Buscar

apost_vib_mec_214p

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 3, do total de 214 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 6, do total de 214 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes
Você viu 9, do total de 214 páginas

Faça como milhares de estudantes: teste grátis o Passei Direto

Esse e outros conteúdos desbloqueados

16 milhões de materiais de várias disciplinas

Impressão de materiais

Agora você pode testar o

Passei Direto grátis

Você também pode ser Premium ajudando estudantes

Prévia do material em texto

9LEUDFaRHV 0HFADQLFDV
5HVXPR GD WHRULD H H[HUF˜•FLRV
&� :ROWHU� 5� 6DPSDLR� (� &DWDOGR
5LR GH -DQHLUR� PDUFR GH �����
˜,QGLFH
� 5HVSRVWD OLYUH GH XP VLVWHPD �
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � �
����� 6LVWHPD PDVVD�PROD � � � � � � � � � � � � � � � � � � � �
����� $PRUWHFLPHQWR YLVFRVR � � � � � � � � � � � � � � � � � � �
����� /XJDU JHRP˜HWULFR GDV UD˜•]HV � � � � � � � � � � � � � � � �
����� (QHUJLD GR VLVWHPD � � � � � � � � � � � � � � � � � � � � �
����� 'LDJUDPD GH IDVH � � � � � � � � � � � � � � � � � � � � � �
����� /LQHDUL]DFaDR GH XP VLVWHPD � � � � � � � � � � � � � � � ��
��� 0RGHORV GH H[HUF˜•FLRV � � � � � � � � � � � � � � � � � � � � � � � ��
� 5HVSRVWD —D H[FLWDFaDR KDUPARQLFD ��
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � ��
����� 6LVWHPDV VHP DPRUWHFLPHQWR � � � � � � � � � � � � � � � ��
����� 6LVWHPD DPRUWHFLGR � � � � � � � � � � � � � � � � � � � � ��
����� ([FLWDFaDR GH EDVH � � � � � � � � � � � � � � � � � � � � � ��
����� 'HVEDODQFHDPHQWR HP URWDFaRHV � � � � � � � � � � � � � ��
����� 'LVSRVLWLYRV GH PHGLFaDR� � � � � � � � � � � � � � � � � � ��
��� 0RGHORV GH H[HUF˜•FLRV � � � � � � � � � � � � � � � � � � � � � � � ��
� 5HVSRVWD SDUD IRUFDPHQWR JHUDO� ��
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � ��
����� )XQFaDR UHVSRVWD LPSXOVLRQDO � � � � � � � � � � � � � � � ��
����� 5HVSRVWD SDUD XPD HQWUDGD DUELWU˜DULD � � � � � � � � � � ��
����� 5HVSRVWD SDUD XPD HQWUDGD SHUL˜RGLFD DUELWU˜DULD � � � � ��
��� 0RGHORV GH ([HUF˜•FLRV � � � � � � � � � � � � � � � � � � � � � � ��
� 0˜XOWLSORV JUDXV GH OLEHUGDGH ��
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � ��
L
����� 'RLV JUDXV GH OLEHUGDGH �VHP DPRUWHFLPHQWR� � � � � � ��
����� $XWRYDORUHV H IUHT¦XAHQFLDV QDWXUDLV � � � � � � � � � � � � ��
����� $Q˜DOLVH PRGDO � � � � � � � � � � � � � � � � � � � � � � � ��
����� 0DLV GH GRLV JUDXV GH OLEHUGDGH � � � � � � � � � � � � � ��
����� 6LVWHPDV FRP DPRUWHFLPHQWR � � � � � � � � � � � � � � � ��
����� $Q˜DOLVH 0RGDO GD 5HVSRVWD )RUFDGD � � � � � � � � � � � ��
��� 0RGHORV GH ([HUF˜•FLRV � � � � � � � � � � � � � � � � � � � � � � ��
� 9LEUDFaRHV GH VLVWHPDV FRQW˜•QXRV ��
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � ��
����� 9LEUDFaRHV GH XPD FRUGD RX FDER� � � � � � � � � � � � � ��
����� 0RGRV H IUHT¦XAHQFLDV QDWXUDLV � � � � � � � � � � � � � � ��
����� 9LEUDFaRHV ORQJLWXGLQDLV GH XPD EDUUD � � � � � � � � � � ��
����� 9LEUDFaDR WRUFLRQDO � � � � � � � � � � � � � � � � � � � � ��
����� )OH[aDR GH YLJDV �YLJDV HVEHOWDV� � � � � � � � � � � � � � ��
��� 0RGHORV GH H[HUF˜•FLRV � � � � � � � � � � � � � � � � � � � � � � � ���
� 0˜HWRGR GH HOHPHQWRV ‘QLWRV ���
��� 5HVXPR GD WHRULD � � � � � � � � � � � � � � � � � � � � � � � � � ���
����� ([HPSOR� D EDUUD � � � � � � � � � � � � � � � � � � � � � ���
����� %DUUD FRP WAUHV HOHPHQWRV � � � � � � � � � � � � � � � � ���
����� 9LJDV � � � � � � � � � � � � � � � � � � � � � � � � � � � � ���
����� 0DWUL] GH PDVVD LQFRQVLVWHQWH � � � � � � � � � � � � � � ���
����� 7UHOLFDV � � � � � � � � � � � � � � � � � � � � � � � � � � ���
$ ([HUF˜•FLRV GR (QJLQHHULQJ 9LEUDWLRQ ���
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � ���
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
LL
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$����� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$�� 3UREOHPDV UHVROYLGRV GR FDS˜•WXOR � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ��� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
LLL
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
$���� ([HUF˜•FLR ���� � � � � � � � � � � � � � � � � � � � � � � � ���
5HIHUAHQFLDV ELEOLRJU˜D‘FDV
�
&DS˜•WXOR �
5HVSRVWD OLYUH GH XP VLVWHPD
��� 5HVXPR GD WHRULD
����� 6LVWHPD PDVVD�PROD
&RQVLGHUHPRV XP VLVWHPD PDVVD�PROD FRPR LQGLFD D ‘JXUD� RQGHP ˜H D PDVVD
H N ˜H D ULJLGH] GD PROD�
)LJXUD ���� 6LVWHPD PDVVD�PROD�
'LQADPLFD GR VLVWHPD� P¦[�W� ƒN[�W� RX P¦[�W� � N[�W� �
3URSRPRV XPD VROXFaDR GR WLSR [�W� $H
šW
� $VVLP�
B[�W� $šH
šW
H ¦[�W� $š
�
H
šW
6XEVWLWXLQGR QD HTXDFaDR GD GLQADPLFD GR PRYLPHQWR� WHPRV TXH
P$š
�
H
šW
� N$H
šW��
�
&RPR $H
šW
� �� SRGHPRV FDQFHODU HVWH WHUPR� FKHJDQGR D
Pš
�
� N �� š 
U
ƒ
N
P
 ‰ L
U
N
P
�
$VVLP� š ‰L�
Q
RQGH �
Q
 
T
N
P
˜H GH‘QLGD FRPR D IUHTXAHQFLD QDWXUDO GR
VLVWHPD H WHPRV FRPR VROXFaDR�
[�W� $
�
H
L�
Q
W
�$
�
H
ƒL�
Q
W
�
&RPR WHPRV GXDV FRQVWDQWHV DUELWU˜DULDV� $
�
H $
�
� SDUD GHWHUPLQ˜D�ODV� SUH�
FLVDPRV GH GXDV FRQGLFaRHV LQLFLDLV [��� [
�
H B[��� Y
�
� RQGH D SULPHLUD
UHSUHVHQWD D SRVLFaDR LQLFLDO H D VHJXQGD D YHORFLGDGH LQLFLDO�
&RPR VDEHPRV� H
L�
Q
W
˜H D IRUPD H[SRQHQFLDO SDUD FRV�
Q
W � L VHQ�
Q
W H
DVVLP� SRGHPRV UHHVFUHYHU D HTXDFaDR TXH GHVFUHYH D GLQADPLFD GR VLVWHPD GH
RXWUDV IRUPDV� WDLV FRPR�
[�W� & FRV�
Q
W�' VHQ �
Q
W RX
[�W� ( FRV��
Q
W� £� RX
[�W� ) VHQ��
Q
W� £�
RQGH QRYDPHQWH SUHFLVDPRV GHWHUPLQDU DV � FRQVWDQWHV DUELWU˜DULDV GH FDGD
HTXDFaDR DWUDY˜HV GDV FRQGLFaRHV LQLFLDLV� 1HVWHV � FDVRV� DV FRQVWDQWHV VaDR UHDLV
H £ UHSUHVHQWD D IDVH GR PRYLPHQWR KDUPARQLFR�
����� $PRUWHFLPHQWR YLVFRVR
&RQVLGHUHPRV R VLVWHPD PDVVD�PROD�DPRUWHFHGRU FRPR LQGLFD D ‘JXUD ���� H
FXMD GLQADPLFD GR VLVWHPD ˜H UHSUHVHQWDGD SHOD HTXDFaDR DEDL[R�
P¦[�W� � F B[�W� � N[�W� ��
3RGHPRV SURSRU QRYDPHQWH XPD VROXFaDR GR WLSR�
[�W� $H
šW
�
�
)LJXUD ���� 6LVWHPD PDVVD�PROD�DPRUWHFHGRU�
$VVLP�
B[�W� $šH
šW
H ¦[�W� $š
�
H
šW
�
6XEVWLWXLQGR QD HTXDFaDR GD GLQADPLFD GR VLVWHPD� WHPRV TXH
�Pš
�
� Fš� N�$H
šW
 ��
&RPR $H
šW
� �� HOLPLQDPRV HVWH WHUPR QD HTXDFaDR� GH IRUPD TXH
�Pš
�
� Fš� N� ��
TXH ˜H FKDPDGD GH HTXDFaDR FDUDFWHU˜•VWLFD�
$V VROXFaRHV SDUD D HTXDFaDR DFLPD VaDR
š
���
 ƒ
F
�P
‰
�
�P
S
F
�
ƒ �PN�
3RGHPRV UHHVFUHYAH�OD QD IRUPD
š
���
 ƒ
F
�P
‰
U
F
�
ƒ �PN
�P
�
 ƒ
F
�P
‰
U
•
F
�P
–
�
ƒ
N
P
 
 ƒ
F
�P
‰
V
™
N
P
ƒ
•
F
�P
–
�
š
�ƒ�� ƒ
F
�P
‰ L
U
�
�
Q
ƒ
•
F
�P
–
�
_ ^] `
�
G
�
'HVWD IRUPD� D VROXFaDR GR VLVWHPD� VH DV UD˜•]HV IRUHP GLVWLQWDV� ˜H GD IRUPD
[�W� $H
š
�
W
�%H
š
�
W
 
 $H
t
ƒ
F
�P
�L
T
�
�
Q
ƒ
�
F
�P
�
�
u
W
�%H
t
ƒ
F
�P
ƒL
T
�
�
Q
ƒ
�
F
�P
�
�
u
W
 
 H
ƒ
F
�P
W
™
$H
L
T
�
�
Q
ƒ
�
F
�P
�
�
W
�%H
ƒL
T
�
�
Q
ƒ
�
F
�P
�
�
W
š
 
 H
ƒ
F
�P
W
ƒ
$H
L�
G
W
�%H
ƒL�
G
W
„
�
2X� QD IRUPD WULJRQRP˜HWULFD�
[�W� H
ƒ
F
�P
W
�& FRV�
G
W�' VHQ�
G
W� �
9HUL‘FDPRV TXH š SRGH VHU UHDO RX FRPSOH[R� GHSHQGHQGR GR YDORU GR WHUPR
F
�
ƒ ƒ�PN� $VVLP� WHPRV � FDVRV SRVV˜•YHLV� 'H‘QLPRV R DPRUWHFLPHQWR
FU˜•WLFR GD VHJXLQWH PDQHLUD�
F
FU
 �P�
Q
 �
S
PN�
TXH YHP D VHU R YDORU GR FRH‘FLHQWH GH DPRUWHFLPHQWR TXH DQXOD D H[SUHVVaDR
F
�
ƒ �PN�
3RGHPRV� DLQGD� GH‘QLU D UD]aDR GH DPRUWHFLPHQWR GH XP VLVWHPD FRPR�
• 
F
F
FU
 
F
�P�
Q
�
/RJR� DV UD˜•]HV GD HTXDFaDR FDUDFWHU˜•VWLFD SRGHP VHU HVFULWDV FRPR
š
���
 ƒ•�
Q
ƒ L�
Q
S
�ƒ •
�
�
$VVLP� SURFHGHPRV SDUD D GH‘QLFaDR GRV � WLSRV GH PRYLPHQWR SRVV˜•YHLV
” 0RYLPHQWR VXE�DPRUWHFLGR
4XDQGR F
�
ƒ �PN � � RX� DQDORJDPHQWH� • � �� WHPRV
š ƒ
F
�P
‰ L
U
N
P
ƒ
•
F
�P
–
�
�
( D VROXFaDR JHUDO VHU˜D
[�W� H
ƒ
F
�P
W
>$ FRV�
G
W�% VHQ�
G
W@ �
1HVWH FDVR� RFRUUH RVFLODFaDR� $ VROXFaDR JU˜D‘FD SDUD XP VLVWHPD FRP
P �� N � H F � ˜H PRVWUDGD QD ‘JXUD ����
�
)LJXUD ���� 6LVWHPD VXE�DPRUWHFLGR�
” 0RYLPHQWR FULWLFDPHQWH DPRUWHFLGR
1HVWH FDVR� F
�
ƒ �PN � RX • � H� FRPR M˜D YLPRV F F
FU
� /RJR�
š ƒ
F
�P
RX VHMD� D HTXDFaDR FDUDFWHU˜•VWLFD SRVVXL GXDV UD˜•]HV UHDLV H LJXDLV� $
VROXFaDR JHUDO ˜H� HQWaDR�
[�W� �$�%W�H
ƒ
F
�P
W
�
1aDR K˜D RVFLODFaDR� LVWR ˜H� D PDVVD QaDR SDVVD SHOD VXD SRVLFaDR RULJLQDO FRP
R PHVPR VHQWLGR GD VXD YHORFLGDGH LQLFLDO XPD VHJXQGD YH]� 3ORWDPRV
QRYDPHQWH D UHVSRVWD GR VLVWHPD DQWHULRU FRP F ��
)LJXUD ���� 6LVWHPD FULWLFDPHQWH DPRUWHFLGR�
” 0RYLPHQWR VXSHU�DPRUWHFLGR
�
$TXL� F
�
ƒ �PN ! � RX • ! � H WHPRV GXDV UD˜•]HV UHDLV SDUD š H D
VROXFaDR GR VLVWHPD DVVXPH D IRUPD�
[�W� $H
ƒF�
S
F
�
ƒ�PNW
�P
�%H
ƒFƒ
S
F
�
ƒ�PNW
�P
1HVWH FDVR� WDPE˜HP QaDR K˜D RVFLODFaDR� $ UHVSRVWD GR VLVWHPD SDUD F �
SORWDGD QR 0$7/$% ˜H�
)LJXUD ���� 6LVWHPD VXSHU�DPRUWHFLGR�
&RQY˜HP OHPEUDU TXH WRGDV DV FRQVWDQWHV DUELWU˜DULDV XVDGDV VaDR GHWHUPLQDGDV
GDV FRQGLFaRHV LQLFLDLV GR VLVWHPD�
����� /XJDU JHRP˜HWULFR GDV UD˜•]HV
3RGHPRV WDPE˜HP HVWXGDU R FRPSRUWDPHQWR GR VLVWHPD HP IXQFaDR GH • 
F
F
FU
�
-˜D VDEHPRV TXH VH • � � K˜D RVFLODFaDR� VH • � R DPRUWHFLPHQWR ˜H FU˜•WLFR H
FDVR • ! � R VLVWHPD ˜H VXSHU�DPRUWHFLGR H� GD PHVPD IRUPD� QaDR K˜D RVFLODFaDR�
3RGHPRV UHHVFUHYHU R WHUPR • GDV VHJXLQWHV PDQHLUDV�
• 
F
�
S
PN
 
