'(3(1'(1&,$(175(/263$5È0(7526'(81
6,67(0$<'(8102'(/2%255262'(/7,32
7$.$*,68*(12
0LJXHO3HxD6DQGUD3LxyQ (GXDUGR)&DPDFKR
'SWRGH6LVWHPDV $XWRPiWLFD(VFXHOD6XSHULRUGH,QJHQLHURV8QLYHUVLGDGGH6HYLOOD
&DPLQRGHORV'HVFXEULPLHQWRVVQ6HYLOOD(VSDxD
PLJXHOS#FDUWXMDXVHV
5HVXPHQ
(Q HVWH WUDEDMR VH SUHVHQWD XQD GLVFXVLyQ VREUH ODV
SURSLHGDGHV GH ORV SDUiPHWURV GH XQ 6LVWHPDV GH
,QIHUHQFLD%RUURVDGHO7LSR7DNDJL6XJHQR76),6
SRUVXVVLJODVHQLQJOpVXVDGRFRPRPRGHORGHXQ
VLVWHPD'LFKDGLVFXVLyQH[WLHQGHWUDEDMRVDQWHULRUHV
GRQGH VH SUHVHQWy HQ GHWDOOH HO 76 ),6 VH
DQDOL]DURQ WUHV SURSLHGDGHV GHO PLVPR OD =RQD GH
9DOLGH]GHO0RGHOR09=ODSRVLELOLGDGGHREWHQHU
ORV SDUiPHWURV GHO PRGHOR SRU PHGLR GH XQD
OLQHDOL]DFLyQ GH XQ PRGHOR PDWHPiWLFR OD
SRVLELOLGDG GH DFRSODPLHQWR R IXVLyQ HQWUH GRV
PRGHORVERUURVRV$TX VHKDFHXQDFRUWDUHYLVLyQGH
WDOHV WySLFRV /XHJR VH DQDOL]D OD GLIHUHQFLD HQWUH
DGDSWDFLyQGHSDUiPHWURV DMXVWHGHSDUiPHWURVHQ
ORV PRGHORV)LQDOPHQWHVHGHVFULEHODGHSHQGHQFLD
HQWUHORVSDUiPHWURVGHOVLVWHPD ORVSDUiPHWURVGHO
PRGHOR VH SUHVHQWD XQ HMHPSOR SDUD LOXVWUDU ODV
SURSLHGDGHVGHORVSDUiPHWURVGLVFXWLGDV
,1752'8&&,Ï1
(O FRQFHSWR GH LGHQWLILFDFLyQ LPSOLFD HO XVR GH
PpWRGRV SDUD HVWDEOHFHU PRGHORV GH SURFHVRV
PDWHPiWLFRV R VLPEyOLFRV FRQ OD LQIRUPDFLyQ GHO
SURFHVR FRQWHQLGD HQ XQ FRQMXQWR GH GDWRV GH
HQWUDGDVDOLGD$TX VHKDDGRSWDGRFRPRPRGHORXQ
6LVWHPDGH,QIHUHQFLD%RUURVR),6GHOWLSR7DNDJL
6XJHQR 76 ),6 HVWDEOHFLGR HQ >@ (Q >@ VH
SUHVHQWDXQDGLVFXVLyQGHWDOODGDVREUHXQDSURSXHVWD
GHLGHQWLILFDFLyQFRQHVWHWLSRGHPRGHORV$GHPiV
HQ>@VHGHVDUUROODURQODVSURSLHGDGHVGHODV=RQDV
GH 9DOLGDFLyQ GHO 0RGHOR 09= OD SURSLHGDG GH
REWHQFLyQ GH XQ PRGHOR ERUURVR PHGLDQWH OD
OLQHDOL]DFLyQGHOPRGHORPDWHPiWLFR SRU~OWLPROD
SURSLHGDG GH HO DFRSODPLHQWR R IXVLyQ HQWUH GRV
PRGHORV ERUURVRV (Q >@ VH UHVXPH HVWD
