VWDVGXDV~OWLP DVVLWXDo}HVHVWmRUHSUHVHQWDGDVQDVWDEHODVSHOR VtP EROR³― ´ $ VWDEHODVDVHJXLUDSUHVHQWDP RVYDORUHVP tQLP RP pGLRHP i[LP RSDUDRgap GHRWLP DOLGDGHHP REWLGRRWHP SRFRP SXWDFLRQDOHP VHJXQGRVXWLOL]DGRHDIUDomRGH YROXP HHP RFXSDGRSHODVFDL[DVFDUUHJDGDVGHQWURGRFRQWrLQHU' HVWDFDVHDTXLTXH HVWHVYDORUHVIRUDP FDOFXODGRVDSHQDVSDUDRVH[HP SORVTXHIRUDP UHVROYLGRVRWLP DP HQWHRX SDUDDTXHOHVHP TXHSHORP HQRVXP DVROXomRLQWHLUDVXEyWLP DIRLHQFRQWUDGD1 RWHTXHD SULP HLUDFROXQDGDVWDEHODVUHIHUHVHjVGLP HQV}HVGRFRQWrLQHUL W H 2 VUHVXOWDGRVREWLGRVFRP RVH[HP SORVGRVJUXSRV$ $ $ H$ HRV P RGHORV0 0 H0 HVWmRDSUHVHQWDGRVQDV7DEHODVD&RQYpP QRWDUTXHFRP RHUD HVSHUDGRHP IXQomRGDP DQHLUDFRP RIRUDP JHUDGRVRVH[HP SORVGHFDGDJUXSR$ mDIUDomR P pGLDGHYROXP HRFXSDGRDXP HQWDjP HGLGDTXHm FUHVFHFRP SDUHSRUH[HP SORRV UHVXOWDGRVGDV7DEHODVHFRP m H UHVSHFWLYDP HQWH3RURXWURODGRSDUDFDGD JUXSR$ mDIUDomRP pGLDGHYROXP HRFXSDGRGHFUHVFHjP HGLGDTXHDVGLP HQV}HV L W H GRVFRQWrLQHUHVDXP HQWDP FRP RWDP EpP HUDHVSHUDGR1 RWHTXHRDSOLFDWLYR * $ 0 6&3/(; FRP HoDDWHUGLILFXOGDGHVDFHQWXDGDVSDUDUHVROYHURVP RGHORVFRP RJUXSR $ HP IXQomRGDVQHFHVVLGDGHVGHWHP SRHP HP yULDFRP SXWDFLRQDLVVLWXDo}HVLLLHLY P HQFLRQDGDVDQWHVSDUDGLP HQV}HVL W H UHODWLYDP HQWHP RGHUDGDVLJXDLVDH (VW 1 R ([ min. med. max. min. med. max. min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR V ([ V ([ V 9 RO (VW 1 R ([ min. med. max. min. med. max. min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR V ([ V ([ V 9 RO (VW 1 R ([ min. med. max. min. med. max. min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO V ([ V ([ V (VW 1 R ([ min. med. max. min. med. max. min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR$ 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO V ([ V ([ V ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― $ 7DEHODDSUHVHQWDXP UHVXP RGRVUHVXOWDGRVFRP RVH[HP SORVWHVWDGRVGRV JUXSRV$ m3DUDFDGDXP GRVP RGHORVVmRDSUHVHQWDGRVUHVSHFWLYDP HQWHRQ~P HURGH H[HP SORVWHVWDGRVRQ~P HURGHH[HP SORVHP TXHSHORP HQRVXP DVROXomRLQWHLUDIRLREWLGD HRQ~P HURGHH[HP SORVTXHIRUDP UHVROYLGRVRWLP DP HQWH&RP RSRGHVHUREVHUYDGRQHVWD WDEHODFRP RP RGHOR0 HP GRVH[HP SORVGHSHORP HQRVXP DVROXomR LQWHLUDIRLREWLGDHHP GHVWHVGHXP DVROXomRyWLP DIRLHQFRQWUDGD&RP RVP RGHORV0 H0 HVWHVQ~P HURVUHVXOWDUDP HP H HHP H UHVSHFWLYDP HQWH 7DEHOD5HVXP RGRVH[SHULP HQWRVFRP H[HP SORVGRVJUXSRV$ m 0 RGHOR0 0 RGHOR0 0 RGHOR0 1 R 1 R6RO 1 R6RO 1 R 1 R6RO 1 R6RO 1 R 1 R6RO 1 R6RO ([S ,QWHLUD Ï WLP D ([S ,QWHLUD Ï WLP D ([S ,QWHLUD Ï WLP D $ $ $ $ 7RWDO $ )LJXUDLOXVWUDRVSDGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRV JUXSRV$ mUHVROYLGRRWLP DP HQWHFRP RVP RGHORV0 0 H0 2 P RGHOR0 HP SDFRWD FDL[DVHP GRYROXP HGRFRQWrLQHU1 RWHTXHRVHVSDoRVYD]LRVHVWmRGLVWULEXtGRVSRU HQWUHDVFDL[DVHFRP RFRQVHTrQFLDKiFDL[DVHP EDODQoRRX³IOXWXDQGR´GHQWURGR FRQWrLQHU2 P RGHOR0 SRUVXDYH]HP SDFRWDFDL[DVHP GRYROXP HGR FRQWrLQHU1 RWHTXHDSHVDUGRP HQRUYROXP HHP SDFRWDGRRVHVSDoRVYD]LRVHVWmRDFLP DGH WRGDVDVFDL[DVJDUDQWLQGRXP FDUUHJDP HQWR HVWiYHOYHUWLFDOP HQWH-iRP RGHOR0 GHYLGRDOLP LWDo}HVGDSUHVVmRP i[LP DDGP LVVtYHOHP SDFRWDDSHQDVFDL[DVHP GR YROXP HGRFRQWrLQHU )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRVJUXSRV$ mHRVP RGHORV0 0 H0 2 VUHVXOWDGRVREWLGRVFRP RVH[HP SORVGRVJUXSRV% % % H% HRV P RGHORV0 0 H0 HVWmRDSUHVHQWDGRVQDV7DEHODVD1 