F
�P�
Q
�
$ VROXFaDR GD HTXDFaDR FDUDFWHU˜•VWLFD WDPE˜HP SRGH VHU FRORFDGD HP IXQFaDR GH
•�
š
���
 ƒ
•�P�
Q
�P
‰ L
V
�
�
Q
ƒ
—
�•P�
Q
�P
˜
�
 
 ƒ•�
Q
‰ L
S
�
�
Q
ƒ •
�
�
�
Q
� š
���
 �
Q
� ƒ•
_^]`
$
‰L
S
� ƒ •
�
_ ^] `
%
�
�
2EVHUYH TXH $
�
�%
�
 � H� SRUWDQWR� PDQWHQGR �
Q
FRQVWDQWH� DV UD˜•]HV FRP�
SOH[DV GD HTXDFaDR FDUDFWHU˜•VWLFD VH HQFRQWUDP VREUH XPD VHPL�FLUFXQIHUAHQFLD
GH UDLR �
Q
� FRPR PRVWUD R JU˜D‘FR QD ‘JXUD ���� UHSUHVHQWDGR QR SODQR FRP�
SOH[R�
)LJXUD ���� &RPSRUWDPHQWR GDV UD˜•]HV�
4XDQGR • �� DV UD˜•]HV VaDR FRPSOH[DV FRQMXJDGDV GH YDORU ‰L�
Q
�
—
$
PHGLGD TXH • FUHVFH� HODV VH DIDVWDP GR HL[R LPDJLQ˜DULR VREUH D FLUFXQIHUAHQFLD�
DW˜H TXH� SDUD • �� WHPRV XPD ˜XQLFD UDL] UHDO�ƒ�
Q
�� 4XDQGR • XOWUDSDVVD
R YDORU �� DV UD˜•]HV SDVVDP D VHU UHDLV H WHQGHP D VH VHSDUDU FDGD YH] PDLV
DW˜H TXH QR OLPLWH XPD WHQGH D � H D RXWUD D ��
����� (QHUJLD GR VLVWHPD
&RQVLGHUH D GLQADPLFD GR VLVWHPD DPRUWHFLGR�
P¦[� F B[� N[ ��
�
0XOWLSOLFDQGR WRGRV DV SDUFHODV SRU B[ WHPRV
P¦[ B[� F B[ B[� N[ B[ ��
3RGHPRV UHHVFUHYHU HVWD HTXDFaDR VRE D IRUPD GH GHULYDGDV H LQWHJUDU� RX VHMD�
=
W
�
G
GW
—
P B[
�
�
˜
GW�
=
W
�
F B[
�
GW�
=
W
�
G
GW
—
N[
�
�
˜
GW ��
(IHWXDQGR D LQWHJUDFaDR FKHJDPRV D
P B[
�
�W�
�
ƒ
P B[
�
���
�
�
=
W
�
F B[
�
GW�
N[
�
�W�
�
ƒ
N[
�
���
�
 �
� (
F
�W� � (
S
�W� (
F
��� � (
S
���ƒ
=
W
�
F B[
�
GW
RQGH (
F
˜H D HQHUJLD FLQ˜HWLFD H (
S
˜H D HQHUJLD SRWHQFLDO GR VLVWHPD� $VVLP�
(
7
�W� (
7
���ƒ
=
W
�
F B[
�
(VWD HTXDFaDR QRV PRVWUD TXH D HQHUJLD WRWDO GR VLVWHPD HP XP LQVWDQWH
TXDOTXHU W ˜H D HQHUJLD LQLFLDO GR VLVWHPD� PHQRV D HQHUJLD GLVVLSDGD SHOR
DPRUWHFHGRU� 'HVWD IRUPD� XP VLVWHPD PDVVD�PROD ˜H FRQVHUYDWLYR �FDVR HP
TXH F ���
����� 'LDJUDPD GH IDVH
&RQVLGHUHPRV R GLDJUDPD PRVWUDGR QD ‘JXUD ���� 'LYLGLQGR WRGDV DV SDUFH�
ODV GD HTXDFaDR GD GLQADPLFD GR VLVWHPD SRU P� WHPRV TXH
¦[�
F
P
B[�
N
P
 ��
&KDPDQGR R QRYR FRH‘FLHQWH GD VHJXQGD SDUFHOD GH , H R GD WHUFHLUD GH 5�
SRGHPRVUHHVFUHYHU D H[SUHVVaDR FRPR
¦[� , B[�5 ��
�
)LJXUD ���� 'LDJUDPD GH IDVH�
/RJR�
š ƒ, ‰
S
,
�
ƒ �5
�
�
6H FKDPDUPRV R WHUPR
S
,
�
ƒ �5 GH '� SRGHPRV HVFUHYHU TXH SDUD
�
�
�
' � �� š
���
VaDR FRPSOH[DV FRQMXJDGDV H R VLVWHPD ˜H VXE�DPRUWHFLGR�
' �� š ˜H UHDO H R DPRUWHFLPHQWR ˜H FU˜•WLFR�
' � �� š
���
VaDR UHDLV H R DPRUWHFLPHQWR ˜H VXSHUFU˜•WLFR�
'R GLDJUDPD GH IDVH SRGHPRV WHU XPD LG˜HLD JOREDO VREUH D HVWDELOLGDGH H
FRPSRUWDPHQWR GR VLVWHPD� 3ULPHLUDPHQWH� SRGHPRV REVHUYDU TXH D FXUYD
TXH GHVFUHYH D FRQGLFaDR GH ' � ˜H XPD SDU˜DEROD� &RPR VLVWHPDV PHFADQLFRV
��
HVWaDR UHVWULWRV DR SULPHLUR TXDGUDQWH GR GLDJUDPD� SRLV F H N VaDR SRVLWLYRV�
YDPRV QRV OLPLWDU D DQDOLVDU HVWD SDUWH� $FLPD GD SDU˜DEROD� HQFRQWUDP�VH
DTXHOHV VLVWHPDV TXH SRVVXHP GXDV UD˜•]HV UHDLV SDUD D HTXDFaDR FDUDFWHU˜•VWLFD�
RX VHMD� VLVWHPDV VXSHU�DPRUWHFLGRV� 2V VLVWHPDV VLWXDGRV QD SDU˜DEROD VaDR
DTXHOHV FULWLFDPHQWH DPRUWHFLGRV� FRP XPD UDL] UHDO� $EDL[R GD SDU˜DEROD
H DFLPD GR HL[R 5� HVWaDR RV VLVWHPDV VXE�DPRUWHFLGRV FRP GXDV UD˜•]HV FRP�
SOH[DV FRQMXJDGDV� )LQDOPHQWH� RV VLVWHPDV ORFDOL]DGRV VREUH R HL[R 5 H TXH�
SRU LVVR� SRVVXHP F � VaDR RV VLVWHPDV FRQVHUYDWLYRV FRP GXDV UD˜•]HV LPD�
JLQ˜DULDV SXUDV� $V WUDMHW˜RULDV HO˜•SWLFDV PRVWUDGDV UHSUHVHQWDP RV GLIHUHQWHV
Q˜•YHLV GH HQHUJLD TXH R VLVWHPD SRGH DVVXPLU� 2EVHUYD�VH TXH VLVWHPDV ORFD�
OL]DGRV DEDL[R GR HL[R 5 VHULDP DTXHOHV FRP FRH‘FLHQWH GH DPRUWHFLPHQWR F
SRVLWLYR� $VVLP� VHULDP VLVWHPDV QaDR FRQVHUYDWLYRV RQGH KDYHULD JHUDFaDR GH
HQHUJLD�
7DPE˜HP SRGHPRV WHU XPD LG˜HLD VREUH D HVWDELOLGDGH GRV VLVWHPDV DWUDY˜HV
GRV GLDJUDPDV GH IDVH PRVWUDGRV� 6LVWHPDV ORFDOL]DGRV VREUH R HL[R 5 VaDR
HVW˜DYHLV H� FRPR PRVWUD D ‘JXUD IRUPDP FHQWURV� -˜D RV VLVWHPDV VXE�DPRUWH�
FLGRV VaDR DVVLQWRWLFDPHQWH HVW˜DYHLV IRUPDQGR XP SRQWR HVSLUDO� )LQDOPHQWH�
RV VLVWHPDV FULWLFDPHQWH H VXSHU DPRUWHFLGRV WDPE˜HP VaDR DVVLQWRWLFDPHQWH
HVW˜DYHLV IRUPDQGR Q˜RGXORV LPSU˜RSULRV�
����� /LQHDUL]DFaDR GH XP VLVWHPD
&RQVLGHUHPRV D HTXDFaDR
¦[� I �W� [� B[� ��
'H PRGR JHUDO HVVD HTXDFaDR ˜H QaDR OLQHDU� 3RU˜HP� SRGHPRV HQFRQWUDU
XPD HTXDFaDR GLIHUHQFLDO OLQHDU TXH DSUR[LPD D HTXDFaDR DFLPD SDUD SRQWRV
SU˜R[LPRV GRV SRQWRV GH HTXLO˜•EULR GR VLVWHPD� VHQGR HVWHV GH‘QLGRV FRPR RV
SRQWRV RQGH I�W� [� �� ��
8VDQGR XPD H[SDQVaDR HP V˜HULHV GH 7D\ORU HP WRUQR GR SRQWR GH HTXLO˜•EULR�
SRGHPRV HVFUHYHU TXH�
I �W� [� B[� I�W� [
HT
� B[
HT
� �
#I
#[
�[
HT
� B[
HT
��[ƒ [
HT�
�
#I
# B[
�[
HT
� B[
HT
�� B[ƒ B[
HT
��
1RWH TXH RV WHUPRV GH RUGHP VXSHULRU IRUDP GHVSUH]DGRV H TXH R SULPHLUR
WHUPR —D GLUHLWD GD LJXDOGDGH ˜H ]HUR SHOD SU˜RSULD GH‘QLFaDR GH SRQWR GH HTXLO˜•EULR�
��
&RPR H[HPSOR� FRQVLGHUHPRV D HTXDFaDR GR SAHQGXOR VLPSOHV�
¦
— �
J
O
VHQ — ��
1HVWH FDVR�
I �W� —�
B
—� 
J
O
VHQ —�
3DUD DFKDUPRV RV SRQWRV GH HTXLO˜•EULR GR VLVWHPD GHYHPRV WHU� HQWaDR� TXH
J
O
VHQ — �
RX VHMD�
— �� ž� � � � � Qž� � � � Q � =�
2EVHUYH TXH� QD UHDOLGDGH� K˜D GRLV SRQWRV GH HTXLO˜•EULR� � H ž� /LQHDUL]HPRV
D HTXDFaDR HP WRUQR GH ��� ��� $VVLP�
¦
— � I��� �� �
#I
#—
��� ���— ƒ �� �
#I
#
B
—
��� ���
B
— ƒ �� ��
RX� VLPSOL‘FDQGR�
¦
— �
J
O
— ��
��� 0RGHORV GH H[HUF˜•FLRV
([HUF˜•FLR �
$ FRUGD HVW˜D VRE WUDFaDR 7 TXH VXSRPRV SHUPDQHFHU FRQVWDQWH
SDUD SHTXHQRV GHVORFDPHQWRV� 3DUD SHTXHQDV RVFLODFaRHV� DFKDU D
IUHT¦XAHQFLD QDWXUDO GH YLEUDFaDR YHUWLFDO GD FRUGD�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
6HMD [ D SRVLFaDR GH XP SRQWR JHQ˜HULFR GD FRUGD� (VWD ˜H XPD YLEUDFaDR
OLYUH QaDR DPRUWHFLGD� $ IRUFD UHVWDXUDGRUD ˜H D WUDFaDR QD FRUGD� &RPR D
WUDFaDR ˜H HVVHQFLDOPHQWH FRQVWDQWH� D UHVXOWDQWH YHUWLFDO DWXDQGR QD PDVVD ˜H
7
—
[
D
�
[
/ ƒ D
˜
�
��
)LJXUD ���� &RUGD HP YLEUDFaDR YHUWLFDO�
2EVHUYH TXH IRL IHLWD XPD KLS˜RWHVH VLPSOL‘FDGRUD� D GH TXH 7 LQGHSHQGH GH
[
��(TXDFLRQDPHQWR�
$SOLFDQGR D VHJXQGD OHL GR PRYLPHQWR GH 1HZWRQ� D HTXDFaDR GR PRYL�
PHQWR ˜H
P¦[� 7
—
[
D
�
[
/ ƒ D
˜
 �
RX
P¦[� 7
™
/
D
[
�/ƒ D�
š
 �
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
7/
PD�/ƒD�
UDG�V�
([HUF˜•FLR �
8P PDQARPHWUR XVDGR HP XP ODERUDW˜RULR GH PHFADQLFD GRV ’XLGRV
WHP XP GLADPHWUR XQLIRUPH� FXMD ˜DUHD GD VHFaDR WUDQVYHUVDO ˜H LJXDO D
$� 6H D FROXQD GH O˜•TXLGR GH PDVVD HVSHF˜•‘FD Ÿ H FRPSULPHQWR / ˜H
SRVWD HP PRYLPHQWR FRPR PRVWUD D ‘JXUD ���� DFKDU D IUHT¦XAHQFLD
GR PRYLPHQWR UHVXOWDQWH�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
,QLFLDOPHQWH� ˜H QHFHVV˜DULR SDUDPHWUL]DU R SUREOHPD� 6HMD [ D GLVWADQFLD
HQWUH D VXSHUI˜•FLH OLYUH GR O˜•TXLGR H XP Q˜•YHO GH UHIHUAHQFLD ‘[DGR� &RPR R
O˜•TXLGR ˜H LQFRPSUHVV˜•YHO� D GLVWADQFLD GD VXSHUI˜•FLH OLYUH —D UHIHUAHQFLD� GH XP
��
)LJXUD ���� 0DQARPHWUR�
ODGR GR PDQARPHWUR� ˜H D PHVPD QR RXWUR ODGR� DSHQDV HP VHQWLGR RSRVWR�
$VVLP� D GLIHUHQFD GH SUHVVaDR WHQGHU˜D D WUD]HU DPEDV DV VXSHUI˜•FLHV OLYUHV
SDUD D OLQKD GH UHIHUAHQFLD� UHVXOWDQGR QR PRYLPHQWR�
5HVROYHPRV GH � IRUPDV GLVWLQWDV�
��(TXDFLRQDPHQWR� /HL GR PRYLPHQWR GH 1HZWRQ�
;
)
[
 P¦[� ƒ�$[JŸ /$Ÿ¦[
GH PDQHLUD TXH
¦[�
�J
/
[ ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
U
�J
O
UDG�V�
0˜HWRGR GD HQHUJLD�
$ HQHUJLD FLQ˜HWLFD GR VLVWHPD SRGH VHU HVFULWD FRPR
7 
�
�
P B[
�
 