DSUR[LPDFLyQ
(Q HO SUHVHQWH WUDEDMR VH GHVDUUROODQ GRV
FRQWULEXFLRQHV3ULPHURVHDQDOL]DODGLIHUHQFLDHQWUH
DGDSWDFLyQ GH SDUiPHWURV DMXVWH GH SDUiPHWURV
6HJXQGR VH GHVFULEH OD GHSHQGHQFLD HQWUH HO
SDUiPHWURGHOVLVWHPD ORVSDUiPHWURVGHOPRGHOR
(OWUDEDMRHVWiRUJDQL]DGRFRPRVLJXH(QODVHFFLyQ
VHGDXQDGHVFULSFLyQGHOPRGHORERUURVRXWLOL]DGR
(QODVHFFLyQVHGHVFULEHQODVSURSLHGDGHVGHORV
PRGHORV 76 ),6 3ULPHUDPHQWH VH KDQ UHYLVDGR
SURSLHGDGHV D HVWXGLDGDV DQWHULRUPHQWH VH
GHVDUUROODQ QXHYDV SURSLHGDGHV )LQDOPHQWH VH GDQ
DOJXQDVFRQFOXVLRQHVHQODVHFFLyQ
02'(/2%25526287,/,=$'2
(QHVWHWUDEDMRVHKDXWLOL]DGRXQPRGHORERUURVRGHO
WLSR7DNDJL6XJHQR76),6SHURPRGLILFDGRFRQHO
REMHWR GH XWLOL]DU HQ HO DQWHFHGHQWH FRQMXQWRV
ERUURVRV PXOWLGLPHQVLRQDOHV (VWD SURSXHVWD VH
SUHVHQWy HQ >@ (VWH 76 ),6 SXHGH UHSUHVHQWDU R
PRGHODUXQDFODVHGHVLVWHPDVQROLQHDOHVHVWiWLFRV
GLQiPLFRV (Q GLFKR PRGHOR ODV UHJODV VRQ GH OD
IRUPD
[
[
%
[
HQWRQFHV
H
L
L
L
L
I
V
6L
5
GRQGH
>
@
0
[
[
[
VRQODV0HQWUDGDVGHOPRGHOR
[%
L
HV XQ FRQMXQWR ERUURVR GH GLPHQVLyQ 0H
L
HVODVDOLGDSDUDFDGDUHJODGHILQLGDSRUPHGLR
GHODIXQFLyQIL[(QJHQHUDOVHHOLJHXQDIXQFLyQ
OLQHDODI QGHODVHQWUDGDVGHODIRUPD
0
L
0
L
L
L
[
D
[
D
D
I
[
GRQGH
L
M
D
VRQ HVFDODUHV /D VDOLGD GHO PRGHOR VH
REWLHQHPHGLDQWHXQSURPHGLRSHVDGRGHODVVDOLGDV
LQGLYLGXDOHV GH ODV UHJODV
L
6RQ XWLOL]DGDV
IXQFLRQHV GH QRUPDOL]DFLyQ VREUH ODV HQWUDGDV
VDOLGDV 3RUWDQWR OD QXHYD IRUPXODFLyQ SDUD HO76
),6FRQQRUPDOL]DFLyQVREUHODVHQWUDGDV VDOLGDHV
HQWRQFHV
HV
6L
5
Q
L
L
Q
Q
L
Q
L
[
[
[
I
%
FRQ
Q
7
L
L
Q0
L
0
Q
L
L
Q
L
D
[
D
[
D
D
I
[
D
[
GRQGH
>
@
7
L
0
L
L
D
D
D
/D VDOLGD GHO PRGHOR QRUPDOL]DGR
Q
VH FDOFXOD
FRPRXQSURPHGLRSHVDGRGHODFRQWULEXFLyQGHFDGD
UHJOD
Q
/
L
L
L
Q
Q
/
L
L
Q
Z
Z
[
[
¦
¦
(VWDHFXDFLyQJHQHUDOPHQWHVHH[SUHVDFRPR
¦
/
L
Q0
L
0
Q
L
L
Q
L
Q
[
D
[
D
D