RYDP HQWHFRQYpP QRWDU TXHFRP RHUDHVSHUDGRHP IXQomRGDP DQHLUDFRP RIRUDP JHUDGRVRVH[HP SORVGHFDGD JUXSR% mDIUDomRP pGLDGHYROXP HRFXSDGRDXP HQWDjP HGLGDTXHm FUHVFHFRP SDUHSRU H[HP SORRVUHVXOWDGRVGDV7DEHODVHFRP m HUHVSHFWLYDP HQWH3RURXWURODGR SDUDFDGDJUXSR% mDIUDomRP pGLDGHYROXP HRFXSDGRGHFUHVFHjP HGLGDTXHDVGLP HQV}HV L W H GRVFRQWrLQHUHVDXP HQWDP FRP RWDP EpP HUDHVSHUDGR1 RWHTXHRDSOLFDWLYR * $ 0 6&3/(; FRP HoDDWHUGLILFXOGDGHVDFHQWXDGDVSDUDUHVROYHURVP RGHORVFRP RVJUXSRV % H% HP IXQomRGDVQHFHVVLGDGHVGHWHP SRHP HP yULDFRP SXWDFLRQDLVVLWXDo}HVLLLH LYP HQFLRQDGDVDQWHVP HVP RSDUDGLP HQV}HVL W H UHODWLYDP HQWHSHTXHQDVLJXDLVD H (VW 1 R ([ min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR V ([ V ([ V 9 RO 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR V ([ V ([ V 9 RO (VW 1 R ([ min. med. max. min. med. max. min. med. max. (VW 1 R ([ min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO V ([ V ([ V ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― (VW 1 R ([ min. med. max. min. med. max. min. med. max. 7DEHOD5HVXOWDGRVREWLGRVFRP H[HP SORVGRJUXSR% 0 RGHOR0 0 RGHOR0 0 RGHOR0 gap 7HP SR 9 RO 1 R gap 7HP SR 9 RO 1 R gap 7HP SR V ([ V ([ V ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― ― 9 RO ― ― ― ― ― ― $ 7DEHODDSUHVHQWDXP UHVXP RGRVUHVXOWDGRVFRP RVH[HP SORVWHVWDGRV GRVJUXSRV% m3DUDFDGDXP GRVP RGHORVVmRDSUHVHQWDGRVUHVSHFWLYDP HQWHRQ~P HURGH H[HP SORVWHVWDGRVRQ~P HURGHH[HP SORVHP TXHSHORP HQRVXP DVROXomRLQWHLUDIRLREWLGD HRQ~P HURGHH[HP SORVTXHIRUDP UHVROYLGRVRWLP DP HQWH&RP RSRGHVHUREVHUYDGRQHVWD WDEHODFRP RP RGHOR0 HP GRVH[HP SORVGHSHORP HQRVXP DVROXomR LQWHLUDIRLREWLGDHHP GHVWHVGHXP DVROXomRyWLP DIRLHQFRQWUDGD&RP RV P RGHORV0 H0 HVWHVQ~P HURVUHVXOWDUDP HP H HHP H UHVSHFWLYDP HQWH 7DEHOD5HVXP RGRVH[SHULP HQWRVFRP H[HP SORVGRVJUXSRV% m 0 RGHOR0 0 RGHOR0 0 RGHOR0 1 R 1 R6RO 1 R6RO 1 R 1 R6RO 1 R6RO 1 R 1 R6RO 1 R6RO ([S ,QWHLUD Ï WLP D ([S ,QWHLUD Ï WLP D ([S ,QWHLUD Ï WLP D % % % % 7RWDO $ )LJXUDLOXVWUDRVSDGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRV JUXSRV% mUHVROYLGRRWLP DP HQWHFRP RVP RGHORV0 0 H0 2 P RGHOR0 HP SDFRWD FDL[DVHP GRYROXP HGRFRQWrLQHU1 RWHTXHRVHVSDoRVYD]LRVHVWmRGLVWULEXtGRVSRU HQWUHDVFDL[DVHFRP RFRQVHTrQFLDKiFDL[DVHP EDODQoRRX³IOXWXDQGR´GHQWURGR FRQWrLQHU2 P RGHOR0 SRUVXDYH]HP SDFRWDFDL[DVQRVP HVP RV GRYROXP HGR FRQWrLQHU1 RWHTXHDOpP GRLJXDOYROXP HHP SDFRWDGRRVHVSDoRVYD]LRVHVWmRDFLP DGH WRGDVDVFDL[DVJDUDQWLQGRXP FDUUHJDP HQWR HVWiYHOYHUWLFDOP HQWH-iRP RGHOR0 GHYLGRDOLP LWDo}HVGDSUHVVmRP i[LP DDGP LVVtYHOHP SDFRWDDSHQDVFDL[DVHP GR YROXP HGRFRQWrLQHU )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORGRVJUXSRV% mHRVP RGHORV0 0 H0 8 P RXWUR UHVXOWDGR FRP HVWHV P RGHORV QmR P HQRV LQWHUHVVDQWH HVWi UHODFLRQDGRDRTXHVHSRGHFKDP DUGHR³FXVWR´GHQmRVHFRQVLGHUDUDHVWDELOLGDGHGR FDUUHJDP HQWRHVHUHIHUHjIUDomRGHH[HP SORVHP TXHIRLHQFRQWUDGRXP P HVP RYROXP HGH FDL[DVHP SDFRWDGDVWDQWRSHORP RGHOR0 TXDQWRSHORP RGHOR0 P DVHP TXHDVROXomR REWLGDSHORP RGHOR0 pYHUWLFDOP HQWHLQVWiYHO(P RXWUDVSDODYUDVRP RGHOR0 HP SDFRWDR P HVP RYROXP HGHFDL[DVTXHRP RGHOR0 P DVQmRREWpP XP FDUUHJDP HQWRYHUWLFDOP HQWH HVWiYHOFRP RQRH[HP SORLOXVWUDGRQD)LJXUD3DUDRVJUXSRV$ mLVWRRFRUUHXFRP GRVH[HP SORVUHVROYLGRVGHHQTXDQWRTXHSDUDRVJUXSRV% mLVWRRFRUUHX FRP GRVH[HP SORVUHVROYLGRVGH 2 