�
�
�/$Ÿ� B[
�
H D SRWHQFLDO
9 
�
�
N[
�
 
�
�
�$[ŸJ
[
[
�
 $[
�
ŸJ�
&RPR R VLVWHPD ˜H FRQVHUYDWLYR� WHPRV REULJDWRULDPHQWH TXH
G
GW
�7 � 9 � �� /$Ÿ B[¦[� �$ŸJ[ B[ �
��
GRQGH
¦[�
�J
/
[ ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
�J
O
UDG�V � FRPR DQWHV�
([HUF˜•FLR �
8P PRWRU HO˜HWULFR ˜H DSRLDGR HP � PRODV� FDGD XPD WHQGR XPD
FRQVWDQWH N� FRPR VH YAH QD ‘JXUD ����� 6H R PRPHQWR GH LQ˜HUFLD
GR HL[R FHQWUDO GH URWDFaDR GR PRWRU ˜H -
�
� DFKDU VXD IUHT¦XAHQFLD
QDWXUDO GH RVFLODFaDR� FRQVLGHUDQGR TXH R PRYLPHQWR ˜H QR SODQR GD
‘JXUD H TXH R SRQWR 2 ‘FD ‘[R�
)LJXUD ����� 9LVWD ODWHUDO GR PRWRU�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
9DPRV VXSRU TXH R PRYLPHQWR VHMD DSHQDV GH URWDFaDR QXP SODQR� (VWH
˜H R FDVR RQGH DV GXDV PRODV GH XP PHVPR ODGR GR PRWRU VaDR GHIRUPGDV
LJXDOPHQWH� &DVR 2 QaDR IRVVH ‘[R KDYHULD XP PRYLPHQWR DGLFLRQDO H� HP
XP FDVR PDLV UHDOLVWD VHULD QHFHVV˜DULR XVDU PDLV SDUADPHWURV SDUD GHVFUHYHU R
VLVWHPD� (QWUHWDQWR� YDPRV LQWURGX]LU FRPR SDUADPHWUR R ADQJXOR — GH URWDFaDR
GR PRWRU HP WRUQR GR HL[R FHQWUDO�
��(TXDFLRQDPHQWR�
��
$ OHL GR PRYLPHQWR GH 1HZWRQ SDUD PRPHQWRV ˜H
;
0 -
�
¦
—�
RX VHMD� WRUTXH UHVWDXUDGRU WRUTXH GR PRWRU� $VVLP�
ƒ�ND
�
— -
�
¦
—�
¦
— �
�ND
�
-
�
— ��
��3UHYLVaDR GR PRGHOR�
�
Q
 �D
U
N
-
�
UDG�V
5HVROYHQGR SHOR P˜HWRGR GH /DJUDQJH WHPRV�
(TXDFLRQDPHQWR�
7 
�
�
-
�
B
—
�
�
9 � …
�
�
ND
�
—
�
�
M˜D FRQVLGHUDQGR SHTXHQRV GHVORFDPHQWRV� /RJR� R ODJUDQJHDQR ˜H
/ 7 ƒ 9 
�
�
-
�
B
—
�
ƒ �ND
�
—
�
�
�
#/
#
B
—
 -
�
B
—�
G
GW
—
#/
#
B
—
˜
 -
�
¦
— H
#/
#—
 ƒ�ND
�
—
H� SRUWDQWR� D GLQADPLFD GR VLVWHPD ˜H
-
�
¦
— � �ND
�
— ��
��
)LJXUD ����� 'LVFR VHPLFLUFXODU�
([HUF˜•FLR �
8P GLVFR KRPRJAHQHR VHPLFLUFXODU GH UDLR U H PDVVD P RVFLOD OLYUH�
PHQWH� FRPR PRVWUD D ‘J� ����� 'HWHUPLQDU VXD IUHT¦XAHQFLD QDWXUDO
GH RVFLODFaDR SDUD SHTXHQRV GHVORFDPHQWRV�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
9DPRV XVDU R ADQJXOR—� FRP VHQWLGR SRVLWLYR LQGLFDGR QD ‘JXUD� SDUD
SDUDPHWUL]DU R SUREOHPD� 8VDUHPRV D HTXDFaDR GH 1HZWRQ SDUD R WRUTXH�
3
0 -
�
¦
—� RQGH -
�
 
�
�
PU
�
H D GLVWADQFLD GR FHQWUR GH PDVVD DR SRQWR GH
SLYRWHDPHQWR ˜H 5 �U �ž� FRPR PRVWUDGR�
��(TXDFLRQDPHQWR�
2 WRUTXH UHVWDXUDGRU ˜H PJ5 VHQ — H D HTXDFaDR GR PRYLPHQWR ˜H GDGD SRU
—
�
�
PU
�
˜
¦
— ƒPJ5 VHQ —�
RQGH R VLQDO QHJDWLYR ˜H XVDGR SRUTXH D IRUFD PJ HVW˜D DWXDQGR GH IRUPD D
RSRU�VH DR VHQWLGR GH — FUHVFHQWH� 3DUD SHTXHQRV YDORUHV GH —� VHQ — ž — H D
HTXDFaDR GR PRYLPHQWR WRUQD�VH
¦
— �
�J
�Už
— ��
TXH ˜H D HTXDFaDR GLIHUHQFLDO GH XP VLVWHPD FRPPRYLPHQWR KDUPARQLFR VLPSOHV�
��3UHYLVaDR GR PRGHOR�
��
�
Q
 
T
�J
�Už
UDG�V�
([HUF˜•FLR �
'HWHUPLQDU D IUHT¦XAHQFLD QDWXUDO GR VLVWHPD PROD�PDVVD�SROLD UH�
SUHVHQWDGR QD ‘J� �����
)LJXUD ����� 6LVWHPD�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
$ SDUDPHWUL]DFaDR ˜H IHLWD DWUDY˜HV GD FRRUGHQDGD [ FRP VHQWLGR PRVWUDGR
QD ‘JXUD H GH‘QLGD FRPR � FRP R VLVWHPD HP HTXLO˜•EULR HVW˜DWLFR� 1RYDPHQWH�
UHVROYHPRV R SUREOHPD GH GXDV IRUPDV GLIHUHQWHV�
��(TXDFLRQDPHQWR� /HL GR PRYLPHQWR GH 1HZWRQ�
3DUD D PDVVD P�
PJ ƒ 7 P¦[�
3DUD D SROLD GH PDVVD 0 �
-
�
¦
— 7U ƒ NU
�
�— � —
�
��
��
RQGH -
�
 
�
�
0U
�
˜H R PRPHQWR GH LQ˜HUFLD GD SROLD� 0DV� QR HTXLO˜•EULR HVW˜DWLFR�
PJU NU
�
—
�
�DVVLP� D VHJXQGD GDV HTXDFaRHV DFLPD WRUQD�VH
�
�
0U
�
¦
— U�PJ ƒP¦[�ƒ NU
�
— ƒPJU�
6XEVWLWXLQGR [ SRU U— RX ¦[ SRU U
¦
—� D HTXDFaDR GLIHUHQFLDO GR PRYLPHQWR
WRUQD�VH
—
�
�
0U
�
�PU
�
˜
¦
— � NU
�
— ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
N
0 ��P
UDG�V�
��(TXDFLRQDPHQWR� 0˜HWRGR GD HQHUJLD�
7 7
PDVVD
� 7
SROLD
 
�
�
P B[
�
�
�
�
-
�
B
—
�
 
 
�
�
PU
�
B
—
�
�
�
�
-
�
B
—
�
�
9 
�
�
N[
�
 
�
�
NU
�
—
�
�
&RPR D HQHUJLD WRWDO GR VLVWHPD SHUPDQHFH LQYDUL˜DYHO�
G
GW
�7 � 9 � �� PU
�
B
—
¦
— � -
�
B
—
¦
— � NU
�
—
B
— �
H
B
—�PU
�
¦
— � -
�
¦
— � NU
�
—� �
&RPR
B
— QHP VHPSUH ˜H ]HUR� �PU
�
¦
— � -
�
¦
— � NU
�
—� ˜H LJXDO D ]HUR�
��6ROXFaDR GR PRGHOR�
$VVLP�
¦
— �
NU
�
-
�
�PU
�
— � H �
Q
 
T
N
0 ��P
UDG�V�
��
)LJXUD ����� 0ROD FRP PDVVD QaDR GHVSUH]˜•YHO�
([HUF˜•FLR �
'HWHUPLQDU D IUHT¦XAHQFLD QDWXUDO GR VLVWHPD PRVWUDGR QD ‘J� �����
RQGH D PDVVD GD PROD QaDR ˜H GHVSUH]˜•YHO�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
6HMD [ D SRVLFaDR GD PDVVD PHGLGD —D SDUWLU GD SRVLFaDR HVW˜DWLFD GR VLVWHPD�
LVWR ˜H� TXDQGR D IRUFD QD PROD ˜H LJXDO DR SHVR GD PDVVD� FRP VHQWLGR SRVLWLYR
SDUD EDL[R� 6H D PDVVD GD PROD QaDR GHYH VHU LJQRUDGD
7
VLVWHPD
 7
PDVVD
� 7
PROD
 
�
�
P B[
�
�
=
/
�
�ŸGH�
K•
H
/
–
B[
L
�
RQGH
ƒ
H
/
„
[ ˜H R GHVORFDPHQWR GH XP SRQWR LQWHUPHGL˜DULR GD PROD D XPD
GLVWADQFLD H GD H[WUHPLGDGH VXSHULRU H Ÿ ˜H D PDVVD GD PROD SRU XQLGDGH GH
FRPSULPHQWR�
��(TXDFLRQDPHQWR�
��
0˜HWRGR GH 5D\OHLJK� 7
PD[
 9
PD[
�
7
PD[
 
�
�
P B[
�
PD[
�
�
�
Ÿ
—
B[
PD[
/
˜
�
=
/
�
H
�
GH 
 
�
�
P B[
�
PD[
�
�
�
Ÿ
—
B[
PD[
/
˜
�
—
/
�
�
˜
 
�
�
—
P�
�
�
Ÿ/
˜
B[
�
PD[
�
9
PD[
 
�
�
N[
�
PD[
�
��3UHYLVaDR GR PRGHOR�
3DUD RVFLODFaRHV VHQRLGDLV� [ $ VHQ�
Q
W� $VVLP� LJXDODQGR DV GXDV H[�
SUHVVaRHV GH HQHUJLDV P˜D[LPDV FKHJDPRV D
�
�
—
P�
�
�
Ÿ/
˜
��
Q
$�
�
 
�
�
N$
�
�
R TXH QRV IRUQHFH
�
Q
 
T
N
P�
�
�
Ÿ/
UDG�V�
��'LVFXVVaDR GR UHVXOWDGR�
6H Ÿ ˜H GHVSUH]˜•YHO FRPSDUDGR D P� D H[SUHVVaDR DFLPD UHGX]�VH D �
Q
 
S
N P� TXH ˜H D IUHT¦XAHQFLD QDWXUDO GH XP VLVWHPD VLPSOHV PDVVD�PROD�
([HUF˜•FLR �
8PD KDVWH U˜•JLGD H XQLIRUPH ˜H UHVWULQJLGD D PRYHU�VH YHUWLFDOPHQWH
SRU PRODV WDQWR OLQHDUHV FRPR GH WRUFaDR� FRQIRUPH VH PRVWUD QD
‘J� ����� &DOFXODU D IUHT¦XAHQFLD GD RVFLODFaDR YHUWLFDO GD KDVWH�
$ SDUDPHWUL]DFaDR GR VLVWHPD ˜H IHLWD DWUDY˜HV GR ADQJXOR — GH URWDFaDR GD
KDVWH U˜•JLGD HP WRUQR GR SRQWR RQGH ˜H SUHVD D PROD WRUVLRQDO�
��(TXDFLRQDPHQWR�
$SOLFDQGR D HTXDFaDR GR WRUTXH
3
0 -
¦
—�
ƒ.— ƒ �N/
�
VHQ — 
P/
�
�
¦
—�
��
)LJXUD ����� 6LVWHPD�
RQGH P ˜H D PDVVD GD KDVWH H - R PRPHQWR GH LQ˜HUFLD GD KDVWH FRP UHODFaDR
DR HL[R SHUSHQGLFXODU DR SODQR GD ‘JXUD H TXH SDVVD SRU VXD H[WUHPLGDGH�
$VVLP�
P/
�
�
¦
— �.— � �N/
�
VHQ — ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
�.��N/
�
P/
�
UDG�V�
([HUF˜•FLR �
$ PDVVD 0 QD H[WUHPLGDGH GR FDER GR SAHQGXOR FARQLFR HVW˜D JLUDQGR
HP WRUQR GR HL[R YHUWLFDO FRPR VH YAH QD ‘J� ����� 2 SODQR GR SHU�
FXUVR FLUFXODU ˜H KRUL]RQWDO H HOHYD�VH TXDQGR D YHORFLGDGH DQJXODU
GH URWDFaDR ˜H DXPHQWDGD� 'HWHUPLQDU D IUHT¦XAHQFLD GR VLVWHPD�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
2 GLDJUDPD GR FRUSR OLYUH GD PDVVD 0 � QRV OHYD D
;
)
Q
 0D
Q
RX 7 VHQ — 0/ VHQ —�
�
�
��
)LJXUD ����� 3AHQGXOR FARQLFR�
RQGH � ˜H D YHORFLGDGH DQJXODU GD PDVVD QR LQVWDQWH FRQVLGHUDGR� 7DPE˜HP
;
)
Y
 0D
Y
RX 7 FRV — ƒ0J 0D
Y
�
3RU˜HP� D
Y
 � H� FRQVHT¦XHQWHPHQWH� 7 FRV — 0J RX 7 0J �FRV —��
��(TXDFLRQDPHQWR�
6XEVWLWXLQGR HVWH YDORU GH 7 QD SULPHLUD HTXDFaDR� WHPRV TXH
0J
FRV —
VHQ — 0/ VHQ —�
�
�
��3UHYLVaDR GR PRGHOR�
�
Q
 
S
J
/ FRV —
UDG�V�
��'LVFXVVaDR GR UHVXOWDGR�
6H — �� WHPRV TXH FRV — �� H �
Q
 
S
J / TXH ˜H D IUHT¦XAHQFLD QDWXUDO GH
XP SAHQGXOR VLPSOHV� ,VWR TXHU GL]HU TXH R SAHQGXOR FARQLFR �—DV YH]HV FKDPDGR
HVI˜HULFR� ˜H UHGX]LGR D XP SAHQGXOR VLPSOHV VH — ˜H LJXDO D ]HUR�
([HUF˜•FLR �
8P FLOLQGUR FLUFXODU GH PDVVD P H UDLR U ˜H OLJDGR D XPD PROD GH
FRQVWDQWH N� FRPR PRVWUD D ‘J� ����� $FKDU D IUHT¦XAHQFLD� TXDQGR
HOH UROD OLYUH QD VXSHUI˜•FLH KRUL]RQWDO ˜DVSHUD� VHP GHVOL]DU�
6ROXFaDR� 3RGHPRV UHVROYHU R SUREOHPD GH GXDV PDQHLUDV GLVWLQWDV� 3ULPHLUD
VROXFaDR�
��
)LJXUD ����� 6LVWHPD�
��'HVFULFaDR GR SUREOHPD� 0˜HWRGR GD HQHUJLD�
$ HQHUJLD WRWDO GR VLVWHPD FRQVLVWH HP HQHUJLD FLQ˜HWLFD �GH URWDFaDR H
WUDQVODFaDR� H HP HQHUJLD SRWHQFLDO H GHYH SHUPDQHFHU FRQVWDQWH WRGR R WHPSR�
7
WUDQVO
 
�
�
P B[
�
�
7
URWD
 
�
�
-
�
B
—
�
�
RQGH R PRPHQWR GH LQ˜HUFLD GR FLOLQGUR ˜H -
�
 
�
�
PU
�
� 7DPE˜HP� U— [� RX
U
B
— B[�
��(TXDFLRQDPHQWR�
3DUD R VLVWHPD HP TXDOTXHU LQVWDQWH�
7 
�
�
P B[
�
�
�
�
—
�
�
PU
�
˜—
B[
U
˜
�
 
�
�
P B[
�
�
9 
�
�
N[
�
H
G
GW
�7 � 9 � ��
—
�
�
P¦[� N[
˜
B[ ��
&RPR� B[ QHP VHPSUH ˜H ]HUR� D HTXDFaDR GR PRYLPHQWR WRUQD�VH
�
�
P¦[� N[ ��
��3UHYLVaDR GR PRGHOR�
��
�
Q
 
T
�N
�P
UDG�V
6HJXQGD VROXFaDR� /HL GR PRYLPHQWR GH 1HZWRQ�
��'HVFULFaDR GR SUREOHPD�
$SOLFDQGR D OHL GR PRYLPHQWR GH 1HZWRQ DR FLOLQGUR� WHPRV TXH
;
) PD RX P¦[ ƒN[� )
I
�
RQGH )
I
˜H D IRUFD GH DWULWR�
8VDQGR D HTXDFaDR GH WRUTXH
3
0 -
�
¦
—�
-
�
¦
— ƒ)
I
U RX
—
�
�
PU
�
˜—
¦[
U˜
 ƒ)
I
U
H� DVVLP�
)
I
 ƒ
�
�
P¦[�
��(TXDFLRQDPHQWR�
6XEVWLWXLQGR HVWD H[SUHVVaDR GH )
I
QD HTXDFaDR GH IRUFD� REWHPRV
P¦[ ƒN[ƒ
�
�
P¦[�
�
�
P¦[� N[ ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
�N
�P
UDG�V�
([HUF˜•FLR ��
8VH R P˜HWRGR GH 5D\OHLJK SDUD DFKDU D IUHT¦XAHQFLD QDWXUDO GH XP
WXER VHPLFLUFXODU GH PDVVD P H UDLR U TXH UROD GH ODGR D ODGR VHP
GHVOL]DU� FRPR PRVWUDGR QD ‘J� ���� DFLPD�
6ROXFaDR�
��(TXDFLRQDPHQWR�
7
PD[
 