[
M
FRQ
¦
¦
/
L
Q
L
/
L
Q
L
Q
L
Z
Z
[
[
[
M
GRQGH/HVHOQ~PHURGHUHJODV
Z
L
HVHOJUDGRGH
YHUGDGYDORUGHSHUWHQHQFLDGHODLpVLPD UHJOD(O
YDORUGHSHUWHQHQFLDVHREWLHQHFRPRXQDIXQFLyQGH
GLVWDQFLDGHODIRUPD
¦
/
M
M
L
L
G
G
Z
SDUD[QzYL ZL SDUD [Q YL (Q HVWD
H[SUHVLyQ
L
Q
7
L
Q
L
G
Y
[
Y
[
HVHOFXDGUDGR
GHODGLVWDQFLDGHVGH HOGDWR
[
Q
KDVWDHOFHQWUR
L
Y
/RV YHFWRUHV
L
Y
VRQ HOHPHQWRV UHSUHVHQWDWLYRV GH
FDGD UHJOD /RV UHVXOWDGRV REWHQLGRV PXHVWUDQ XQD
IRUPD HVIpULFD HQ HO HVSDFLR PGLPHQVLRQDO GH ODV
YDULDEOHV GH HQWUDGD 'HELGR D VH FXPSOH OD
FRQGLFLyQ
Z
L
L
/
¦
SRUWDQWRGH
Z
L
M
(VWD
IXQFLyQ GH SHUWHQHQFLD OOHYD D FDER XQD SDUWLFLyQ
ERUURVDGHOHVSDFLRGHHQWUDGD>@
/D HQWUDGD OD VDOLGD QRUPDOL]DGDV [QH Q VH
REWLHQHQFRPR
[
[
[
Q
Q
J
J
/DV IXQFLRQHV GH QRUPDOL]DFLyQ VH XWLOL]DQ FRQ HO
REMHWRGHIDFLOLWDU HOSURFHGLPLHQWRSDUD GHWHUPLQDU
OD HVWUXFWXUD GHO PRGHOR SDUD PHMRUDU VX
GHVHPSHxR (VWDV IXQFLRQHV GH QRUPDOL]DFLyQ WUDHQ
FRQVLJRXQD FRUUHFFLyQ GHHVFDODV XQD FRUUHFFLyQ
HVWDG VWLFDHQORVGDWRV1yWHVHTXHODQRUPDOL]DFLyQ
GHODVDOLGDGHEHWHQHULQYHUVD
3523,('$'(6'(/02'(/2
%255262
5(9,6,Ï1 '( /$6 3523,('$'(6 '(
/2602'(/2676),6
(Q HVWD VHFFLyQ VH SUHVHQWDQ DOJXQDV GH ODV
SURSLHGDGHV TXH D VH KDE DQ GDGR HQ >@
3ULPHUDPHQWHVHFRQVLGHUDOD]RQDGHYDOLGH]SDUDHO
PRGHOR 76 ),6 /XHJR VH DQDOL]D OD FDSDFLGDG GH
OLQHDOL]DFLyQGHOPRGHOR ILQDOPHQWHVHLQWURGXFHOD
SURSLHGDG GH DFRSOH R IXVLyQ GHO PRGHOR FRQ
UHVSHFWRDOGDWRGLVSRQLEOH
=RQDGH9DOLGH]GHO0RGHOR
/DSULPHUDSURSLHGDGH[SORUDOD=RQDGH9DOLGH]GHO
0RGHOR 09= SDUD XQ PRGHOR 76 ),6 (VWD
SURSLHGDG GD XQD IXHUWH FDUDFWHUL]DFLyQ GHO PRGHOR
SDUDGHWHUPLQDUODYDOLGH]GHVXVDOLGDFRQUHVSHFWRD
XQYHFWRUGHHQWUDGDSDUWLFXODU3RU WDQWRFXDOTXLHU
GDWR GH HQWUDGD DO PRGHOR 76 ),6 SURGXFLUi XQD
VDOLGDYiOLGDVLHVWHHVWiGHQWURGHOD09=