VUHVXOWDGRVFRP SXWDFLRQDLVDSUHVHQWDGRVDWpDTXLP RVWUDP DVOLP LWDo}HVGR DSOLFDWLYR* $ 0 6&3/(; FRP SDUkP HWURVdefaultSDUDUHVROYHURVP RGHORV0 0 H0 FRP H[HP SORVJHUDGRVDOHDWRULDP HQWHGHWDP DQKRVEHP P RGHUDGRV,VVRLQGLFDTXHHVWD DERUGDJHP WHUiGLILFXOGDGHVSDUDWUDWDUSUREOHP DVUHDOLVWDVGHFDUUHJDP HQWRGHFRQWrLQHUHV HQYROYHQGRXP JUDQGHQ~P HURGHSRVVtYHLVSRVLo}HVSDUDDUUDQMDUDVFDL[DVGHQWURGR FRQWrLQHUSRUH[HP SORRVSUREOHP DVHP * HRUJHH5RELQVRQ%LVFKRIIH5DWFOLII DH&HFtOLRH0 RUDELWR1 RHQWDQWRFRQYpP REVHUYDUTXHRVH[HP SORV UHVROYLGRVDWpDTXLHQYROYHQGRP RGHORVFRP P LOKDUHVGHYDULiYHLVHUHVWULo}HVHVWmRORQJH GHVHUHP FRQVLGHUDGRVGHIiFLOUHVROXomR 2 VUHVXOWDGRVFRP SXWDFLRQDLVDSUHVHQWDGRVDSDUWLUGDTXLWrP DSUHWHQVmRGH P HUDP HQWHYDOLGDUHLOXVWUDUDDSOLFDELOLGDGHGRVP RGHORV0 0 0 H0 3DUDWDOXP H[HP SORGHFDGDXP GRVRLWRJUXSRVDQWHULRUP HQWHGHVFULWRVIRLVHOHFLRQDGR2 VFULWpULRVSDUD DVHOHomRIRUDP H[HP SORVFRP FRQWrLQHUHVGHGLP HQV}HVL W H LJXDLVDHTXHIRUDP UHVROYLGRVRWLP DP HQWHSHORP RGHOR0 $ VFDL[DVSUHVHQWHVQDVROXomRyWLP DGHFDGD H[HP SORIRUDP XQLIRUP HP HQWHVRUWHDGDVHQWUHWUrVGHVWLQRVGLIHUHQWHV3DUDRVP RGHORV0 H 0 RYDORUD GRSDUkP HWURGHHVWDELOLGDGHHP UHODomRDRHL[Rz IRLGHILQLGRFRP RVHQGR LVWRpDVIDFHVLQIHULRUHVGHWRGDVDVFDL[DVGHYHP HVWDU VXSRUWDGDVSHODVIDFHV VXSHULRUHVGHXP DRXP DLVFDL[DVFRORFDGDVLP HGLDWDP HQWHDEDL[RGHODVRXSHORSLVRGR FRQWrLQHU $ V7DEHODVHDSUHVHQWDP RVUHVXOWDGRVREWLGRVFRP HVWHVH[HP SORVHRV P RGHORV0 H0 H0 H0 UHVSHFWLYDP HQWH6mRDSUHVHQWDGRVUHVSHFWLYDP HQWHRQ~P HUR WRWDOGHFDL[DVHP SDFRWDGDVGHWRGRVRVGHVWLQRVRVWDP DQKRVGRVFRQMXQWRVX Y HZ R Q~P HURYDULiYHLVELQiULDVHUHVWULo}HVHRWHP SRFRP SXWDFLRQDOHP VHJXQGRVXWLOL]DGR 3DUDRVP RGHORV0 H0 HVWHVYDORUHVFRUUHVSRQGHP jVRP DGRVYDORUHVQHFHVViULRVSDUD UHVROYHURVP RGHORVSDUDWRGRVRVk GHVWLQRV/HP EUHVHTXHHVWHVP RGHORVVmRUHVROYLGRV LQGHSHQGHQWHP HQWHSDUDFDGDGHVWLQRk YHMDVHomR3RUILP VmRDSUHVHQWDGRVRV FRP SULP HQWRVP tQLP RVQHFHVViULRVSDUDHP SDFRWDUDVFDL[DVGHFDGDGHVWLQRk 1 RWHTXH SDUDRVP RGHORV0 H0 HVWHVYDORUHVHVWmRQDIRUP DDJUHJDGDLVWRpVmRRVFRP SULP HQWRV P tQLP RVQHFHVViULRVSDUDHP SDFRWDUWRGDVDVFDL[DVGRGHVWLQRDWXDOP DLVDVFDL[DVGRV GHVWLQRVSUHFHGHQWHV 7DEHOD5HVXOWDGRVREWLGRVFRP RVJUXSRV$ $ $ $ % % % H% HRVP RGHORV0 H0 1 R3DG1 RUP DLV 0 RGHOR0 0 RGHOR0 1 R n 1 R9 DU R 7HP SR 7HP SR n R L L 1 5HV &[ X Y Z L L L L L L 1 5HV V ¦ k k V ¦ k k $ $ $ $ % % % % 7DEHOD5HVXOWDGRVREWLGRVFRP RVJUXSRV$ $ $ $ % % % H% HRVP RGHORV0 H0 1 R3DG1 RUP DLV 0 RGHOR0 0 RGHOR0 1 R 1 R9 DU R 7HP SR 7HP SR R &[ X Y Z 1 5HV L 1 5HV V L L L L V L L L $ $ $ $ % % % % &RQYpP QRWDUTXHFRP RHUDHVSHUDGRHP IXQomRGDP DQHLUDFRP RIRUDP GHVHQYROYLGDVDVGXDVYHUV}HVSDUDFRQVLGHUDUFDUJDIUDFLRQDGDHP P ~OWLSORVGHVWLQRVRV UHVXOWDGRVREWLGRVFRP RVP RGHORV0 H0 VmRVHP SUHP HOKRUHVRXLJXDLVUHVSHFWLYDP HQWH GR TXH RV UHVXOWDGRV REWLGRV FRP RV P RGHORV 0 H 0 $ OpP GLVVR RV WHP SRV FRP SXWDFLRQDLVREWLGRVFRP RVP RGHORV0 H0 WDP EpP VmRUHVSHFWLYDP HQWHP DLRUHVTXH RVWHP SRVFRP SXWDFLRQDLVREWLGRVFRP RVP RGHORV0 H0 1 RWHHP DOJXQVFDVRVTXHRV P RGHORV0 H0 HQFRQWUDP RYDORUSDUDRFRP SULP HQWRP tQLP RQHFHVViULRTXHHUDR YDORUFRQVLGHUDGRRULJLQDOP HQWHSHORP RGHOR0 ,VWRpHVWHVP RGHORVFRQVHJXLUDP P HVP R FRP DFDUJDIUDFLRQDGDHQWUHGLIHUHQWHVGHVWLQRVHQFRQWUDURP HVP RFRP SULP HQWRXWLOL]DGR SDUDHP SDFRWDUDP HVP DFDUJDQmRIUDFLRQDGD (P SDUWLFXODUQRWHQD7DEHODTXHSDUDRH[HP