�
�
,
$
�
�
Q
 PU�U ƒ D��
�
Q
�
��
)LJXUD ����� 7XER VHPLFLUFXODU�
RQGH
,
$
 ,
F�J�
�P�U ƒ D�
�
 ,
�
ƒPD
�
�P�U ƒ D�
�
 �PU�U ƒ D��
(QWaDR�
7
PD[
 9
PD[
� PU�U ƒ D��
�
Q
 PJD�� ƒ FRV —��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
JD��ƒFRV —�
U�UƒD�
UDG�V�
([HUF˜•FLR ��
$ FRUGD SRGH VHU FRQVLGHUDGD FRPR LQH[WHQV˜•YHO QR VLVWHPD PDVVD�
PROD�SROLD PRVWUDGR QD ‘J� ����� $FKDU D IUHT¦XAHQFLD QDWXUDO GH
YLEUDFaDR VH D PDVVD P ˜H GHVORFDGD OLJHLUDPHQWH H ODUJDGD� 8VH R
P˜HWRGR GD HQHUJLD�
6ROXFaDR�
��'LVFXVVaDR GR SUREOHPD�
7
VLVWHPD
 7
PDVVD
� 7
SROLD
 
�
�
P B[
�
�
�
�
0 B\
�
�
�
�
-
�
B
—
�
 
 
�
�
P B[
�
�
�
�
0� B[
�
 �� �
�
�
—
�
�
0U
�
˜
� B[ U�
�
 
�
�
P B[
�
�
�
�
0 B[
�
�
��
)LJXUD ����� 6LVWHPD�
9
VLVWHPD
 HQHUJLD HO˜DVWLFD GD PROD 
�
�
N\
�
 
 
�
�
N
—
�
�
[
˜
�
 
�
�
N[
�
�
��(TXDFLRQDPHQWR�
$VVLP�
G
GW
�7 � 9 � �� P B[¦[�
�
�
0 B[¦[�
�
�
N[ B[ �
� B[��P¦[� �0 ¦[� N[� �� ¦[��P� �0� � N[ ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
N
�P��0
UDG�V�
��
)LJXUD ����� 6LVWHPD�
([HUF˜•FLR ��
6H D PDVVD GDV SROLDV PRVWUDGDV QD ‘J� ���� DEDL[R ˜H SHTXHQD H R
FDER LQH[WHQV˜•YHO� DFKDU D IUHT¦XAHQFLD QDWXUDO GR VLVWHPD�
6ROXFaDR�
��'HVFULFaDR GR SUREOHPD�
&KDPHPRV 7 D WUDFaDR QR FDER H [
D
H [
E
RV GHVORFDPHQWRV GDV SROLDV $ H
%� UHVSHFWLYDPHQWH� $VVLP� VH D SROLD % ˜H ‘[D� [ �[
D
� PDV VH� DR FRQWU˜DULR�
D SROLD $ ˜H ‘[D� [ �[
E
� 3RU˜HP� FRPR QHP D SROLD $ QHP D SROLD % VaDR
‘[DV WHPRV TXH
[ �[
D
� �[
E
�
��(TXDFLRQDPHQWR�
&RQVLGHUH D SROLD % FRPR XP FRUSR OLYUH H VRPH DV IRUFDV�
�7 ƒ N
E
[
E
 ��
'R PHVPR PRGR� SDUD D SROLD $�
�7 N
D
[
D
�
$VVLP�
[ �[
D
� �[
E
 �7 �� N
D
� � N
E
� 7 N
HT
�
��
RQGH
N
HT
 
�
��� N
D
� � N
E
�
�
˜H D FRQVWDQWH GD PROD HTXLYDOHQWH� ,VWR UHGX]LX R SUREOHPD D XP VLPSOHV
VLVWHPD PDVVD�PROD� FRP D FRQVWDQWH GD PROD LJXDO D N
HT
�
��3UHYLVaDR GR PRGHOR�
0DV� P¦[ � N[ � ˜H D HTXDFaDR GR PRYLPHQWR SDUD XP VLPSOHV VLVWHPD
PDVVD�PROD FRP IUHT¦XAHQFLD QDWXUDO
S
N
HT
 P� 'HVWD IRUPD�
�
Q
 
S
N
HT
 P 
T
N
D
N
E
�P�N
D
�N
E
�
UDG�V�
([HUF˜•FLR ��
$ PDVVD P ˜H SUHVD —D H[WUHPLGDGH GH XPD KDVWH U˜•JLGD VHP SHVR
TXH ˜H ‘UPHPHQWH OLJDGD DR FHQWUR GH XP FLOLQGUR KRPRJAHQHR GH
UDLR U� FRPR QRV PRVWUD D ‘J� ����� 6H R FLOLQGUR UROD VHP GHVOL]DU�
TXDO D IUHT¦XAHQFLD QDWXUDO GH RVFLODFaDR GR VLVWHPD"
)LJXUD �����
6ROXFaDR�
��
��'HVFULFaDR GR SUREOHPD� 3HOR P˜HWRGR GH 1HZWRQ�
(P TXDOTXHU LQVWDQWH FRQVLGHUDGR� DV PDVVDV 0 H P HVWaDR JLUDQGR HP
WRUQR GR SRQWR &� R FHQWUR LQVWDQWADQHR GH URWDFaDR� $VVLP� D HTXDFaDR GR
PRYLPHQWR WRPD D IRUPD
3
0
F
 -
F
¦
— VHQGR -
F
R PRPHQWR GH LQ˜HUFLD GDV
PDVVDV 0 H P HP UHODFaDR DR SRQWR &� $VVLP�
��(TXDFLRQDPHQWR�
-
F
 
—
�
�
0U
�
�0U
�
˜
�P5
�
�
RQGH
5
�
 /
�
� U
�
ƒ �U/ FRV —�
3DUD SHTXHQDV RVFLODFaRHV� WHPRV TXH
VHQ — ž — H FRV — ž �
H
-
F
 �0U � �P�/ƒ U�
�
�
'HVWH PRGR� D HTXDFaDR GR PRYLPHQWR VH WRUQD
>�0U � �P�/ƒ U�
�
@
¦
— ƒPJ/ VHQ — ƒPJ/—
RX
¦
— �
PJ/
�0U � �P�/ƒ U�
�
— ��
��3UHYLVaDR GR PRGHOR�
�
Q
 
T
PJ/
�0U ��P�/ƒU�
�
UDG�V�
��
&DS˜•WXOR �
5HVSRVWD —D H[FLWDFaDR KDUPARQLFD
��� 5HVXPR GD WHRULD
����� 6LVWHPDV VHP DPRUWHFLPHQWR
&RQVLGHUH R VLVWHPD VHP DPRUWHFLPHQWR PRVWUDGR QD ‘JXUD ��� H FRP XP
IRUFDPHQWR KDUPARQLFR GD IRUPD ) �W� )
�
FRV�
I
W� $VVLP� D GLQADPLFD GR
VLVWHPD ˜H GHVFULWD SRU
P¦[�W� � N[�W� )
�
FRV�
I
W�
'LYLGLQGR D H[SUHVVaDR SRU P� SRGHPRV UHHVFUHYAH�OD FRPR
)LJXUD ���� 6LVWHPD PDVVD�PROD VHP DPRUWHFLPHQWR H FRP IRUFDPHQWR�
¦[� �
�
Q
[�W� I
�
FRV
I
W�
��
VHQGR I
�
 )
�
 P H �
�
Q
 N P� (VWD ˜H XPD HTXDFaDR GLIHUHQFLDO OLQHDU QaDR�
KRPRJAHQHD FXMD VROXFaDR ˜H D VRPD GD VROXFaDR KRPRJAHQHD DVVRFLDGD� [
K
� �GLV�
FXWLGD QR FDS˜•WXOR ��� FRP XPD VROXFaDR SDUWLFXODU� [
S
� $ VROXFaDR SDUWLFXODU
DVVXPH D PHVPD IRUPD GR IRUFDPHQWR� TXDQGR �
I
� �
Q
� $VVLP�
[
S
�W� $
�
FRV�
I
W�
6XEVWLWXLQGR HVWH YDORU QD HTXDFaDR GLIHUHQFLDO� FKHJDPRV D
ƒ�
�
I
$
�
FRV�
I
W� �
�
Q
$
�
FRV�
I
W I
�
FRV�
I
W�
'D˜•�
$
�
 
I
�
�
�
Q
ƒ �
�
I
H D VROXFaDR SDUWLFXODU ˜H GDGD SRU
[
S
�W� 
I
�
�
�
Q
ƒ �
�
I
FRV�
I
W�
$ VROXFaDR JHUDO GDGD SRU [�W� [
K
�W� � [
S
�W� VH WRUQD
[�W� $
�
VHQ�
Q
W�$
�
FRV�
Q
W�
I
�
�
�
ƒ �
�
I
FRV�
I
W�
RQGH $
�
H $
�
VaDR GHWHUPLQDGDV D SDUWLU GDV FRQGLFaRHV LQLFLDLV� 6H [��� [
�
H B[��� Y
�
� D HTXDFaDR DFLPD SRGH VHU HVFULWD FRPR
[�W� 
Y
�
�
VHQ �
Q
W�
¥
[
�
ƒ
I
�
�
�
Q
ƒ �
�
I
�
FRV�
Q
W�
I
�
�
�
Q
ƒ �
�
I
FRV�
I
W�
” %DWLPHQWR
3DUD R FDVR SDUWLFXODU HP TXH DV FRQGLFaRHV LQLFLDLV VaDR QXODV� D VROXFaDR
JHUDO VH WRUQD VLPSOHVPHQWH
[�W� 
I
�
�
�
Q
ƒ �
�
I
�FRV�
I
Wƒ �
Q
W��
)D]HQGR DOJXPDV WUDQVIRUPDFaRHV WULJRQRP˜HWULFDV� SRGHPRV UHHVFUHYHU
HVWD ˜XOWLPD HTXDFaDR FRPR
[�W� 
�I
�
�
�
Q
ƒ �
�
I
VHQ
—
�
Q
ƒ �
I
�
W
˜
VHQ
—
�
Q
� �
I
�
W
˜
�
��
4XDQGR �
I
VH WRUQD PXLWR SU˜R[LPD GH �
Q
� RFRUUH R IHQARPHQR GH EDWL�
PHQWR� ,VWR VH GHYH DR IDWR GH ��
Q
ƒ �
I
� VH WRUQDU PXLWR SHTXHQR H�
FRQVHT¦XHQWHPHQWH� ��
Q
��
I
� JUDQGH HP FRPSDUDFaDR� 3RU LVVR� XP VHQR
RVFLOD FRP XP SHU˜•RGR PXLWR PDLRU TXH R RXWUR� JHUDQGR R EDWLPHQWR�
3DUD R FDVR HP TXH I
�
 �� � 1�NJ� �
I
 � UDG�V H �
Q
 ��� UDG�V
PRVWUDPRV R JU˜D‘FR GD UHVSRVWD QD ‘JXUD ����
)LJXUD ���� 5HSUHVHQWDFaDR JU˜D‘FD GD VROXFaDR�
” 5HVVRQADQFLD
6H �
I
VH WRUQD LJXDO —D IUHT¦XAHQFLD QDWXUDO GR VLVWHPD� �
Q
� RFRUUH R
IHQARPHQR GD UHVVRQADQFLD H D VROXFaDR SDUWLFXODU XVDGD DQWHV QaDR VHUYH
PDLV� SRLV SDVVD D VHU WDPE˜HP VROXFaDR GD HTXDFaDR KRPRJAHQHD� $VVLP�
SURSRPRV QRYD VROXFaDR SDUWLFXODU GD IRUPD
[
S
�W� W$
�
VHQ�W�
6XEVWLWXLQGR QD GLQADPLFD GR VLVWHPD H UHVROYHQGR� FRPR ‘]HPRV DQWHV�
FKHJDPRV D
[
S
�W� 
I
�
��
W VHQ�W
H D VROXFaDR JHUDO� SDUD FRQGLFaRHV LQLFLDLV [
�
H Y
�
WRUQD�VH
[
S
�W� 
Y
�
�
VHQ�W� [
�
FRV�W�
I
�
��
W VHQ�W�
��
2 JU˜D‘FR GD VROXFaDR� SDUD FRQGLFaRHV LQLFLDLV QXODV� PRVWUDGRQD ‘JXUD ���
PRVWUD TXH R GHVORFDPHQWR FUHVFHULD LOLPLWDGDPHQWH FRP R WHPSR�
)LJXUD ���� 5HSUHVHQWDFaDR JU˜D‘FD GD VROXFaDR�
����� 6LVWHPD DPRUWHFLGR
$ HTXDFaDR TXH GHVFUHYH D GLQADPLFD GR VLVWHPD DPRUWHFLGR FRP IRUFDPHQWR
KDUPARQLFR� FRPR R PRVWUDGR QD ‘JXUD ���� ˜H
)LJXUD ���� 6LVWHPD PDVVD�PROD FRP DPRUWHFLPHQWR H IRUFDPHQWR�
P¦[� F B[� N[ )
�
FRV�
I
W
��
RX� DQDORJDPHQWH�
¦[� �•�
Q
B[� �
�
Q
[ I
�
FRV�
I
W�
VHQGR
�
�
Q
 
N
P
H • 
F
�P�
Q
�
$VVXPLQGR VROXFaDR SDUWLFXODU GD IRUPD
[
S
�W� $
�
FRV��
I
ƒ ‹��
FKHJDPRV D
[
S
�W� 
I
�
T
��
�
Q
ƒ �
�
I
�
�
� ��•�
Q
�
I
�
�
FRV
¥
�
I
Wƒ DUFWDQ
�•�
Q
�
I
�
�
Q
ƒ �
�
I
�
H D VROXFaDR JHUDO VHU˜D
[�W� $H
ƒ•�W
VHQ��
G
W� —� �$
�
FRV��
I
Wƒ ‹��
VHQGR �
G
 �
Q
S
� ƒ •
�
� $ H — VaDR GHWHUPLQDGDV GDV FRQGLFaRHV LQLFLDLV� PDV
VaDR GLIHUHQWHV GRV YDORUHV HQFRQWUDGRV SDUD D UHVSRVWD OLYUH� SRLV SDUWH GR
WHUPR WUDQVLHQWH GD HTXDFaDR DFLPD ˜H GHYLGR DR IRUFDPHQWR�
)DFDPRV DJRUD XPD DQ˜DOLVH GD DPSOLWXGH H GD IDVH GD UHVSRVWD HVWD�
FLRQ˜DULD� $S˜RV DOJXPD PDQLSXODFaDR SRGHPRV HVFUHYHU D DPSOLWXGH QRUPDOL�
]DGD H D IDVH HP IXQFaDR GH U� �U �
I
 �
Q
�� LVWR ˜H
$
�
N
)
�
 