&XDOTXLHUPRGHORQROLQHDOLGHQWLILFDGRSRUPHGLRGH
ORV GDWRV GH HQWUDGD VDOLGD KHUHGD WRGDV ODV
OLPLWDFLRQHV TXHFRQWLHQH HO FRQMXQWR GH GDWRV3RU
WDQWRODYDOLGH]GHOPRGHORHVWiUHVWULQJLGDDOD]RQD
GHWHUPLQDGD SRU VHxDOHV XWLOL]DGDV SDUD SURGXFLU HO
FRQMXQWRGHGDWRV>@
&RQVLGHUDQGR HO PRGHOR 76 ),6 HVWDEOHFLGR HQ ODV
HFXDFLRQHV D OD HO FRQMXQWR ERUURVR GHO
DQWHFHGHQWH HV XQD IXQFLyQ GH OD GLVWDQFLD HQWUH HO
GDWR HOFHQWURGHOJUXSR'HELGRDHVWRQRVHWLHQH
XQDLQIRUPDFLyQH[SO FLWDHQWUHHOGDWR OD09=/D
)LJPXHVWUDXQDDOWHUQDWLYDSDUDGHWHUPLQDUVLXQ
GDWRGHHQWUDGDHVWiGHQWURGHOD 09=(OHMHPSOR
SRU VLPSOLFLGDG HVWi HQ GRV GLPHQVLRQHV SHUR VH
SXHGHH[WHQGHUDPiV
3HTXHxRV F UFXORV UHSUHVHQWDQ ORV GDWRV GH HQWUDGD
XWLOL]DGRV SDUD OD LGHQWLILFDFLyQ /D ILJXUD WDPELpQ
PXHVWUDXQDDOWHUQDWLYDUHVWULFWLYDSDUDGHWHUPLQDUOD
09=(QHVWHPpWRGRVHUHDOL]DXQDSDUWLFLyQGXUD
HQ OD HQWUDGD FRQVLGHUDQGR HO PLVPR Q~PHUR GH
JUXSRV ORV PLVPRV YDORUHV GH ORV FHQWURV GHO
PRGHOR8QGDWRSHUWHQHFHUiDXQJUXSRVLHOJUDGR
GHSHUWHQHQFLDHVHOPi[LPRHQWUHWRGRVORVJUXSRV
(VWR LQGLFD TXH HO GDWR SHUWHQHFH DO JUXSR FX R
FHQWURHVWiPiVFHUFDGHOPLVPR6HGHWHUPLQDFRPR
YDORU GH FRWD SDUD FDGD JUXSR OD GLVWDQFLD Pi[LPD
GHVGHHOFHQWURKDVWDHOGDWRGHOJUXSRPiVDOHMDGR
L
N
L
Q
1
N
L
PD[
L
Y
[
Y
G
GRQGH
N
L
Q
[
HVHONHVLPRGDWRGHOJUXSRLL /
L
1
HO Q~PHUR GH GDWRV GHO JUXSR L (V SRVLEOH
HVWDEOHFHUXQLQFUHPHQWRGHODFRWDSDUDLQFUHPHQWDU
OD JHQHUDOLGDG GHO PRGHOR SHUR PDQWHQLHQGR XQ
YDORU GHFRWDTXHUHIOHMHODULTXH]DGHOFRQMXQWRGH
GDWRV(O SURFHGLPLHQWRSDUDDQDOL]DU VL XQ GDWR GH
HQWUDGDHVWiGHQWURGHOD09=HV
L&DOFXODUODGLVWDQFLD HQWUHHOGDWR FDGDFHQWURGHO
PRGHOR76),6
LL(QFRQWUDUHOFHQWURDOFXDOFRUUHVSRQGHODP QLPD
GLVWDQFLD GHHVWDPDQHUDGHWHUPLQDUHOJUXSRDOFXDO
FRUUHVSRQGHHVWDP QLPDGLVWDQFLD
LLL6LHVWDP QLPDGLVWDQFLDHVPHQRUTXHODFRWDGHO
JUXSRHQWRQFHVHOGDWRGHHQWUDGDHVWiGHQWURGHOD