SORGRJUXSR% RP RGHOR0 HQFRQWUDXP DVROXomRP HOKRUTXHDVROXomRGRP RGHOR0 RTXHQmRHUDHVSHUDGR,VWR HYHQWXDOP HQWHSRGHRFRUUHUFRP HVWHSURFHGLP HQWRXP DYH]TXHDVFDL[DVGRSULP HLUR GHVWLQRXP DYH]IL[DGDVQmRSRGHP P DLVVHUUHDUUDQMDGDVHRVP RGHORVTXHFRQWHP SODP FRQVLGHUDo}HV GH HVWDELOLGDGH GR FDUUHJDP HQWR WHQGHP D DSUHVHQWDU SDGU}HV GH HP SDFRWDP HQWRP DLVFRP SDFWRVRTXHSURSLFLDTXHFDL[DVGHGHVWLQRVSRVWHULRUHVVHMDP FRORFDGDVP DLVIDFLOP HQWHVREUHDVFDL[DVGHGHVWLQRVSUHFHGHQWHV$ )LJXUDLOXVWUDHVWH FRP HQWiULRFRP DVVROXo}HVHQFRQWUDGDVSDUDHVWHH[HP SORFRP RVP RGHORV0 0 0 H 0 UHVSHFWLYDP HQWH2 EVHUYHTXHQRFDVRGRVUHVXOWDGRVREWLGRVFRP RVP RGHORV0 H0 DOJXP DVFDL[DVGR~OWLP RGHVWLQRD]XOHVWmRDOpP GDVFDL[DVGRSHQ~OWLP RGHVWLQRFLQ]D ,VWRLQGLFDTXHR3URFHGLP HQWRQDVXDYHUVmRDWXDOQmRJDUDQWHTXHFDL[DVGRVGHVWLQRV UHP DQHVFHQWHVQmRSUHFLVHP VHUGHVFDUUHJDGDVHSRVWHULRUP HQWHUHFDUUHJDGDVSDUDTXH FDL[DVGRGHVWLQRSUHVHQWHVHMDP UHWLUDGDV )LJXUD3DGU}HVGHHP SDFRWDP HQWRREWLGRVFRP XP H[HP SORHRVP RGHORV0 0 0 H0 5 (68 /7$ ' 2 6' (( ; (0 3/2 6' $ / ,7(5 $ 78 5 $ (VWDVHomRDSUHVHQWDRVUHVXOWDGRVREWLGRVFRP DOJXQVSRXFRVH[HP SORVGD OLWHUDWXUDGHFRUWHHHP SDFRWDP HQWR0 XLWRVGRVH[HP SORVDSUHVHQWDGRVQDOLWHUDWXUDWUDWDP SUREOHP DVUHDOLVWDVGHFDUUHJDP HQWRGHFRQWrLQHUHVHQYROYHQGRXP JUDQGHQ~P HURGH SRVVtYHLV SRVLo}HV SDUD DUUDQMDU DV FDL[DV GHQWUR GR FRQWrLQHU (P GHFRUUrQFLD GD FRP SOH[LGDGHGRVSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVYHMDVHomRDP DLRUSDUWH GHVWHVH[HP SORVpUHVROYLGDDWUDYpVGHP pWRGRVKHXUtVWLFRVHGLILFLOP HQWHpSDVVtYHOGHVHU WUDWDGDDWUDYpVGHXP DDERUGDJHP H[DWDFRP RDDSUHVHQWDGDQHVWHWUDEDOKR$ OJXQVH[HP SORV GDOLWHUDWXUDHQYROYHQGRXP Q~P HURP RGHUDGRGHSRVVtYHLVSRVLo}HVSDUDVHDUUDQMDUDV FDL[DVGHQWURGRFRQWrLQHUVmRHQFRQWUDGRVHP &KHQet alH/LQVet al 2 H[HP SORDSUHVHQWDGRHP &KHQet alFRQVLGHUDXP ~QLFRFRQWrLQHU FRP DVGLP HQV}HVGHODUJXUDHDOWXUDIL[DVHDGLP HQVmRGHFRP SULP HQWRYDULiYHOHVHLV FDL[DVGLIHUHQWHVTXHGHYHP VHUHP SDFRWDGDVFRP RULHQWDomRYHUWLFDOIL[D2 REMHWLYRp P LQLP L]DURFRP SULP HQWRQHFHVViULRSDUDHP SDFRWDUWRGDVDVFDL[DVGHQWURGRFRQWrLQHU 1 RWHTXHHVWHSUREOHP DpGRWLSR' 5 2 ' 3YHMDVHomR2 FRQWrLQHUWHP GLP HQV}HV W H H DV VHLV FDL[DV WrP GLP HQV}HV lwh l w h lwh l w h lw h H l w h &KHQet alHP SDFRWDP WRGDVDVVHLVFDL[DVXWLOL]DQGRXP FRP SULP HQWRP tQLP RGHXQLGDGHV (VWHH[HP SORpDTXLWHVWDGRFRP RVP RGHORV0 H0 GDVHomR1 R SULP HLURFDVRRREMHWLYRpHP SDFRWDURP DLRUQ~P HURGHFDL[DVSRVVtYHOQRP HVP R FRP SULP HQWRP tQLP RHQFRQWUDGRSRU&KHQet al1 RVHJXQGRFDVRRREMHWLYRp HP SDFRWDUWRGDVDVFDL[DVQRP HQRUFRP SULP HQWRSRVVtYHOLVWRpRP HVP RREMHWLYRGH&KHQ et alQRWHTXHQHVWHFDVRpFRQVLGHUDGRDSHQDVXP GHVWLQRk $ QmRVREUHSRVLomR GDVFDL[DVHDHVWDELOLGDGHYHUWLFDOGRFDUUHJDP HQWRGHYHP VHUJDUDQWLGDVQDVGXDV VLWXDo}HV $ )LJXUDLOXVWUDRVSDGU}HVGHHP SDFRWDP HQWRREWLGRVSRU&KHQet al HFRP RVP RGHORV0 H0 UHVSHFWLYDP HQWH2 P RGHOR0 HP SDFRWDFLQFRFDL[DVHP XP WHP SRGHVHJXQGRVGHL[DQGRDFDL[DIRUDGRSDGUmRP DVJDUDQWLQGR GH HVWDELOLGDGHYHUWLFDOSDUDDVGHP DLVFDL[DV-iRP RGHOR0 HP SDFRWDWRGDVDVVHLVFDL[DVHP XP WHP SRGHVHJXQGRVP DVGHP RGRDJDUDQWLU GHHVWDELOLGDGHYHUWLFDOSDUD WRGDVDVFDL[DVXWLOL]DXP FRP SULP HQWRP tQLP RGHXQLGDGHV )LJXUD6ROXo}HVREWLGDVSDUDRH[HP SORGH&KHQet al 2 VTXDWRU]HH[HP SORVDSUHVHQWDGRVHP /LQVet alFRQVLGHUDP XP ~QLFR FRQWrLQHUFRP GLP HQV}HVIL[DVHFDL[DVGHXP ~QLFRWLSRTXHQmRWrP OLP LWDo}HVTXDQWRj RULHQWDomR2 