$
�
�
�
I
�
 
�
S
�� ƒ U
�
�
�
� ��•U�
�
H
‹ DUFWDQ
�•U
�ƒ U
�
�
2V JU˜D‘FRV GH DPSOLWXGH H IDVH VaDR PRVWUDGRV QD ‘JXUD ����
��
)LJXUD ���� 0DJQLWXGH QRUPDOL]DGD H IDVH GD UHVSRVWD SHUPDQHQWH�
����� ([FLWDFaDR GH EDVH
2 SUREOHPD GD H[FLWDFaDR GH EDVH SRGH VHU PRGHODGR FRPR QD ‘JXUD ����
,VRODQGR R FRUSR GH PDVVD P� REWHPRV D GLQADPLFD GR VLVWHPD GDGD SRU
P¦[� F� B[� B\� � N�[ƒ \� ��
$VVXPLQGR TXH D EDVH VH PRYD KDUPRQLFDPHQWH� LVWR ˜H \�W� < VHQ�
E
W H
UHDUUDQMDQGR D HTXDFaDR DFLPD� WHPRV
P¦[� F B[� N[ F< �
E
FRV�
E
W� N< VHQ �
E
W�
TXH SRGH VHU YLVWR FRPR XP VLVWHPD PDVVD�PROD�DPRUWHFHGRU FRP GXDV HQ�
WUDGDV KDUPARQLFDV� 8VDQGR D OLQHDULGDGH GD HTXDFaDR� D VROXFaDR SDUWLFXODU
VHU˜D D VRPD GDV VROXFaRHV SDUWLFXODUHV SDUD FDGD IRUFDPHQWR� 'LYLGLQGR D
H[SUHVVaDR DFLPD SRU P� WHPRV TXH
¦[� �•�
Q
B[� �
�
Q
[ �•�
Q
�
E
< FRV�
E
W� �
�
Q
< VHQ�
E
W�
��
)LJXUD ���� 3UREOHPD GH H[FLWDFaDR GH EDVH�
$VVLP� D SULPHLUD VROXFaDR SDUWLFXODU SDUD I
�
 �•�
Q
�
E
< FRV�
E
VHU˜D
[
���
S
 
�•�
Q
�
E
<
S
��
�
Q
ƒ �
�
E
�
�
� ��•�
Q
�
E
�
�
FRV��
E
Wƒ‹
�
��
VHQGR
‹
�
 DUFWDQ
�•�
Q
�
E
�
�
Q
ƒ �
�
E
�
$QDORJDPHQWH� D VHJXQGD VROXFaDR SDUWLFXODU VHU˜D
[
���
S
 
�
�
Q
<
S
��
�
Q
ƒ �
�
E
�
�
� ��•�
Q
�
E
�
�
VHQ��
E
Wƒ ‹
�
��
(QWaDR� SHOD VXSHUSRVLFaDR GDV VROXFaRHV� D VROXFaDR SDUWLFXODU ‘QDO ˜H
[
S
�W� �
Q
<
™
�
�
Q
� ��•�
E
�
�
��
�
Q
ƒ �
�
E
�
�
� ��•�
Q
�
E
�
�
š
�
�
FRV��
E
Wƒ‹
�
ƒ ‹
�
��
VHQGR
‹
�
 DUFWDQ
�
Q
�•�
E
�
��
$ UHODFaDR HQWUH D DPSOLWXGH GD VROXFaDR SDUWLFXODU GHQRWDGD SRU ; H D PDJ�
QLWXGH GR PRYLPHQWR GD EDVH < ˜H
;
<
 
™
� � ��•U�
�
��ƒ U
�
�
�
� ��•U�
�
š
�
�
�
RQGH U �
E
 �
Q
˜H D UD]aDR GH IUHT¦XAHQFLDV�
2XWUD TXDQWLGDGH GH LQWHUHVVH ˜H D IRUFD WUDQVPLWLGD SDUD D PDVVD FRPR
UHVXOWDGR GR PRYLPHQWR GD EDVH� &RPR HVWD IRUFD ˜H WUDQVPLWLGD DWUDY˜HV GD
PROD H GR DPRUWHFHGRU� HOD ˜H GDGD SRU
) �W� N�[ƒ \� � F� B[ƒ B\� ƒP¦[�W��
1R UHJLPH SHUPDQHQWH� D VROXFaDR SDUD [ M˜D ˜H FRQKHFLGD� 'HULYDQGR GXDV
YH]HV H VXEVWLWXLQGR QD H[SUHVVaDR DFLPD� WHPRV TXH
) �W� P�
�
E
�
Q
<
™
�
�
Q
� ��•�
E
�
�
��
�
Q
ƒ �
�
E
�
�
� ��•�
Q
�
E
�
�
š
�
�
FRV��
E
Wƒ ‹
�
ƒ ‹
�
��
1RYDPHQWH� UHHVFUHYHQGR HVWD ˜XOWLPD H[SUHVVaDR HP IXQFaDR GH U� FKHJDPRV D�
) �W� )
7
FRV��
E
Wƒ‹
�
ƒ ‹
�
��
RQGH D PDJQLWXGH )
7
˜H GDGD SRU
)
7
 N< U
�
™
� � ��•U�
�
��ƒ U
�
�
�
� ��•U�
�
š
�
�
�
R TXH QRV OHYD D GH‘QLU D WUDQVPLVVLELOLGDGH GH IRUFD QD IRUPD GD UD]aDR
)
7
N<
 U
�
™
� � ��•U�
�
�� ƒ U
�
�
�
� ��•U�
�
š
�
�
�
����� 'HVEDODQFHDPHQWR HP URWDFaRHV
8PD IRQWH LPSRUWDQWH GH YLEUDFaRHV ˜H R GH P˜DTXLQDV URWDWLYDV TXH DSUHVHQWDP
DOJXP WLSR GH GHVEDODQFHDPHQWR� &RQVLGHUH R HVTXHPD PRVWUDGR QD ‘JXUD
���� $ IUHT¦XAHQFLD GH URWDFaDR GD P˜DTXLQD ˜H �
U
� $ FRPSRQHQWH [ GR PRYLPHQWR
GD PDVVD P
�
˜H [
U
 H VHQ�
U
W H D IRUFD GH UHDFaDR )
U
JHUDGD SHOD PDVVD P
�
WHP XPD FRPSRQHQWH QD GLUHFaDR [ GDGD SRU
)
U
 P
�
¦[
U
 HP
�
G
�
GW
�
�VHQ�
U
W� ƒHP
�
�
�
U
VHQ�
U
W�
��
)LJXUD ���� 0RGHOR GH XPD P˜DTXLQD URWDWLYD FRP GHVEDODQFHDPHQWR�
D TXDO DWXD QD PDVVD P�
'LYLGLQGR D PDVVD GD P˜DTXLQD HP GXDV SDUWHV H VRPDQGR DV IRUFDV QD
GLUHFaDR [� REWHPRV
�PƒP
�
�¦[�P
�
G
�
GW
�
�[� H VHQ�
U
W� ƒN[ƒ F B[
RX
P¦[� F B[� N[ P
�
H�
�
U
VHQ �
U
W�
GHSRLV GH UHDUUXPDU RV WHUPRV� 2 SURFHGLPHQWR GH VROXFaDR GHVWD HTXDFaDR
˜H R PHVPR TXH R GHOLQHDGR QDV VHFaRHV DQWHULRUHV� RX VHMD� DVVXPLPRV XPD
VROXFaDR SDUWLFXODU GD IRUPD
[
S
�W� ; VHQ��
U
Wƒ ‹��
RQGH� SDUD U �
U
 �
Q
�
; 
P
�
H
P
U
�
S
�� ƒ U
�
�
�
� ��•U�
�
H
‹ DUFWDQ
�•U
�ƒ U
�
�
��
����� 'LVSRVLWLYRV GH PHGLFaDR�
8PD LPSRUWDQWH DSOLFDFaDR GR SUREOHPD GH H[FLWDFaDR GH EDVH ˜H R SURMHWR GH
DFHOHUARPHWURV� FXMR HVTXHPD ˜H PRVWUDGR QD ‘JXUD ����
)LJXUD ���� 0RGHOR GH XP DFHOHUARPHWUR�
2 EDODQFR GH IRUFDV QD PDVVD P ˜H
P¦[ ƒF� B[ƒ B\�ƒ N�[ƒ \��
3RU KLS˜RWHVH� D EDVH PRQWDGD VREUH D HVWUXWXUD REMHWR GD PHGLFaDR UHDOL]D
XP PRYLPHQWR KDUPARQLFR \ < FRV�
E
W� 2 PRYLPHQWR GD PDVVD P UHODWLYR
—D EDVH� GHQRWDGR SRU ]�W� ˜H GH‘QLGR FRPR
]�W� [�W�ƒ \�W��
'HVWD IRUPD� SRGHPRV UHHVFUHYHU D HTXDFaDR GD GLQADPLFD GR VLVWHPD GD
VHJXLQWH PDQHLUD�
P¦] � F B] � N] P�
�
E
< FRV�
E
W�
FXMD VROXFaDR QR UHJLPH HVWDFLRQ˜DULR ˜H GDGD SRU
]�W� 
�
�
E
<
S
��
�
Q
ƒ �
�
E
�
�
� ��•�
Q
�
E
�
�
FRV
—
�
E
Wƒ DUFWDQ
�•�
Q
�
E
�
�
Q
ƒ �
�
E
˜
�
��
RQGH �
Q
 
S
N P ˜H IUHT¦XAHQFLD QDWXUDO GR DFHOHUARPHWUR� 8PD PDQLSXODFaDR
GDV DPSOLWXGHV GRV PRYLPHQWRV QRV OHYD D�
=
<
 
U
�
S
�� ƒ U
�
�
�
� ��•U�
�
H
¥ DUFWDQ
�•U
�ƒ U
�
SDUD D PXGDQFD GH IDVH�
3RGHPRV� WDPE˜HP� HVFUHYHU
�
�
Q
]�W� 
�
S
�� ƒ U
�
�
�
� ��•U�
�
�
�
E
< FRV��
E
Wƒ‹��
&RPR \ < FRV��
E
Wƒ‹�� R ˜XOWLPR WHUPR SRGH VHU YLVWR FRPR ƒ¦\�W�� /RJR�
�
�
Q
]�W� 
ƒ�
S
��ƒ U
�
�
�
� ��•U�
�
¦\�W��
(VWD H[SUHVVaDR PRVWUD TXH SDUD SHTXHQRV YDORUHV GH U D PRYLPHQWR UHODWLYR
GD EDVH ˜H SURSRUFLRQDO —D DFHOHUDFaDR GD EDVH� SRLV R WHUPR DEDL[R WHQGH D �
TXDQGR U WHQGH D �� LVWR ˜H�
OLP
U��
�
S
�� ƒ U
�
�
�
� ��•U�
�
 ��
(VWD SURSULHGDGH QRV LQWHUHVVD SDUD UHDOL]DU DV PHGLFaRHV�$ IDL[D GH XWL�
OL]DFaDR GH XP DFHOHUARPHWUR ˜H GH‘QLGD FRPR
� �
�
E
�
Q
� ���� � � �
E
� �� ��
Q
RX
� � I
P
� �� �I
Q
�
VHQGR I
P
˜H D IUHT¦XAHQFLD D VHU PHGLGD SHOR DFHOHUARPHWUR HP KHUW]�
��
��� 0RGHORV GH H[HUF˜•FLRV
([HUF˜•FLR �
$ PDVVD TXH VH YAH QD ‘J� ��� HVW˜D LQLFLDOPHQWH HP UHSRXVR TXDQGR
OKH GDPRV XPD YHORFLGDGH GH � P�V� $FKDU R GHVORFDPHQWR VXE�
VHT¦XHQWH H D YHORFLGDGH GD PDVVD� 'DGRV� F ���� 1�V�P� N ��
1�P H P ����� J�
)LJXUD ���� 6LVWHPD�
��'HVFULFaDR GR PRGHOR�
$ HTXDFaDR GR PRYLPHQWR ˜H
P¦[� F B[� �N[ ��
��6ROXFaDR GR PRGHOR�
[�W� H
ƒ�
Q
W
�$ FRV�
G
W�% VHQ�
G
W��
FRP �
Q
 
S
�N P 
S
�� P �� UDG�V�
 
F
�P�
Q
 
�� ��
���� �������
 �� ����
�
G
 
S
� ƒ 
�
�
Q
 ��
S
� ƒ �� ���
�
 ��� � UDG�V�
��
6XEVWLWXLQGR HVVHV YDORUHV QDV HTXDFaRHV WHPRV
[ H
ƒ����W
�$ FRV ��� �W�% VHQ ��� �W�
H
B[ ƒ����H
ƒ����W
�$ FRV ��� �W�% VHQ ��� �W��
���� �H
ƒ����W
�ƒ$ VHQ ��� �W�% FRV ��� �W��
4XDQGR W �� [ � H� DVVLP� $ �� 4XDQGR W �� B[ �� /RJR�
% � ���� �� ���� (QWaDR�
[�W� �� ���H
ƒ����W
VHQ ��� �W�
B[ H
ƒ����W
�� FRV ��� �Wƒ �� ��� VHQ ��� �W��
B[ �� ��H
ƒ����W
FRV���� �W� �� �
“
��
([HUF˜•FLR �
&DOFXODU D UHVSRVWD WUDQVLW˜RULD H SHUPDQHQWH GD PDVVD QR SUREOHPD
DQWHULRU VH XPD IRUFD H[FLWDGRUD )
�
VHQ �W �� VHQ ��W HVW˜D DWXDQGR
QD PDVVD�
��6ROXFaDR GR PRGHOR�
&RPR GDGR QR SUREOHPD DQWHULRU� D UHVSRVWD WUDQVLW˜RULD ˜H
[
K
�W� H
ƒ����W
VHQ���� �W� £��
RQGH £ DUFWDQ$ %�
$ UHVSRVWD SHUPDQHQWH ˜H
[
S
 
)
�
S
�N ƒP�
�
�
�
� �F��
�
VHQ��Wƒ ¥� 
 
��
T
���ƒ �� ���� … ��
�
�
�
� ��� ��… ���
�
VHQ���Wƒ ¥� �� ��� VHQ���Wƒ ��
“
��
��
RQGH
¥ DUFWDQ
�� �
Q
�ƒ �� �
Q
�
�
 
���� ������ ���
�ƒ ��� ���
�
 ��
“
$JRUD [ [
K
� [
S
 (H
ƒ����W
VHQ���� �W� £� � �� ��� VHQ���Wƒ ��
“
��
&RQGLFaRHV LQLFLDLV�
” (P W �� [ � H ( VHQ £� �� ��� VHQ���Wƒ ��
“
� ��
” (P W �� B[ � H (>ƒ�� �� VHQ£� ��� � FRV£@ � ��� ��������
FRV�ƒ��
“
� ��
5HVROYHQGR HVVDV GXDV HTXDFaRHV REWHPRV ( �� ��� H £ ��
“
� $VVLP�
[�W� �� ���H
ƒ����W
VHQ���� �W� ��
“
� � �� ��� VHQ���Wƒ ��
“
��
([HUF˜•FLR �
$FKH D YLEUDFaDR SHUPDQHQWH GR SUREOHPD DQWHULRU SHOR P˜HWRGR GD
,PSHGADQFLD 0HFADQLFD�
��6ROXFaDR GR PRGHOR�
$ HTXDFaDR GR PRYLPHQWR ˜H GDGD SRU P¦[ � F B[ � N[ )
�
VHQ�W� RQGH N
M˜D OHYD HP FRQWD DV GXDV PRODV� RX VHMD� M˜D ˜H D ULJLGH] HTXLYDOHQWH�
&RPR ) )
�
H
L�W
 )
�
�FRV�W� L VHQ�W�� XVDUHPRV DSHQDV D SDUWH LPDJ�
LQ˜DULD GD VROXFaDR�
&RQVLGHUHPRV R YHWRU GHVORFDPHQWR ; ;H
L��Wƒ¥�
� YHWRU YHORFLGDGH
 L�; � YHWRU DFHOHUDFaDR ƒ�
�
;� 6XEVWLWXLQGR HVWHV YDORUHV QD HTXDFaDR
GR PRYLPHQWR� WHPRV TXH
…
�N ƒP�
�
� � LF�
†
;H
L��W�¥�
 )
�
H
L�W
� �N ƒP�
�
� LF��;H
ƒL¥
 )
�
RX
;H
ƒL¥
 
)
�
�N ƒP�
�
 LF��
�
0DV� ;H
ƒL¥
 ;�FRV¥ ƒ VHQ¥�� RQGH ¥ DUFWDQ >��F� �N ƒP�
�
�@� $VVLP�
; 
)
�
S
�N ƒP�
�
�
�
� �F��
�
��
H
[
S
 ,P�;� 
)
�
S
�N ƒP�
�
�
�
� �F��
�
VHQ��Wƒ ¥��
/RJR� VXEVWLWXLQGR RV YDORUHV QXP˜HULFRV WHPRV�
>�� ƒ ��� ���������
�
� L��� �������@;H
ƒL¥
 ���
���� � � L�����;H
ƒL¥
 ��� ;H
ƒL¥
 