09=
02'(/2%2552620(',$17(
/,1($/,=$&,Ï1
'HELGR D OD IRUPD OLQHDO GH OD IXQFLyQ GHO
FRQVHFXHQWHHO76),6SUHVHQWDXQDFDUDFWHU VWLFDGH
OLQHDOL]DFLyQ TXH SXHGH DSURYHFKDUVH SDUD OD
FRQVWUXFFLyQ GH PRGHORV $ SDUWLU GH XQ PRGHOR
PDWHPiWLFR GHO SURFHVR SRU PHGLR GH VX
OLQHDOL]DFLyQSXHGHREWHQHUVHXQPRGHOR76),6/D
VLJXLHQWH SURSRVLFLyQ VXVWHQWD OD HTXLYDOHQFLD HQWUH
ODOLQHDOL]DFLyQGHOPRGHORPDWHPiWLFR GHOPRGHOR
76),6'HHVWDIRUPDHVSRVLEOHXWLOL]DUHOPRGHOR
PDWHPiWLFR OLQHDOL]DGR SDUD REWHQHU ORV SDUiPHWURV
GHO76),6/DSURSRVLFLyQVXSRQHTXHODIXQFLyQGH
SHUWHQHQFLD XWLOL]DGD HVWi GDGD SRU TXH
P
Q
Y
Y
z
SDUD WRGR
Q
P
z
HV GHFLU QR H[LVWHQ
FHQWURVUHSHWLGRVHQODEDVHGHUHJODV
3URSRVLFLyQ /LQHDOL]DFLyQ GH XQD IXQFLyQ
FRQWLQXDHQHOFHQWURGHODEDVHGHUHJODVERUURVDV
'DGDXQDIXQFLyQFRQWLQXD
I
Q
Q
[
[
HOPRGHOR76),6GHODIRUPD
¦
/
M
M
Q
7
M
M
Q
I
D
Z
[
D
[
FRQ OD IXQFLyQ GH SHUWHQHQFLD FRQVLGHUDQGR
P
Q
Y
Y
z
SDUD
PQ
/
O
Q
Q
Q
O
Y
[
[
[
D
w
w
O
O
7
O
O
D
Y
Y
D
(QWRQFHVSXHGHYHULILFDUVHTXH
D
Q
I
Q
OLP
OLP
L
Q
L
Q
[
[
Y
[
Y
[
o
o
/
D
L
E
Q
Q
I
Q
Q
OLP
OLP
L
Q
L
Q
[
[
[
[
Y
[
Y
[
w
w
w
w
o
o
D/
L
Q
/D SURSRVLFLyQ DQWHULRU PXHVWUD TXH OD IXQFLyQ
PDWHPiWLFD ODIXQFLyQJHQHUDGDSRUHOPRGHOR76
),6 WLHQHQ HO PLVPR YDORU GH VDOLGD ODV PLVPDV
GHULYDGDVHQHOFHQWURGHOJUXSR8QDLQWHUSUHWDFLyQ
GHHVWRVXJLHUHTXHHOPRGHOR76 ),6 HO SURFHVR
WLHQHQ OD PLVPD OLQHDOL]DFLyQ HQ ORV FHQWURV GH ORV
JUXSRVERUURVRV(VWRVJUXSRVVHJHQHUDQ FXDQGRHO
PRGHOR76),6GLYLGHHOHVSDFLRGHHQWUDGD$V OD
OLQHDOL]DFLyQ GHO PRGHOR PDWHPiWLFR HQ ORV FHQWURV
GHOPRGHOR76),6GDQORVSDUiPHWURVGHOPRGHOR76
),6XWLOL]DQGR
$&23/$0,(1722)86,Ï1'(
02'(/2676),6
(VWD SURSLHGDG SHUPLWH TXH GRV PRGHORV 76 ),6
LGHQWLILFDGRV FRQ GRV FRQMXQWRV GH GDWRV GLIHUHQWHV
GH XQ PLVPR VLVWHPD SXHGDQ VHU DFRSODGRV R
IXVLRQDGRV HQ XQ ~QLFR PRGHOR 76 ),6 (VWD