REMHWLYRpP D[LP L]DURYROXP HWRWDOGHFDL[DVHP SDFRWDGDVGHQWURGRFRQWrLQHU 1 RWHTXHHVWHSUREOHP DpGRWLSR' 5 ,,33YHMDVHomR(P IXQomRGDVQHFHVVLGDGHV GHWHP SRHP HP yULDFRP SXWDFLRQDLVVLWXDo}HVLLLHLYP HQFLRQDGDVQDVHomRDSHQDV RVWUrVSULP HLURVH[HP SORVIRUDP FRQVLGHUDGRVQHVWHWUDEDOKR2 FRQWrLQHUWHP GLP HQV}HV LW H HRVWUrVWLSRVGHFDL[DVWrP GLP HQV}HV lwh l w h Hlwh (VWHVWUrVH[HP SORVVmRDTXLWHVWDGRVFRP RVP RGHORV0 H0 GDVHomR 1 RVGRLVFDVRVRREMHWLYRpHP SDFRWDURP DLRUQ~P HURGHFDL[DVSRVVtYHOGHQWURGRFRQWrLQHU $ QmRVREUHSRVLomRGDVFDL[DVGHYHVHUJDUDQWLGDQDVGXDVVLWXDo}HVHQTXDQWRDHVWDELOLGDGH YHUWLFDOGRFDUUHJDP HQWRGHYHVHUJDUDQWLGDDSHQDVQDVHJXQGD $ 7DEHODDSUHVHQWDRVUHVXOWDGRVREWLGRVFRP RVWUrVH[HP SORVHRV P RGHORV0 H0 DOpP GDP HOKRUVROXomRDSUHVHQWDGDHP /LQVet al1 RYDP HQWHR WHP SRFRP SXWDFLRQDOSDUDUHVROYHUFDGDP RGHORIRLOLP LWDGRHP KRUDVHJXQGRV 1 RWHTXHRP RGHOR0 HQFRQWUDDVVROXo}HVyWLP DVSDUDRVWUrVH[HP SORV-iRP RGHOR0 HQFRQWUDVROXo}HVLQWHLUDVSLRUHVTXHDVHQFRQWUDGDVSRU/LQVet alP DVJDUDQWLQGR GHHVWDELOLGDGHYHUWLFDOSDUDWRGDVDVFDL[DV 7DEHOD5HVXOWDGRVREWLGRVFRP RVWUrVH[HP SORVGH/LQVet alHRVP RGHORV0 H0 1 R3DG1 RUP DLV 0 RGHOR0 /LQVet al 0 RGHOR0 R R 1 R9 DU R gap 7HP SR 1 gap 7HP SR 1 1 R R X Y Z 1 5HV 1 5HV V &[ V &[ &[ $ )LJXUDLOXVWUDRVSDGU}HVGHHP SDFRWDP HQWRREWLGRVFRP RVWUrV H[HP SORVUHVROYLGRVFRP RVP RGHORV0 DFLP DH0 DEDL[R )LJXUD6ROXo}HVREWLGDVSDUDRVH[HP SORVGH/LQVet al & $ 3Ë78 /2 & 2 1 & /8 6® (6(3(5 63(& 7,9 $ 6)8 78 5 $ 6 1 HVWHWUDEDOKRIRUDP DSUHVHQWDGRVP RGHORVGHSURJUDP DomRP DWHP iWLFDSDUD GHVFUHYHUSUREOHP DVGHFDUUHJDP HQWRGHFDL[DVGHQWURGHFRQWrLQHUHVRXFDP LQK}HVYDJ}HV IHUURYLiULRVHSDOHWHVFRQWHP SODQGRDOJXP DVH[LJrQFLDVSUiWLFDVTXHSRGHP VHUOHYDGDVHP FRQVLGHUDomRTXDQGRVHGHVHMDP RGHODUSUREOHP DVGHFDUUHJDP HQWRGHFRQWrLQHUHVP DLV UHDOLVWDV([SHULP HQWRVFRP SXWDFLRQDLVIRUDP UHDOL]DGRVFRP DOJXQVGRVP RGHORVXWLOL]DQGR RDSOLFDWLYR* $ 0 6&3/(; HFHQWHQDVGHH[HP SORVJHUDGRVDOHDWRULDP HQWHHDOJXQV H[HP SORVGDOLWHUDWXUD2 VUHVXOWDGRVP RVWUDUDP TXHRVP RGHORVVmRFRHUHQWHVHUHSUHVHQWDP DGHTXDGDP HQWHDVVLWXDo}HVWUDWDGDVHP ERUDHVWDDERUGDJHP QDVXDYHUVmRDWXDOHVWHMD OLP LWDGDDUHVROYHURWLP DP HQWHDSHQDVSUREOHP DVGHWDP DQKREHP P RGHUDGRLVWRpHP TXHR Q~P HURGHSRVVtYHLVSRVLo}HVSDUDVHDUUDQMDUDVFDL[DVGHQWURGRFRQWrLQHUpUHODWLYDP HQWH SHTXHQR 1 RHQWDQWRDFUHGLWDVHTXHRVP RGHORVDSUHVHQWDGRVSRVVDP VHU~WHLVSDUD P RWLYDUSHVTXLVDVIXWXUDVH[SORUDQGRP pWRGRVGHGHFRP SRVLomRP pWRGRVGHUHOD[DomR P pWRGRVKHXUtVWLFRVHQWUHRXWURVSDUDUHVROYHUSUREOHP DVP DLVUHDOLVWDVGHFDUUHJDP HQWRGH FRQWrLQHUHV1 XP IXWXURSUy[LP RSUHWHQGHVHUHDOL]DUHDQDOLVDUH[SHULP HQWRVFRP SXWDFLRQDLV FRP RXWURVGRVP RGHORVDTXLDSUHVHQWDGRVFRP RP RGHORVFRP P ~OWLSORVFRQWrLQHUHVFRP REVWiFXORVGHIHLWRVFRP FRQWrLQHUHVFDL[DVQmRUHWDQJXODUHVFRP FRQVLGHUDo}HVGHOLP LWH GHSHVRHFRP HVWDELOLGDGHKRUL]RQWDOGRFDUUHJDP HQWR3UHWHQGHVHWDP EpP DSHUIHLoRDURV SURFHGLP HQWRVGHVHQYROYLGRVSDUDWUDWDUFRQVLGHUDo}HVGHFDUJDIUDFLRQDGDHP P ~OWLSORV GHVWLQRVHUHDOL]DUH[SHULP HQWRVFRP SXWDFLRQDLVDGLFLRQDLVFRP RVP HVP RV 2 XWUDVSHUVSHFWLYDVLQWHUHVVDQWHVSDUDSHVTXLVDIXWXUDVmRLHVWHQGHURV P RGHORVSDUDFRQVLGHUDURXWUDVH[LJrQFLDVSUiWLFDVDOpP GDVDSUHVHQWDGDVQHVWHWUDEDOKRWDLV FRP RFDUUHJDP HQWRFRP SOHWRGHJUXSRVGHLWHQVSULRULGDGHVGLVWULEXLomRGHSHVRGHQWURGR FRQWrLQHU HQWUH RXWUDV DSUHVHQWDGDV HP %LVFKRII H 5DWFOLII D LL WHVWDU HP SODQHMDP