��
���� � L��� �
H ; �� ��� FRP ¥ DUFWDQ���� � ��� �� ��
“
� $VVLP�
; ;H
L��Wƒ¥�
 �� ���H
L���Wƒ��
“
�
�
H
[
S
 ,P�;� ; VHQ��Wƒ ¥� �� ��� VHQ���Wƒ ��
“
��
([HUF˜•FLR �
2 URWRU GH PDVVD P ˜H PRQWDGR HP XP HL[R HO˜DVWLFR� FXMD PDVVD ˜H
GHVSUH]˜•YHO FRPSDUDGD —D GR URWRU� (VWH WHP XPD H[FHQWULFLGDGH H�
$FKDU D YHORFLGDGH FU˜•WLFD GR HL[R� VH D IUHT¦XAHQFLD QDWXUDO GR URWRU
˜H
S
N P RQGH N ˜H D FRQVWDQWH GH PROD HTXLYDOHQWH GR HL[R�
��'HVFULFaDR GR PRGHOR�
6HMD 5 R FHQWUR GH URWDFaDR� 2 R FHQWUR JHRP˜HWULFR H * R FHQWUR GH JUDYL�
GDGH GR URWRU FRPR PRVWUDGR QD ‘J� �����
��(TXDFLRQDPHQWR�
(P TXDOTXHU LQVWDQWH GXUDQWH D URWDFaDR� D IRUFD UHVWDXUDGRUD� GHYLGR DR
HL[R HO˜DVWLFR� ˜H NU� HQTXDQWR D IRUFD FHQWU˜•IXJD� GHYLGR DR GHVHTXLO˜•EULR� ˜H
P�H� U��
�
� (VWDV GXDV IRUFDV GHYHP VHU LJXDLV� LVWR ˜H�
NU P�H� U��
�
RX
N
P
 
�
�
�H� U�
U
�
0DV� N P �
�
Q
H GHVWH PRGR� D HTXDFaDR VH WRUQD
�
�
Q
U
—
�ƒ
�
�
�
�
Q
˜
 H�
�
RX U 
H��
�
 �
�
Q
�
� ƒ ��
�
 �
�
Q
�
�
��6ROXFaDR GR PRGHOR�
6H �
�
 �
�
Q
� R YDORU GH U WRUQDU�VH�˜D PXLWR JUDQGH� LVWR ˜H� R HL[R ˜H LQVW˜DYHO�
$VVLP� D YHORFLGDGH FU˜•WLFD GR HL[R ˜H � 
S
N P �
Q
� 1HVWD YHORFLGDGH
HVSHFLDO GH URWDFaDR� RFRUUHU˜D D UHVVRQADQFLD�
��
)LJXUD ����� (VTXHPD�
([HUF˜•FLR �
$ DUPDGXUD GH XP PRWRU HO˜HWULFR SHVD ����� 1 H VHX FHQWUR GH
JUDYLGDGH HVW˜D ����� PP GHVORFDGR GR FHQWUR GR HL[R GRV PDQ�
FDLV� 2 PRWRU� FRP XP SHVR WRWDO GH ������ 1� DS˜RLD�VH HP TXDWUR
PRODV GH ULJLGH] ���� N1�P FDGD� $FKDU D YHORFLGDGH FU˜•WLFD GR
PRWRU H D DPSOLWXGH YHUWLFDO GD VXD YLEUDFaDR� TXDQGR JLUDQGR D
XPD YHORFLGDGH LJXDO DR WULSOR GD VXD YHORFLGDGH FU˜•WLFD
&RQVWDQWH WRWDO GDV PRODV ����� �� ���� � N1�P�
$ IUHT¦XAHQFLD QDWXUDO GR PRWRU ˜H �
Q
 
S
N P 
S
���� � … ��
�
��� ��� ���� �� 
��� � UDG�V RX ��� U�S�P� $VVLP� D YHORFLGDGH FU˜•WLFD GR PRWRU ˜H ��� U�S�P�
�YHU SUREOHPD DFLPD�� &RQVLGHUDQGR R WULSOR GHVWD YHORFLGDGH FU˜•WLFD� D IRUFD
SURYRFDGD SHOR GHVHTXLO˜•EULR GH URWDFaDR ˜H
) PH�
�
 ���� �� �� ������ ���… ��
ƒ�
������ ��
�
 ��� � 1�
��
$ UHVSRVWD SHUPDQHQWH VHP DPRUWHFLPHQWR ˜H
[
S
 
) N
U
�
ƒ �
 
PH�
�
 N
�� �
�
Q
ƒ ��
 
��� � ����� �… ��
�
�
�ƒ �
 ����… ��
ƒ�
P�
([HUF˜•FLR �
2EVHUYRX�VH TXH� DS˜RV FLQFR FLFORV FRQVHFXWLYRV� D DPSOLWXGH GH
YLEUDFaDR GR VLVWHPD PRVWUDGR QD ‘J� ���� GHFUHVFHX DW˜H �� � GH
VHX YDORU LQLFLDO� 'HWHUPLQDU R FRH‘FLHQWH F GH DPRUWHFLPHQWR GR
VLVWHPD VH N ���� 1�P H P ���� .J�
)LJXUD ����� 6LVWHPD
��'HVFULFaDR GR PRGHOR�
3DUD YLEUDFaRHV OLYUHV DPRUWHFLGDV VDEHPRV TXH
[�W� &H
ƒ�
Q
W
VHQ��
G
W� £��
��6ROXFaDR GR PRGHOR�
$ DPSOLWXGH P˜D[LPD HP XP FLFOR RFRUUH TXDQGR VHQ��
G
W � £� ˜H LJXDO —D
XQLGDGH� $VVLP VHQGR� DV DPSOLWXGHV P˜D[LPDV VaDR
[
�
 &H
ƒ�
Q
W
�
H [
�
 &H
ƒ�
Q
W
�
�
[
�
 [
�
 H
�
Q
�W
�
ƒW
�
�
 H
�
Q
�ž �
G
�
 H
�ž 
S
�ƒ
�
�
��
2 ORJDULWPR GD UHODFaDR [
�
 [
�
˜H OQ�[
�
 [
�
� �ž 
S
�ƒ 
�
 “ VHQGR “
FKDPDGR GHFUHPHQWR ORJDU˜•WPLFR� &RPR R FRH‘FLHQWH GH DPRUWHFLPHQWR ˜H
F �
S
NP� FRQKHQGR�VH D UHODFaDR GH GXDV DPSOLWXGHV FRQVHFXWLYDV RX R
GHFUHPHQWR ORJDU˜•WPLFR “� FRQKHFH�VH R IDWRU GH DPRUWHFLPHQWR  H� FRQ�
VHT¦XHQWHPHQWH� F�
1HVWH SUREOHPD� [
�
 [
�
 � �� ��� 0DV�
[
�
 [
�
 �[
�
 [
�
��[
�
 [
�
��[
�
 [
�
��[
�
 [
�
��[
�
 [
�
� H OQ�[
�
 [
�
� “�
7RPDQGR R ORJDULWPR GH DPERV RV ODGRV GD HTXDFaDR� WHPRV TXH
OQ � OQ�[
�
 [
�
� � OQ�[
�
 [
�
� � OQ�[
�
 [
�
� � OQ�[
�
 [
�
� � OQ�[
�
 [
�
�
RX
OQ � �“� “ �� �� 
�ž
S
�ƒ 
�
�  �� ����
(QWaDR�F �
S
NP ���� ����
S
��������� ��� ����� 1�V�P�
([HUF˜•FLR �
8P YHQWLODGRU FHQWU˜•IXJR SHVD ����� 1 H WHP XP GHVHTXLO˜•EULR URWD�
WLYR GH ����� OE ORDFOL]DGR D ���� PP GR FHQWUR GH URWDFaDR� 4XDQGR
VaDR XVDGRV DPRUWHFHGRUHV FRP IDWRU GH DPRUWHFLPHQWR  ���� HV�
SHFL‘TXH DV PRODV SDUD PRQWDJHP WDLV TXH VRPHQWH �� � GD IRUFD
GH GHVHTXLO˜•EULR VHMD WUDQVPLWLGD SDUD R FKaDR� 'HWHUPLQDU WDPE˜HP
D LQWHQVLGDGH GD IRUFD WUDQVPLWLGD� 2 YHQWLODGRU JLUD D XPD YHORFL�
GDGH GH ����� U�S�P�
��(TXDFLRQDPHQWR�
$ IRUFD WRWDO WUDQVPLWLGD ˜H D VRPD GDV UHDFaRHV QDV H[WUHPLGDGHV ‘[DV GD
PROD H GR DPRUWHFHGRU
)
W
 N[� F B[�
��6ROXFaDR GR PRGHOR�
6RE FRQGLFaRHV GH YLEUDFaDR SHUPDQHQWH� M˜D GLVFXWLGDV DQWHULRUPHQWH� D
DPSOLWXGH GH YLEUDFaDR ˜H
[
S
 
)
�
 N
S
�� ƒ U
�
�
�
� ��U�
�
VHQ��Wƒ ¥��
��
3RU FRQYHQLAHQFLD� VHMD [
S
 $ VHQ��Wƒ ¥�� $VVLP� B[
S
 $� FRV��Wƒ ¥� H
)
W
 N$ VHQ��Wƒ ¥� � F$� FRV��Wƒ ¥��
0DV� D IRUFD GD PROD ˜H P˜D[LPD TXDQGR D YHORFLGDGH ˜H LJXDO D ]HUR �RX R
GHVORFDPHQWR ˜H XP P˜D[LPR�� HQTXDQWR TXH D IRUFD GH DPRUWHFLPHQWR ˜H XP
P˜D[LPR TXDQGR R GHVORFDPHQWR ˜H LJXDO D ]HUR �RX D YHORFLGDGH ˜H P˜D[LPD��
&RPR D IRUFD GD PROD HVW˜D GHIDVDGD GH ��
R
HP UHODFaDR —D IRUFD GH DPRUWHFL�
PHQWR� D P˜D[LPD IRUFD UHVXOWDQWH WUDQVPLWLGD ˜H $
S
N
�
� �F��
�
� 'HVWD IRUPD�
)
W
 $
S
N
�
� �F��
�
FRV��W� £�� £ DUFWDQ�F� N��
$ WUDQVPLVVLELOLGDGH 75� TXH ˜H D UD]aDR HQWUH D IRUFD WUDQVPLWLGD P˜D[LPD H
D IRUFD P˜D[LPD LPSULPLGD� WRPD D IRUPD
75 
$
S
N
�
� �F��
�
)
�
FRV��W� £��
0DV� [ [
S
SDUD YLEUDFaDR HP HVWDGR HVWDFLRQ˜DULR H� GHVWH PRGR�
75 
S
� � ��U�
�
S
�� ƒ U
�
�
�
� ��U�
�
� 75 
S
� � �� ��U
�
S
� � U
�
ƒ �U
�
� ����U
�
�
VHQGR U � �
Q
�  F �P�
Q
� H 75 �� �� $VVLP�
� � �� ��U
�
U
�
ƒ �� ��U
�
� �
 ���� RX U
�
ƒ �� ��U
�
ƒ ��U ƒ �� ��
R TXH QRV IRUQHFH U �� �� $VVLP� �
Q
 � U ��� �� � ��� � UDG�V H
N P�
�
Q
 ���� �� �� �� „ ��� �
�
 ����� 1�P�
$PSOLWXGH GD IRUFD WUDQVPLWLGD�
)
W
 ��� ���PH�
�
� 
�� � „ ��� �� „ ����
ƒ�
„ �����
�
�� ��
 ��� 1�
��
([HUF˜•FLR �
$ ‘P GH GLPLQXLU R PRYLPHQWR YLEUDW˜RULR WUDQVPLWLGR SDUD RV LQV�
WUXPHQWRV� RV SDLQ˜HLV GH LQVWUXPHQWRV VaDR PRQWDGRV HP LVRODGRUHV
FRPR DFRQWHFH QRV DYLaRHV� 6H R LVRODGRU� WHQGR PXLWR SHTXHQR
DPRUWHFLPHQWR� DEDL[D ����� PP VRE XP SHVR GH ����� 1� FDOFXODU
D SHUFHQWDJHP GH PRYLPHQWR WUDQVPLWLGR DR SDLQHO GH LQVWUXPHQ�
WRV VH D YLEUDFaDR GR DYLaDR RFRUUH D ���� U�S�P�
��(TXDFLRQDPHQWR�
75 
S
� � ��U�
�
S
�� ƒ U
�
�
�
� ��U�
�
�
��6ROXFaDR GR PRGHOR�
&RPR� SRU˜HP� R DPRUWHFLPHQWR ˜H SHTXHQR� F ž � H  ž ��
8VDQGR �
Q
 
S
N P� RQGH N ) “
VW
� WHPRV TXH
�
�
Q
 
)
P“
VW
 
���� �
����� � �� ������ ���… ��
ƒ�
�
 ����� �UDG�V�
�
�
RX I
Q
 ��� � �ž �� �� +] RX ��� URWDFaRHV SRU PLQXWR �U�S�P�� $VVLP�
U I I
Q
 ���� ��� �� �� H
75 
�
U
�
ƒ �
 
�
��� �ƒ �
 �� ����
��'LVFXVVaDR GRV UHVXOWDGRV�
/RJR� XVDQGR LVRODGRUHV� DSHQDV �� �� GR PRYLPHQWR YLEUDW˜RULR GR DYLaDR
˜H WUDQVPLWLGR DR SDLQHO GH LQVWUXPHQWRV�
([HUF˜•FLR �
8P FDSWDGRU GH YLEUDFaDR PDVVD�PROD VLPSOL‘FDGR FRPR R GD ‘J�
���� ˜H XVDGR SDUD PHGLU D DFHOHUDFaDR YHUWLFDO GH XP WUHP TXH WHP
XPD IUHT¦XAHQFLD YHUWLFDO GH �� UDG�V� $ PDVVD SHVD ����� 1 H
D FRQVWDQWH GD PROD ˜H ����� 1�P� $ DPSOLWXGH GR PRYLPHQWR
UHODWLYR GD PDVVD ˜H ���� PP FRPR UHJLVWUDGR SHOR LQVWUXPHQWR�
$FKDU D DFHOHUDFaDR YHUWLFDO P˜D[LPD H D DPSOLWXGH GH YLEUDFaDR GR
WUHP�
��(TXDFLRQDPHQWR�
��
)LJXUD ����� &DSWDGRU GH YLEUDFaDR
$ DPSOLWXGH GR PRYLPHQWR UHODWLYR GD PDVVD ˜H GDGD SRU
[
S
 
$U
�
S
�� ƒ U
�
�
�
� ��U�
�
�
��6ROXFaDR GR PRGHOR�
&RPR QaDR K˜D DPRUWHFLPHQWR QHVWH VLVWHPD�
[
S
 
$U
�
�ƒ U
�
 
$�
�
�
�
Q
ƒ �
�
�
$VVLP� D P˜D[LPD DFHOHUDFaDR YHUWLFDO GR WUHP ˜H
$�
�
 [
S
��
�
Q
ƒ �
�
� ��� �� … ��
ƒ�
�>����� ���� �� �� ���ƒ ���@ ��� � P�V�V�
$ DPSOLWXGH GH YLEUDFaDR�
$ [
S
�
�
Q
ƒ �
�
�
�
 ��� �� … ��
ƒ�
�
������ �ƒ ���
���
 ����� P�
([HUF˜•FLR ��
8PD PDVVD SHVDQGR ����� 1 HVW˜D VXVSHQVD HP XPD FDL[D SRU XPD
PROD YHUWLFDO FXMD FRQVWDQWH ˜H N ���� 1�P FRPR PRVWUD D ‘J�
��
)LJXUD ����� (VTXHPD�
����� $ FDL[D ˜H FRORFDGD HP FLPD GH XPD PHVD YLEUDW˜RULD� SUR�
GX]LQGR XPD YLEUDFaDR [ ���� VHQ �W� $FKDU D DPSOLWXGH DEVROXWD
GD PDVVD�
��(TXDFLRQDPHQWR�
$ DPSOLWXGH GR PRYLPHQWR UHODWLYR GD PDVVD ˜H� FRPR QR SUREOHPD DQWH�
ULRU�
[
S
 