HQWRGHH[SHULP HQWRVTXDLVDVFRP ELQDo}HVGHYDORUHVGRVSDUkP HWURV&3/(; P DLV DGHTXDGDVSDUDUHVROYHURVSUREOHP DVSRUVLP SOLFLGDGHQHVWHWUDEDOKRWRGRVRVSDUkP HWURV &3/(; IRUDP XWLOL]DGRVQRVVHXVYDORUHVdefaultLLLH[SORUDUQRVP RGHORVRXVRGH UHVWULo}HVSDUDUHGXomRGHVLP HWULDQRVSDGU}HVGHHP SDFRWDP HQWRHLQYHVWLJDUVHRV FRQMXQWRVGHSDGU}HVQRUP DLVGHVFULWRVHP HHXWLOL]DGRVQRVP RGHORV SRGHP VHUVXEVWLWXtGRVVHP SHUGDGHJHQHUDOLGDGHSRUFRQMXQWRVGHP HQRUFDUGLQDOLGDGH FRP RRVFRQMXQWRVGHraster points6&+ (,7+ $ 8 (5et al%,5* ,1 et al.SDUD UHGX]LURWDP DQKRGRVP RGHORV 5 ()(5 Ç1 & ,$ 6% ,%/,2 * 5 È ),& $ 6 $ %' 2 8 * $ 5* + $ 9 $ 1 ,-,QWHUDFWLYH,/3SURFHGXUHVIRUVWDFNLQJRSWLP L]DWLRQIRUWKH ' SDOOHWL]DWLRQSUREOHP ,QWHUQDWLRQDO-RXUQDORI3URGXFWLRQ5 HVHDUFKYQS $ 0 $ 5$ /$ /(&+ 7)2 5' $ 1 & RP P HQWRQDQH[DFWDOJRULWKP IRUJHQHUDO RUWKRJRQDO WZ RGLP HQVLRQDO NQDSVDFN SUREOHP V /DQFDVWHU /DQFDVWHU 8 QLYHUVLW\ 0 DQDJHP HQW6FKRRO: RUNLQJ3DSHU $ 5$ 8 -2 2 &%3UREOHP DVGHFRUWHHHP SDFRWDP HQWRWULGLP HQVLRQDOHLQWHJUDomR FRP URWHDP HQWRGHYHtFXORVS7HVH' RXWRUDGRHP (QJHQKDULD(OpWULFD )DFXOGDGHGH(QJHQKDULD(OpWULFDHGH&RP SXWDomR8 QLYHUVLGDGH(VWDGXDOGH&DP SLQDV &DP SLQDV63 $ 5$ 8 -2 2 &%$ 50 (1 7$ 1 2 9 $ $ P XOWLVWDUWUDQGRP FRQVWUXFWLYHKHXULVWLFIRUWKH FRQWDLQHUORDGLQJSUREOHP 3HVTXLVD2 SHUDFLRQDOYQS $ 5(1 $ /(60 0 2 5$ %,72 5< $ 1 $ 66(+ &XWWLQJDQGSDFNLQJSUREOHP V3HVTXLVD 2 SHUDFLRQDOYQS %$ //2 8 5+ * HUHQFLDP HQWRGHFDGHLDGHVXSULP HQWRVSODQHMDP HQWRRUJDQL]DomRH ORJt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b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tVWLFDHP SUHVDULDORSURFHVVRGHLQWHJUDomRGD FDGHLDGHVXSULP HQWR6mR3DXOR$ WODVS %52 : 1 $ 52 SWLP XP SDFNLQJDQGGHSOHWLRQWKHFRP SXWHULQVSDFHDQGUHVRXUFH XVDJHSUREOHP V/RQGRQ0 DFGRQDOGDQG&R1 HZ < RUN$ P HULFDQ(OVHYLHUS &RP SXWHU0 RQRJUDSKV %58 1 (77$ /* 5(* 2 ,5(3$ JHQHUDOSXUSRVHDOJRULWKP IRUWKUHHGLP HQVLRQDO SDFNLQJ,1 )2 5 0 6-RXUQDORQ& RP SXWLQJYQS %5< 0 $ 1 $ 5 HVHDUFKP HWKRGVDQGRUJDQL]DWLRQVWXGLHV/RQGRQ8 QZ LQ+ \P DQ S &$ 0 32 6' 6,QWHJUDomRGRVSUREOHP DVGHFDUUHJDP HQWRHURWHDP HQWRGHYHtFXORV FRP MDQHODGHWHP SRHIURWDKHWHURJrQHDS7HVH' RXWRUDGRHP (QJHQKDULDGH 3URGXomR' HSDUWDP HQWRGH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGHGH6mR3DXOR6mR3DXOR 63 &(&,/,2 )2 + HXUtVWLFDVSDUDRSUREOHP DGHFDUUHJDP HQWRGHFDUJDGHQWURGH FRQWrLQHUHVS' LVVHUWDomR0 HVWUDGRHP (QJHQKDULDGH3URGXomR' HSDUWDP HQWR GH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGH)HGHUDOGH6mR&DUORV6mR&DUORV63 &(&,/,2 )2 0 2 5$ %,72 55HILQDP HQWRVQDKHXUtVWLFDGH* HRUJHH5RELQVRQSDUDR SUREOHP DGHFDUUHJDP HQWRGHFDL[DVGHQWURGHFRQWr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¶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pWRGRKHXUtVWLFREDVHDGRHP UHOD[DomRODJUDQJLDQDSDUDUHVROYHUR SUREOHP DGHFDUUHJDP HQWRGHSDOHWHVGRSURGXWRUS' LVVHUWDomR0 HVWUDGRHP (QJHQKDULDGH3URGXomR' HSDUWDP HQWRGH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGH)HGHUDO GH6mR&DUORV6mR&DUORV63 )$ 52 (2 3,6,1 * (5' =$ &+ $ 5,$ 6(1 0 * XLGHGORFDOVHDUFKIRUWKHWKUHH GLP HQVLRQDOELQSDFNLQJSUREOHP ,1 )2 5 0 6-RXUQDORQ& RP SXWLQJYQS )(55(,5$ $ %+ 1 RYRGLFLRQiULRGDOtQJXDSRUWXJXHVDHG5LRGH-DQHLUR1 RYD )URQWHLUDS * (+ 5,1 * + %2 57)(/' 7$ $ JHQHWLFDOJRULWKP IRUVROYLQJWKHFRQWDLQHUORDGLQJ SUREOHP ,QWHUQDWLRQDO7UDQVDFWLRQVLQ2 SHUDWLRQDO5 HVHDUFKYQS * (+ 5,1 * + %2 57)(/' 7 $ (LQ YHUWHLOWSDUDOOHOHV 7DEX 6HDUFK9 HUIDKUHQ IU &RQWDLQHUEHODGHSUREOHP HP LWVFKZ DFKKHWHURJHQHP . LVWHQYRUUDW,QWHUQDWLRQDO& RQIHUHQFH RQ2 SHUDWLRQV5 HVHDUFK=XULFK3URFHHGLQJV%HUOLQ6SULQJHU9 HUODJS * (+ 5,1 * + %2 57)(/' 7$ $ SDUDOOHOJHQHWLFDOJRULWKP IRUVROYLQJWKHFRQWDLQHU ORDGLQJSUREOHP ,QWHUQDWLRQDO7UDQVDFWLRQVLQ2 SHUDWLRQDO5 HVHDUFKYQS * (+ 5,1 * + 0 (1 6&+ 1 (5. 