$U
�
S
�� ƒ U
�
�
�
� ��U�
�
�
��6ROXFaDR GR PRGHOR�
$VVLP FRPR QD PDLRULD GRV SUREOHPDV PHFADQLFRV� R DPRUWHFLPHQWR GHYLGR
—D SUHVHQFD GR DU ˜H GHVSUH]DGR� $O˜HP GLVVR� QaDR K˜D XP DPRUWHFLPHQWR HIHWLYR�
(QWaDR�
[
S
 
$U
�
�ƒ U
�
 
$�
�
�
�
Q
ƒ �
�
�
0DV� �
�
Q
 N P ������� ��� ��� �� ���� �UDG�V�
�
� � � UDG�V H �
�
 �
�UDG�V�
�
� DVVLP�
[
S
 
�� �����
���� ƒ �
 �� ������ P�
$ DPSOLWXGH DEVROXWD GD PDVVD ˜H
[
�
 [
S
�$ �� ������ � �� �� �� ����� P�
��
([HUF˜•FLR ��
8P DFHOHUARPHWUR� FXMR DPRUWHFLPHQWR ˜H GHVSUH]˜•YHO� ˜H HPSUHJDGR
SDUD VH HQFRQWUDU D LQWHQVLGDGH GD YLEUDFaDR GH XPD HVWUXWXUD GH
P˜DTXLQD� (OH G˜D XPD OHLWXUD GRV GHVORFDPHQWRV UHODWLYRV GH ������
PP� $ IUHT¦XAHQFLD QDWXUDO GR DFHOHUARPHWUR ˜H GH ��� F�S�P� �FLFORV
SUR PLQXWR� H D P˜DTXLQD HVW˜D JLUDQGR D ��� U�S�P� 4XDO VHU˜D D
JUDQGH]D GR GHVORFDPHQWR� YHORFLGDGH H DFHOHUDFaDR GR HOHPHQWR GD
P˜DTXLQD TXH YLEUD"
��(TXDFLRQDPHQWR
&RPR M˜D VDEHPRV�
[
S
 
$U
�
�� ƒ U
�
�
�
�
VHQGR U � �
Q
 ��� ��� �� ����
��6ROXFaDR GR PRGHOR�
'HVWH PRGR� D JUDQGH]D GR GHVORFDPHQWR ˜H GDGD SRU
$ 
[
S
��ƒ U
�
�
U
�
 
�� ������ ƒ �� ���
�
�
� �
 �� ���� PP�
$ JUDQGH]D GD YHORFLGDGH ˜H
$� 
[
S
��ƒ U
�
��
U
�
 �� ����>�����ž ���@ �� �� PP�V�
( D JUDQGH]D GD DFHOHUDFaDR ˜H
$�
�
 
[
S
��ƒ U
�
��
�
U
�
 �� �����
�
 �� ��������� ��� � PP�V
�
�
��
&DS˜•WXOR �
5HVSRVWD SDUD IRUFDPHQWR
JHUDO�
��� 5HVXPR GD WHRULD
����� )XQFaDR UHVSRVWD LPSXOVLRQDO
8PD IRUPD PXLWR LPSRUWDQWH GH H[FLWDFaDR GH XP VLVWHPD ˜H R LPSXOVR� TXH
YHP D VHU XPPRGHOR PDWHP˜DWLFR GH XPD IRUFD DSOLFDGD GXUDQWH XP LQWHUYDOR
GH WHPSR LQ‘QLWHVLPDO� $ UHVSRVWD GH XP VLVWHPD DR LPSXOVR ˜H LGAHQWLFD —D
UHVSRVWD OLYUH GR VLVWHPD VXEPHWLGR D FHUWDV FRQGLFaRHV LQLFLDLV� FRPR YHUHPRV
DGLDQWH�
3ULPHLUDPHQWH� FRQVLGHUHPRV XP SXOVR GH PDJQLWXGH
A
) �” H GXUDFaDR �”
FRPR PRVWUD D ‘JXUD ���� RQGH ” ˜H XP Q˜XPHUR SHTXHQR� 2 LPSXOVR FDXVDGR
SHOD IRUFD ) ˜H GH‘QLGR FRPR
,�”� 
=
¡�”
¡ƒ”
) �W�GW 
=
�
ƒ�
) �W�GW�
$LQGD� QRWDPRV TXH R LPSXOVR ˜H LJXDO —D ˜DUHD VRE D FXUYD GR JU˜D‘FR GH ) � RX
VHMD�
,�”� 
=
�
ƒ�
) �W�GW 
A
)
�”
�” 
A
) �
1R OLPLWH TXDQGR ” � � D LQWHJUDO FRQWLQXD YDOHQGR
A
) � (VWH IDWR ˜H XVDGR
��
)LJXUD ���� 5HSUHVHQWDFaDR JU˜D‘FD GH XPD IRUFD LPSXOVLRQDO�
SDUD GH‘QLU D IXQFaDR LPSXOVR DSOLFDGR QR LQVWDQWH ¡ GD VHJXLQWH IRUPD�
Ÿ
) �Wƒ ¡ � � W � ¡
) �Wƒ ¡ � � W ¡
H
=
�
ƒ�
) �Wƒ ¡ �GW 
A
)
6H D PDJQLWXGH GH
A) ˜H XP� HQWaDR HVWD VH WRUQD D GH‘QLFaDR GR LPSXOVR XQLW˜DULR�
RX IXQFaDR GHOWD GH 'LUDF� GHQRWDGD SRU “�Wƒ ¡ ��
$ VROXFaDR SDUD D UHVSRVWD GH XP VLVWHPD PDVVD�PROD�DPRUWHFHGRU FRP
XP JUDX GH OLEHUGDGH ˜H REWLGD UHFRUGDQGR�VH TXH XP LPSXOVR DSOLFDGR D XP
FRUSR LPSOLFD YDULDFaDR QD TXDQWLGDGH GH PRYLPHQWR GHVWH FRUSR� $VVLP�
FRQVLGHUH XP LPSXOVR DSOLFDGR HP W � H FRQVLGHUH D PDVVD HVWDQGR HP
UHSRXVR DW˜H VXD DSOLFDFaDR� RX VHMD DW˜H R LQVWDQWH W �
ƒ
� $V FRQGLFaRHV
LQLFLDLV VHULDP� SRUWDQWR� [��
ƒ
� [��
�
� �� $ YDULDFaDR GD TXDQWLGDGH GH
PRYLPHQWR GHYLGR DR LPSDFWR ˜H P B[��
�
� ƒ P B[��
ƒ
� PY
�
 )„W� (QWaDR�
DSOLFDU XP LPSXOVR HP XP VLVWHPD PDVVD�PROD�DPRUWHFHGRU GH XP JUDX GH
OLEHUGDGH ˜H R PHVPR TXH DSOLFDU FRQGLFaRHV LQLFLDLV GH GHVORFDPHQWR QXOR H
YHORFLGDGH LJXDO D Y
�
 )„W P� &RQY˜HP REVHUYDU TXH� VH R LPSXOVR IRU
DSOLFDGR HP XP LQVWDQWH SRVWHULRU GH WHPSR� LVWR ˜H� FDVR R VLVWHPD QaDR HVWHMD
HP UHSRXVR� GHYH�VH OHYDU HP FRQWD D SRVLFaDR GD PDVVD QDTXHOD LQVWDQWH�
��
VXD YHORFLGDGH LPHGLDWDPHQWH DQWHV GD DSOLFDFaDR GD IRUFD� FDOFXODU D QRYD
YHORFLGDGH LPHGLDWDPHQWH SRVWHULRU� D TXDO VH WRUQDULD XPD QRYD FRQGLFaDR
LQLFLDO� MXQWDPHQWH FRP D SRVLFaDR� SDUD V˜R HQWaDR FDOFXODU D QRYD UHVSRVWD GR
VLVWHPD� D SDUWLU GHVWH LQVWDQWH GH WHPSR�
&RPR M˜D YLPRV QR FDS˜•WXOR �� SDUD XP VLVWHPD VXE�DPRUWHFLGR �� � • �
��� D UHVSRVWD SDUD FRQGLFaRHV LQLFLDLV [
�
 � H Y
�
 
A
) P ˜H GD IRUPD
[�W� 
A
)H
•�W
P�
G
VHQ�
G
W
RX� GH PDQHLUD PDLV FRPSDFWD�
[�W� 
A
)K�W��
RQGH
K�W� 
�
P�
G
H
ƒ•�W
VHQ�
G
W�
TXH YHP D VHU D UHVSRVWD DR LPSXOVR XQLW˜DULR DSOLFDGR HP W �� 6H HOH IRU
DSOLFDGR HP W ¡ WHUHPRV�
K�Wƒ ¡ � 
�
P�
G
H
ƒ•�Wƒ¡�
VHQ�
G
�Wƒ ¡ � W ! ¡�
����� 5HVSRVWD SDUD XPD HQWUDGD DUELWU˜DULD
$ UHVSRVWD GH XP VLVWHPD PDVVD�PROD�DPRUWHFHGRU SDUD XPD HQWUDGD RX
IRUFDPHQWR DUELWU˜DULR SRGH VHU GHWHUPLQDGD D SDUWLU GH VXD UHVSRVWD K�W�
SDUD XP LPSXOVR XQLW˜DULR� D TXDO M˜D FRQKHFHPRV� 1D YHUGDGH� HVWD ˜H XPD
SURSULHGDGH GH WRGRV RV VLVWHPDV OLQHDUHV LQYDULDQWHV QR WHPSR �/7, � /LQHDU
7LPH ,QYDULDQW 6\VWHPV�� FRPR R TXH HVWXGDPRV� &RQKHFLGD D UHVSRVWD
LPSXOVLRQDO� D UHVSRVWD D XP IRUFDPHQWR TXDOTXHU VHU˜D GDGD SHOD FRQYROXFaDR
GR VLQDO GH HQWUDGD FRP D UHVSRVWD LPSXOVLRQDO� $VVLP� VH ) �W� ˜H D H[FLWDFaDR�
[�W� 
=
W
�
) �¡ �K�Wƒ ¡�G¡ 
�
P�
G
=
W
�
…
) �¡ �H
•�¡
VHQ�
G
�Wƒ ¡ �
†
G¡ 
 
�
P�
G
=
W
�
) �Wƒ ¡�H
ƒ•�¡
VHQ�
G
¡ G¡�
��
����� 5HVSRVWD SDUD XPD HQWUDGD SHUL˜RGLFD DUELWU˜DULD
$TXL FRQVLGHUDUHPRV R FDVR GH XPD HQWUDGD SHUL˜RGLFD TXDOTXHU� $ GH‘QLFaDR
GH IXQFaDR SHUL˜RGLFD ˜H D GH TXH H[LVWH XP YDORU ‘[R GH WHPSR 7 � RX SHU˜•RGR�
SDUD R TXDO I�W� I �W�7 �� 6HJXQGR D WHRULD GD $Q˜DOLVH GH )RXULHU� TXDOTXHU
IXQFaDR SHUL˜RGLFD SRGH VHU UHSUHVHQWDGD SRU XPD VH˜ULH LQ‘QLWD QD IRUPD
) �W� 
D
�
�
�
�
;
Q �
�D
Q
FRVQ�
7
W� E
Q
VHQQ�
7
W��
RQGH �
7
 �ž 7 ˜H D IUHT¦XAHQFLD IXQGDPHQWDO GD RVFLODFaDR� 'HVWD IRUPD� GHYH�
PRV GHFRPSRU D IXQFaDR RULJLQDO HP XPD VRPD LQ‘QLWD GH VHQRV H FRVVHQRV FRP
IUHT¦XAHQFLDV P˜XOWLSODV GD RULJLQDO� FKDPDGDV GH KDUPARQLFDV� (QWaDR� D DQ˜DOLVH
)RXULHU FRQVLVWH HP GHWHUPLQDU RV FRH‘FLHQWHV D
Q
H E
Q
GD V˜HULH� 8PD LPSRU�
WDQWH SURSULHGDGH GDV IXQFaRHV WULJRQRP˜HWULFDV ˜H D RUWRJRQDOLGDGH� PRVWUDGD
DEDL[R
=
7
�
VHQQ�
7
W VHQP�
7
W GW 
Ÿ
� P � Q
7 � P Q
=
7
�
FRVQ�
7
W FRVP�
7
W GW 
Ÿ
� P � Q
7 � P Q
H
=
7
�
FRV Q�
7
W VHQP�
7
W GW ��
(VWD SURSULHGDGH ˜H XVDGD QD GHWHUPLQDFaDR GDV H[SUHVVaRHV TXH GH‘QHP FRH�
‘FLHQWHV GD V˜HULH H PRVWUDGDV D VHJXLU�
D
�
 
�
7
=
7
�
) �W� GW
D
Q
 
�
7
=
7
�
) �W� FRVQ�
7
W GW Q �� �� � � �
E
Q
 
�
7
=
7
�
) �W� VHQQ�
7
W GW Q �� �� � � �
��
” ([HPSOR
(VFUHYD HP WHUPRV GH 6˜HULHV GH )RXULHU D IXQFaDR� GH‘QLGD SDUD XP SHU˜•RGR
FRPR�
) �W� 
Ÿ
W� � ™ W ™ �
��ƒ W��� � W ™ �
6ROXFaDR�
) �W� 
D
�
�
�
�
;
Q �
>D
Q
FRV�Q�
¡
W� � E
Q
VHQ�Q�
¡
W�@ �
�
¡
 
�ž
�
�
D
�
 
�
7
=
7
�
) �W�GW 
�
�
=
�
�
) �W�GW 
=
�
�
W GW�
=
�
�
��ƒ W�GW 
 
™
W
�
�
š
�
�
�
™
�Wƒ
W
�
�
š
�
�
 
�
�
� � �
�
�
 ��
D
Q
 
�
7
=
7
�
) �W� FRV�Q�
¡
W�GW 
=
�
�
W FRV�Q�
¡
W�GW�
=
�
�
��ƒ W� FRV�Q�
¡
�GW 
 
=
�
�
W FRV�QžW�GWƒ
=
�
�
W FRV�QžW�GW� �
=
�
�
FRV�QžW�GW�
&˜DOFXOR GD LQWHJUDO XVDQGR LQWHJUDFaDR SRU SDUWHV�
=
W FRV�QžW�GW� X W� GX GW� GY FRV�QžW�GW� Y 
VHQ�QžW�
Qž
�
=
XGY XY ƒ
=
YGX 
W VHQ�QžW�
Qž
ƒ
=
VHQ�QžW�
Qž
GW 
��
 
W VHQ�QžW�
Qž
�
�
�Qž�
�
FRV�QžW��
6XEVWLWXLQGR HP D
Q
� WHPRV TXH
D
Q
 
™
W VHQ�QžW�
Qž
�
�
�Qž�
�
FRV�QžW�
š
�
�
ƒ
™
W VHQ�QžW�
Qž
�
�
�Qž�
�
FRV�QžW�
š
�
�
�
��
™
W VHQ�QžW�
Qž
š
�
�
 
 
™
VHQ�QžW�
Qž
�
�
�Qž�
�
FRV�QžW�ƒ
�
�Qž�
�
š
ƒ
™
FRV��Qž�
�Qž�
�
ƒ
FRV�Qž�
�Qž�
�
š
 