0 (< (50 $ FRP SXWHUEDVHGKHXULVWLFIRUSDFNLQJ SRROHGVKLSP HQWFRQWDLQHUV(XURSHDQ-RXUQDORI2 SHUDWLRQDO5 HVHDUFKYQS * (1 ' 5($ 8 0 ,2 5,0 /$ 32 57(* 0 $ 57(//2 6$ WDEXVHDUFKDOJRULWKP IRUD URXWLQJDQGFRQWDLQHUORDGLQJSUREOHP 7UDQVSRUWDWLRQ6FLHQFHYQS * (2 5* (-$ $ P HWKRGIRUVROYLQJFRQWDLQHUSDFNLQJIRUDVLQJOHVL]HRIER[-RXUQDORI WKH2 SHUDWLRQDO5 HVHDUFK6RFLHW\YQS * (2 5* (-$ 52 %,1 62 1 ' )$ KHXULVWLFIRUSDFNLQJER[HVLQWRDFRQWDLQHU & RP SXWHUVDQG2 SHUDWLRQV5 HVHDUFKYQS * ,/0 2 5(3&* 2 0 2 5< 5(0 XOWLVWDJHFXWWLQJVWRFNSUREOHP VRIWZ RDQGP RUH GLP HQVLRQV2 SHUDWLRQV5 HVHDUFKYQS * 2 /' (1 %$ SSURDFKHVWRWKHFXWWLQJVWRFNSUREOHP $ ,,(7UDQVDFWLRQVYQS + $ ' -,&2 1 67$ 1 7,1 2 8 ( &+ 5,672 ),' (6 1 $ Q H[DFW DOJRULWKP IRU JHQHUDO RUWKRJRQDO WZ RGLP HQVLRQDO NQDSVDFN SUREOHP V (XURSHDQ -RXUQDO RI 2 SHUDWLRQDO 5 HVHDUFKYQS + $ (66/(55: 7$ /%2 7)%/RDGSODQQLQJIRUVKLSP HQWVRIORZ GHQVLW\SURGXFWV (XURSHDQ-RXUQDORI2 SHUDWLRQDO5 HVHDUFKYQS + $ (66/(55: 6: ((1 (< 3(&XWWLQJVWRFNSUREOHP VDQGVROXWLRQSURFHGXUHV (XURSHDQ-RXUQDORI2 SHUDWLRQDO5 HVHDUFKYQS + $ 1 &3. 1 2 77. (* %(/8 3-$ KHXULVWLFDSSURDFKWRWKHWKUHHGLP HQVLRQDO FDUJRORDGLQJSUREOHP ,QWHUQDWLRQDO-RXUQDORI3URGXFWLRQ5 HVHDUFKYQS + $ 66$ 0 2 1 75-2 QGHFRP SRVLQJ' SDFNLQJSUREOHP LQZ RRGHQIXUQLWXUHLQGXVWU\,Q ,(((,1 7(51 $ 7,2 1 $ /6< 0 32 6,8 0 2 1 &2 0 38 7$ 7,2 1 $ /,1 7(//,* (1 &( ,1 52 %2 7,&6$ 1 ' $ 8 72 0 $ 7,2 1 . REH3URFHHGLQJV1 HZ -HUVH\-RKQ: LOH\ 6RQVS + (' < &+ $ -=5HVHDUFKRQVROXWLRQWRFRP SOH[FRQWDLQHUORDGLQJSUREOHP EDVHGRQ JHQHWLF DOJRULWKP ,Q ,1 7(51 $ 7,2 1 $ / &2 1 )(5(1 &( 2 1 0 $ &+ ,1 ( /($ 51 ,1 * $ 1 ' &< %(51 (7,&6%HLMLQJ3URFHHGLQJV1 HZ -HUVH\-RKQ: LOH\ 6RQVS + (5=-&5HFXUVLYHFRP SXWDWLRQDOSURFHGXUHIRUWZ RGLP HQVLRQDOVWRFNFXWWLQJ,%0 -RXUQDORI5 HVHDUFKDQG' HYHORSP HQWYQS + ,), 0 $ SSUR[LP DWH DOJRULWKP V IRU WKH FRQWDLQHU ORDGLQJ SUREOHP ,QWHUQDWLRQDO 7UDQVDFWLRQVLQ2 SHUDWLRQDO5 HVHDUFKYQSD + ,),0 &XWWLQJDQGSDFNLQJSUREOHP V6WXGLD,QIRUP DWLFD8 QLYHUVDOLVYQS E6SHFLDO,VVXH + ,), 0 ([DFW DOJRULWKP V IRU XQFRQVWUDLQHG WKUHHGLP HQVLRQDO FXWWLQJ SUREOHP V D FRP SDUDWLYHVWXG\& RP SXWHUVDQG2 SHUDWLRQV5 HVHDUFKYQS + ,1 ; 0 $ 1 $ ,7KHWULP ORVVDQGDVVRUWP HQWSUREOHP VDVXUYH\(XURSHDQ-RXUQDORI 2 SHUDWLRQDO5 HVHDUFKYQS + 2 ' * 62 1 7-$ FRP ELQHGDSSURDFKWRWKHSDOOHWORDGLQJSUREOHP ,,(7UDQVDFWLRQVY QS + 8 $ 1 * : + (. $ FDYLQJGHJUHHDSSURDFKIRUWKHVLQJOHFRQWDLQHUORDGLQJSUREOHP (XURSHDQ-RXUQDORI2 SHUDWLRQDO5 HVHDUFKYQSD + 8 $ 1 * : + (. $ QHZ KHXULVWLFDOJRULWKP IRUFXERLGVSDFNLQJZ LWKQRRULHQWDWLRQ FRQVWUDLQWV& RP SXWHUVDQG2 SHUDWLRQV5 HVHDUFKYQSE ,2 5,0 0 HWDKHXULVWLFDOJRULWKP VIRUFRP ELQDWRULDORSWLP L]DWLRQSUREOHP VS ' RWWRUDWRGL5LFHUFDLQ$ XWRP DWLFDH5LFHUFD2 SHUDWLYD' (,6±8 QLYHUVLWj' HJOL6WXGL' L %RORJQD%RORJQD,Wi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tVWLFD' LVSRQt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rLQHUHV3HVTXLVD2 SHUDFLRQDOYQS 0 2 5$ %,72 53UREOHP DVGHFRUWHHHP SDFRWDP HQWRP LQLFXUVR,Q; (6&8 (/$ /$ 7,1 2 $ 0 (5,&$ 1 $ ' ( 9 (5$ 1 2 ' ( ,1 9 (67,* $ &,Ï 1 2 3(5$ 7,9 $ 0 RQWHYLGHR5 HVXP RV6mR&DUORV8 )6&DUS 0 2 5$ /(6652 WLP L]DFDRQRFDUUHJDP HQWRGHSDOHWHVXP DDERUGDJHP KHXULVWLFDSDUD UHVROYHURSUREOHP DGRSURGXWRUS' LVVHUWDomR0 HVWUDGRHP (QJHQKDULDGH 3URGXomR' HSDUWDP HQWRGH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGH)HGHUDOGH6mR&DUORV 6mR&DUORV63 0 2 8 5$ $ 2 /,9 (,5$ -)$ * 5$ 63DSSURDFKWRWKHFRQWDLQHUORDGLQJSUREOHP ,((( ,QWHOOLJHQW6\VWHP VYQS 1 * 2 ,%. $ 7$ < 0 /&+ 8 $ (6$ SSO\LQJVSDWLDOUHSUHVHQWDWLRQWHFKQLTXHVWRWKH FRQWDLQHUSDFNLQJSUREOHP ,QWHUQDWLRQDO-RXUQDORI3URGXFWLRQ5 HVHDUFKYQS 1292 0 ,/Ç1 ,2 9 DQWDJHQV H GHVYDQWDJHQV ' LVSRQtYHO HP KWWSZ Z Z QRYRP LOHQLRLQIEUSRUWRFRQWHLKWP !$ FHVVRHP P DLR 2 /,9 (,5$ /. 0 pWRGRVH[DWRVEDVHDGRVHP UHOD[DomRODJUDQJLDQDHVXUURJDWHSDUDR SUREOHP DGHFDUUHJDP HQWRGHSDOHWHVGRSURGXWRUS7HVH' RXWRUDGRHP (QJHQKDULDGH3URGXomR' HSDUWDP HQWRGH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGH)HGHUDO GH6mR&DUORV6mR&DUORV63 2 /,9 (,5$ -): b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omRGRP pWRGRGHGHFRP SRVLomRGH%HQGHUVSDUDRSUREOHP DGH FDUUHJDP HQWRGHSDOHWHVS' LVVHUWDomR0 HVWUDGRHP (QJHQKDULDGH3URGXomR ' HSDUWDP HQWRGH(QJHQKDULDGH3URGXomR8 QLYHUVLGDGH)HGHUDOGH6mR&DUORV6mR&DUORV 63 6&+ (,7+ $ 8 (5* 7(51 2 -0 RGHOOLQJRISDFNLQJSUREOHP V2 SWLP L]DWLRQYS 6&+ (,7+ $ 8 (5* 7(51 2 -5,(+ 0 (-62 0 0 (5: (,668 $ QHZ KHXULVWLF DSSURDFKIRUVROYLQJWKHP XOWLSDOOHWSDFNLQJSUREOHP ' UHVGHQ7HFKQLVFKH8 QLYHUVLWlW ' UHVGHQ7HFKQLFDO5HSRUW 6,/9 $ -/&62 0 $ 1 < 8 P DOJRULWP RSROLQRP LDOSDUDRSUREOHP DGHHP SDFRWDP HQWR GHFRQWrLQHUHVFRP HVWDELOLGDGHHVWi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tYHOHP 77&B0 RG,QIUDHVWUXWXUDSGI! $ FHVVRHP P DLR : $ 1 * 3< : b 6&+ (5* &XWWLQJDQGSDFNLQJ(XURSHDQ-RXUQDORI2 SHUDWLRQDO 5 HVHDUFKYQS6SHFLDO,VVXH : $ 1 * =/,. : /(9 < -. $ KHXULVWLFIRUWKHFRQWDLQHUORDGLQJSUREOHP DWHUWLDU\ WUHHEDVHGG\QDP LFVSDFHGHFRP SRVLWLRQDSSURDFK(XURSHDQ-RXUQDORI2 SHUDWLRQDO 5 HVHDUFKYQS : b 6&+ (5* + $ 8 661 (5+ 6&+ 8 0 $ 1 1 + $ QLP SURYHGW\SRORJ\RIFXWWLQJDQG SDFNLQJSUREOHP V(XURSHDQ-RXUQDORI2 SHUDWLRQDO5 HVHDUFKYQS ; 8 (-/$ ,. . (IIHFWLYHP HWKRGVIRUDFRQWDLQHUSDFNLQJRSHUDWLRQ0 DWKHP DWLFDODQG & RP SXWHU0 RGHOOLQJYQS < (8 1 * /+ : 7$ 1 * : . 6$ K\EULGJHQHWLFDSSURDFKIRUFRQWDLQHUORDGLQJLQ ORJLVWLFVLQGXVWU\,(((7UDQVDFWLRQVRQ,QGXVWULDO(OHFWURQLFVYQS $ 3Ç1 ' ,' ($ 0 2 ' (/2 6(0 * $ 0 6±3$ 5 7(, 2 P RGHORDVHJXLUHVWiLP SOHP HQWDGRQDOLQJXDJHP GHP RGHODJHP * $ 0 6H FRQVLGHUDFRP ELQDo}HVF{QLFDVSDGU}HVQRUP DLVRULHQWDomRIL[DSDUDDVFDL[DVHVWDELOLGDGH HP UHODomRDRHL[Rz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Ç1 ' ,' (% 0 2 ' (/2 6(0 * $ 0 6±3$ 5 7(,, 2 P RGHORDVHJXLUHVWiLP SOHP HQWDGRQDOLQJXDJHP GHP RGHODJHP * $ 0 6H FRQVLGHUDFRP ELQDo}HVF{QLFDVSDGU}HVQRUP DLVRULHQWDomRIL[DSDUDDVFDL[DVP ~OWLSORV GHVWLQRVSURFHGLP HQWRHHVWDELOLGDGHHP UHODomRDRHL[Rz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
Documentos relacionados
riia - Red - Ictiofauna
GHSURWRFRORVGHHVWXGLRSDUDTXHORVGDWRVDGTXLULGRVHQGLVWLQWRVSDtVHVDPD]yQLFRV SXHGDQ FRPSDUDUVH R XWLOL]DUVH FRQMXQWDPHQWH HQ UD]yQ D TXH EXHQD SDUWH GH ORVUHFXUVRVDFXiWLFRV...
Leia mais._OBJETIVO E CAMPO DE APLICAÇÃO
$ 0e72'26'((16$,2 $ 0e72'263$5$$$9$/,$d2'$/,;,9,$d2(9$=...
Leia mais