 
� FRV��Qž�
�Qž�
�
ƒ
�
�Qž�
�
 
 
�
�Qž�
�
>FRV�Qž�ƒ �@�
E
Q
 
�
7
=
7
�
) �W� VHQ�Q�
¡
W�GW ��
$VVLP� FKHJDPRV D
) �W� 
�
�
�
�
;
Q �
�
�Qž�
�
>
�ƒ��
Q
] `_ ^
FRV�Qž�ƒ�@ FRV�QžW��
(� ID]HQGR Q �Pƒ �� M˜D TXH D
Q
V˜R H[LVWH SDUD Q ˜•PSDU� WHPRV TXH
) �W� 
�
�
�
�
;
P �
ƒ�
>��Pƒ ��ž@
�
FRV>��Pƒ ��žW@�
��
)LJXUD ���� ([FLWDFaDR SHUL˜RGLFD
��� 0RGHORV GH ([HUF˜•FLRV
([HUF˜•FLR �
8PD H[FLWDFaDR SHUL˜RGLFD� FRPR VH YAH QD ‘J� ����˜H DSOLFDGD QD EDVH
GR VLVWHPD PDVVD�PROD�DPRUWHFHGRU� 'HWHUPLQH R PRYLPHQWR UH�
VXOWDQWH GD PDVVD P� VH N �� OE�LQ� P �� OE�V
�
�LQ H F ��
OE�V�LQ�
��(TXDFLRQDPHQWR�
2V PRYLPHQWRV SHUL˜RGLFRV JHUDLV SRGHP VHU UHSUHVHQWDGRV SHOD V˜HULH GH
)RXULHU SRU
) �W� 
�
;
Q �
�D
Q
FRVQ�W� E
Q
VHQQ�W�
RX� VRE D IRUPD GHVHQYROYLGD�
) �W� D
�
� D
�
FRV�W� D
�
FRV ��W� � � �� E
�
VHQ�W� E
�
VHQ ��W� � � �
RQGH
D
�
 
�
¡
=
¡
�
) �W� GW� D
Q
 
�
¡
=
¡
�
) �W� FRV Q�W GW�
E
Q
 
�
¡
=
¡
�
) �W� VHQQ�W GW�
��
H ¡ �ž � ˜H R SHU˜•RGR GH ) �W��
3DUD HVWH PRYLPHQWR SHUL˜RGLFR HP IRUPD GH GHQWH GH VHUUD� ) �W� W H
¡ �� $VVLP� \�W� ) �W� W H
D
�
 
�
¡
=
¡
�
) �W� GW 
=
�
�
W GW 
�
�
�
D
Q
 
�
¡
=
¡
�
) �W� FRVQ�W GW �
=
�
�
W FRV Q�W GW ��
E
Q
 
�
¡
=
¡
�
) �W� VHQQ�W GW �
=
�
�
W VHQ Q�W GW ƒ
�
Qž
�
/RJR� R GHVHQYROYLPHQWR GD V˜HULH GH )RXULHU GH \�W� ˜H
\�W� 
�
�
ƒ
�
ž
�
;
Q �
�
Q
VHQQ�W�
$SOLFDQGR
3
) PD D HVWH VLVWHPD� WHPRV TXH
P¦[ ƒF� B[ƒ B\�ƒ N�[ƒ \� RX P¦[� F B[� N[ F B\ � N\�
FRP
B\ ƒ
�
;
Q �
�
ž
FRVQ�W�
'HVWD IRUPD� D HTXDFaDR GR PRYLPHQWR WRUQD�VH
P¦[� F B[� N[ F
�
ƒ
�
;
Q �
�
ž
FRVQ�W
�
� N
�
�
�
ƒ
�
ž
�
;
Q �
�
Q
VHQ Q�W
�N
�
ƒ
�
;
Q �
™
N
žQ
VHQ Q�W�
F�
ž
FRV Q�W
š
�
0DV� $ VHQQ�W�% FRV Q�W 
S
$
�
�%
�
VHQ�Q�W�£�� RQGH £ DUFWDQ�% $��
$VVLP�
F B\ � N\ 
N
�
ƒ
�
ž
�
;
Q �
�
Q
�
S
N
�
� F
�
�
�
VHQ�Q�W� £��
��
VHQGR £ DUFWDQ�F� N�� (� FRPR �
�
 N P H  F �P�
Q
� WHPRV TXH
F B\ � N\ 
N
�
ƒ
�
ž
�
;
Q �
N
Q
�
S
� � ��UQ�
�
VHQ�Q�W� £��
(VWD ˜H IRUFD LPSULPLGD H D UHVSRVWD SHUPDQHQWH� GH DFRUGR FRP GLVFXVVaRHV
DQWHULRUHV ˜H
[
S
 
�
�
ƒ
�
ž
�
;
Q �
�
Q
�
V
� � ��UQ�
�
��ƒ Q
�
U
�
�
�
� ��UQ�
�
VHQ�Q�Wƒ ¥��
VHQGR
¥ DUFWDQ
—
�QU
� ƒ Q
�
U
�
ƒ £
˜
�
3DUD HVWH FDVR SDUWLFXODU� �
Q
 
S
N P 
S
�� �� � UDG�V� U � �
Q
 
\
�
 �� ��  F �P�
Q
 �� ��…��…�� �� �� 6XEVWLWXLQGR HVWHV YDORUHV QD
HTXDFaDR GR PRYLPHQWR H VLPSOL‘FDQGR� WHPRV D UHVSRVWD SHUPDQHQWH SDUD D
PDVVD P�
[
S
 �� �ƒ �� ��� VHQ��� ��Wƒ ���
“
�ƒ �� ��� VHQ���� ��Wƒ ��� �
“
�ƒ
ƒ�� ��� VHQ���� �Wƒ ��� �
“
�ƒ � � �
��
&DS˜•WXOR �
0˜XOWLSORV JUDXV GH OLEHUGDGH
��� 5HVXPR GD WHRULD
����� 'RLV JUDXV GH OLEHUGDGH �VHP DPRUWHFLPHQWR�
&RQVLGHUH R VLVWHPD GH GXDV PDVVDV PRVWUDGR QD ‘JXUD ���� MXQWDPHQWH FRP
R GLDJUDPD GH FRUSR OLYUH GDV GXDV PDVVDV�
)LJXUD ���� 6LVWHPD FRP GRLV JUDXV GH OLEHUGDGH�
6RPDQGR DV IRUFDV GDV PRODV TXH DWXDP QDV PDVVDV QD GLUHFaDR KRUL]RQWDO�
REWHPRV�
Ÿ
P
�
¦[
�
 ƒN
�
[
�
� N
�
�[
�
ƒ [
�
�
P
�
¦[
�
 ƒN
�
�[
�
ƒ [
�
�
�
Ÿ
P
�
¦[
�
� �N
�
� N
�
�[
�
ƒ N
�
[
�
 �
P
�
¦[
�
ƒ N
�
[
�
� N
�
[
�
 ��
/RJR� FKHJDPRV D GXDV HTXDFaRHV GLIHUHQFLDLV GH VHJXQGD RUGHP DFRSODGDV�
3DUD FDGD XPD GHODV� SUHFLVDPRV GH � FRQGLFaRHV LQLFLDLV� (QWaDR� DV GXDV
HTXDFaRHV HVWDULDP VXMHLWDV D � FRQGLFaRHV LQLFLDLV�
[
�
��� [
��
� B[
�
��� B[
��
� [
�
��� [
��
� H B[
�
��� B[
��
�
��
RQGH B[
��
� B[
��
H [
��
� [
��
UHSUHVHQWDP DV YHORFLGDGHV H GHVORFDPHQWRV LQLFLDLV�
GH FDGD PDVVD� UHVSHFWLYDPHQWH�
2EVHUYDPRV TXH DV GXDV HTXDFaRHV TXH GH‘QHP D GLQADPLFD GR VLVWHPD QaDR
SRGHP VHU UHVROYLGDV VHSDUDGDPHQWH� M˜D TXH DPEDV FRQWAHP WHUPRV WDQWR HP
[
�
TXDQWR HP [
�
� )LVLFDPHQWH� LVWR VLJQL‘FD TXH R PRYLPHQWR GH XPD GDV
PDVVDV DIHWD R GD RXWUD�
3RGHPRV HVFUHYHU DV GXDV HTXDFaRHV DFRSODGDV VRE D IRUPD PDWULFLDO� LVWR
˜H�
™
P
�
�
� P
�
š ™
¦[
�
¦[
�
š
�
™
N
�
� N
�
ƒN
�
ƒN
�
N
�
š ™
[
�
[
�
š
 
™
�
�
š
�
FRP FRQGLFaRHV LQLFLDLV
[
�
 
™
[
�
���
[
�
���
š
� B[
�
 
™
B[
�
���
B[
�
���
š
�
'H IRUPD UHVXPLGD� SRGHPRV HVFUHYHU HVWD HTXDFaDR QD IRUPD
0¦[�.[ ��
3URSRPRV VROXFaDR GR WLSR [�W� XH
M�W
GD PHVPD IRUPD FRPR IRL IHLWR SDUD
DSHQDV XP JUDX GH OLEHUGDGH� X ˜H R YHWRU GDV FRQVWDQWHV D VHUHP GHWHUPL�
QDGDV�
6XEVWLWXLQGR D VROXFaDR SURSRVWD QD HTXDFaDR 0¦[ �.[ �� VHQGR 0 D
PDWUL] GH PDVVD� . D PDWUL] GH ULJLGH]� ¦[ R YHWRU DFHOHUDFaDR H [ R YHWRU
GHVORFDPHQWR� WHPRV TXH
�ƒ�
�
0 �.�XH
M�W
 ��
1RWH TXH R HVFDODU H
M�W
� � SDUD WRGR YDORU GH W� /RJR� � H X GHYHP VDWLVID]HU
D HTXDFaDR YHWRULDO
�ƒ�
�
0 �.�X ��
4XHUHPRV TXH X WDPE˜HP VHMD GLIHUHQWH GH ]HUR� SDUD TXH KDMD GHVORFDPHQWR�
�6H X �� [�W� XH
M�W
 ���W�� 3DUD TXH LVWR DFRQWHFD� D PDWUL] �ƒ�
�
0 �
.� QaDR SRGH VHU LQYHUV˜•YHO H� HQWaDR� GHW�ƒ�
�
0 � .� � �FRQGLFaDR GH
VLQJXODULGDGH�� $VVLP�
GHW
™
ƒ�
�
P
�
� N
�
� N
�
ƒN
�
ƒN
�
ƒ�
�
P
�
� N
�
š
 ��
��
� P
�
P
�
�
�
ƒ �P
�
N
�
�P
�
N
�
�P
�
N
�
��
�
ƒ N
�
N
�
 ��
TXH YHP D VHU GH‘QLGD FRPR D HTXDFaDR FDUDFWHU˜•VWLFD GR SUREOHPD�
8PD YH] TXH RV YDORUHV GRV SDUADPHWURV I˜•VLFRV P
�
� P
�
� N
�
H N
�
VaDR FRQ�
KHFLGRV� SRGHPRV XVDU HVWD HTXDFaDR SDUD GHWHUPLQDU DV FRQVWDQWHV � H ORJR
TXH RV YDORUHV GH � WHQKDP VLGR HQFRQWUDGRV� SRGHPRV DFKDU RV YDORUHV GH
X� XWLOL]DQGR DV VHJXLQWHV HTXDFaRHV�
�ƒ�
�
�
0 �.�X
�
 � H �ƒ�
�
�
0 �.�X
�
 ��
$ VROXFaDR SDUD R VLVWHPD GH HTXDFaRHV DFRSODGDV SRGH VHU FRQVWUX˜•GD D SDUWLU
GRV YDORUHV HQFRQWUDGRV SDUD � H X�
[�W� X
�
H
ƒM�
�
W
� X
�
H
M�
�
W
� X
�
H
ƒM�
�
W
� X
�
H
M�
�
W
�
7HPRV� HQWaDR� TXH D VROXFaDR JHUDO ˜H GDGD SRU
[�W� �DH
M�
�
W
� EH
ƒM�
�
W
�X
�
� �FH
M�
�
W
� GH
ƒM�
�
W
�X
�
�
D TXDO WDPE˜HP SRGH VHU HVFULWD QD IRUPD
[�W� $
�
VHQ��
�
W� £
�
�X
�
�$
�
VHQ��
�
W� £
�
�X
�
�
(VWD ˜XOWLPD HTXDFaDR LQGLFD TXH FDGD PDVVD RVFLOD FRP XPD IUHT¦XAHQFLD TXH ˜H
FRPELQDFaDR OLQHDU GH �
�
H �
�
� DV TXDLV VaDR FRQKHFLGDV FRPR IUHT¦XAHQFLDV QDWX�
UDLV GR VLVWHPD� 6XSRQKDPRV DJRUD TXH DV FRQGLFaRHV LQLFLDLV VHMDP HVFROKLGDV
GH PDQHLUD TXH $
�
 �� &RP HVWDV FRQGLFaRHV LQLFLDLV� DV PDVVDV RVFLODP QD
IUHT¦XAHQFLD �
�
� H DV SRVLFaRHV UHODWLYDV GDV PDVVDV VaDR GHWHUPLQDGDV DWUDY˜HV
GH X
�
� FKDPDGR GH SULPHLUR PRGR GH YLEUDFaDR GR VLVWHPD� 'D PHVPD IRUPD�
SRGHPRV HVFROKHU FRQGLFaRHV LQLFLDLV TXH IDFDP FRP TXH $
�
 �� $V PDVVDV
DJRUD RVFLODP FRP IUHT¦XAHQFLD �
�
H FRP SRVLFaRHV UHODWLYDV GDGDV SHOR YHWRU
X
�
� R VHJXQGR PRGR GH YLEUDFaDR�
����� $XWRYDORUHV H IUHT¦XAHQFLDV QDWXUDLV
6HMD D PDWUL] UDL] TXDGUDGD GH‘QLGD FRPR 0
� �
� WDO TXH 0
� �
0
� �
 0 �
VHQGR 0 D PDWUL] GH PDVVD� 3DUD D PDWUL] GH PDVVD GD VHFaDR DQWHULRU�
WHPRV TXH
0
� �
 
™
S
P
�
�
�
S
P
�
š
�
��
$LQGD� D LQYHUVD GH 0
� �
� GHQRWDGD 0
ƒ� �
� ˜H
0
ƒ� �
 
�
�
S
P
�
�
�
�
S
P
�
�
�
6HMD [ 0
ƒ� �
T� 6XEVWLWXLQGR [ QD HTXDFaDR 0¦[�.[ � H PXOWLSOLFDQGR
D HTXDFaDR UHVXOWDQWH SRU 0
ƒ� �
� FKHJDPRV D
0
ƒ� �
00
ƒ� �
¦T�W� �0
ƒ� �
.0
ƒ� �
T�W� ��
&RPR 0
ƒ� �
00
ƒ� �
 ,� D H[SUHVVaDR DFLPD UHGX]�VH D
,¦T�W� �
a
.T�W� ��
VHQGR
a
. 0
ƒ� �
.0
ƒ� �
� 3URSRUHPRV� QRYDPHQWH� T�W� YH
M�W
FRPR
VROXFaDR� VHQGR Y R YHWRU GDV FRQVWDQWHV� 6XEVWLWXLQGR� REWHPRV
a
.Y �
�
Y RX
a
.Y šY�
VHQGR š �
�
�
2 HVFDODU š TXH VDWLVID] D HTXDFaDR DFLPD SDUD XP YHWRU Y QaDR QXOR ˜H
FKDPDGR GH DXWRYDORU H Y ˜H R VHX DXWRYHWRU FRUUHVSRQGHQWH�
3RGHPRV GHVDFRSODU DV HTXDFaRHV GH PRYLPHQWR GH TXDOTXHU VLVWHPD QaDR
DPRUWHFLGR GH TXDOTXHU RUGHP� FRQVWUXLQGR XPD QRYD PDWUL] 3 � IRUPDGD
SHORV DXWRYHWRUHV QRUPDOL]DGRV� GH IRUPD TXH FDGD YHWRU IRUPH XPD FROXQD
GD PDWUL]� $VVLP�
3 >aY
�
aY
�
aY
�
� � � aY
Q
@�
VHQGR Q R Q˜XPHUR GH JUDXV GH OLEHUGDGH GR VLVWHPD H aY
L
˜H R DXWRYHWRU Y
L
QRUPDOL]DGR� (VWD PDWUL] ˜H FKDPDGD GH 0DWUL] 0RGDO� (VWD PDWUL] SRVVXL D
SURSULHGDGH TXH 3
7
3 ,� FRQVWLWXLQGR�VH� SRUWDQWR� HP XPD PDWUL] RUWRJ�
RQDO� $ 0DWUL] (VSHFWUDO GH
a
. ˜H XPD PDWUL] GLDJRQDO FXMRV HOHPHQWRV VaDR RV
DXWRYDORUHV š
L
GH
a
. H ˜H GH‘QLGD FRPR
† GLDJ�š
L
� 3
7
a
.3�
��
����� $Q˜DOLVH PRGDO
&RPR M˜D IRL GLWR�

Outros materiais