SURSLHGDGHVLQWHUHVDQWHFXDQGRHOVLVWHPDSURFHVR
TXH VH HVWi LGHQWLILFDQGR SRVHHQ GRV R PiV ]RQDV
GRQGHVXFRPSRUWDPLHQWRGLQiPLFRHVPX GLIHUHQWH
8Q PRGHOR 76 ),6 REWHQLGR FRQ XQ FRQMXQWR GH
GDWRV~QLFRJHQHUDOPHQWHLQWHUSRODODVGRVGLQiPLFDV
GHO SURFHVR SURGXFLHQGR XQD UHVSXHVWD EDVWDQWH
GLVWLQWDGHODUHVSXHVWDGLQiPLFDGHOVLVWHPDUHDO6LQ
HPEDUJRVHSXHGHQREWHQHUPRGHORVLQGHSHQGLHQWHV
SDUD FDGD ]RQD FRQ EXHQ FRPSRUWDPLHQWR /D
VLJXLHQWHSURSRVLFLyQVXJLHUHTXHVHSXHGHQDFRSODU
R IXVLRQDU ORV PRGHORV TXH VH KDQ REWHQLGR FRQ
GLVWLQWRVFRQMXQWRVGHGDWRVGDQGROXJDUDXQPRGHOR
~QLFRTXHFRQWHPSODHOFRPSRUWDPLHQWRGHFDGD]RQD
HQSDUWLFXODU
3URSRVLFLyQ $FRSODPLHQWRRIXVLyQGHPRGHORV
76),6 'DGRVGRVPRGHORVERUURVRV
¦
/$
M
M
Q
7
M
/$
M
$
Q
I$
D
Z
[
D
Y
Y
[
¦
¸
¸
¹
·
¨
¨
©
§
/$
N
N
M
/$
M
$
G
G
Z
Y
Y
¦
/%
/$
/$
M
M
Q
7
M
/%
/$
/$
M
%
Q
I%
D
Z
[
D
Y
Y
[
¦
¸
¸
¹
·
¨
¨
©
§
/%
/$
/$
N
N
M
/%
/$
/$
M
%
G
G
Z
Y
Y
GRQGH
N
M
Y
Y
z
SDUD
MN
/$
/%
DVXPLHQGRTXHORVGRVPRGHORV76),6YHULILFDQ
[
[
)LJ 09= WHQLHQGR HQ FXDQWD OD QRUPD
DFRWDGD
HQWRQFHVHVSRVLEOHREWHQHUHOPRGHORERUURVR
DFRSODGRRIXVLRQDGR
¦
/%
/$
M
M
Q
7
M
M
$%
Q
I$%
D
Z
[
D
[
¦
¸
¸
¹
·
¨
¨
©
§
/%
/$
N
N
M
/%
/$
M
$%
G
G
Z
Y
Y
TXHVDWLVIDFHODVLJXLHQWHFRQGLFLyQ
D
Q
Q
I$%
OLP
OLP
L
Q
L
Q
[
[
Y
[
Y
[
o
o
L
WR
/$
/%
E
Q
Q
Q
Q
I$%
OLP
OLP
L
Q
L
Q
[
[
[
[
Y
[
Y
[
w
w
w
w
o
o
L
WR
/$
/%
Q
(VWDSURSRVLFLyQPXHVWUDTXHVLGRVPRGHORV76),6
VRQ YHUVLRQHV OLQHDOL]DGDV GHO PRGHOR PDWHPiWLFR
REWHQLGRVHQ]RQDVSDUWLFXODUHVHQWRQFHVHOPRGHOR
76 ),6 DFRSODGR R IXVLRQDGR REWHQLGR FRQ
/$
/%
WDPELpQ HV XQD YHUVLyQ OLQHDOL]DGD GHO
PRGHOR PDWHPiWLFR (VWR VXJLHUH XQD KHUUDPLHQWD
SDUD OD LGHQWLILFDFLyQ D TXH HV SRVLEOH LGHQWLILFDU
GRVRPiV PRGHORV76),6HQ]RQDVGLIHUHQWHVFRQ
GLQiPLFDV GLIHUHQWHV DFRSODU R IXVLRQDU HQ XQ
PRGHOR76),6~QLFR(VWHPRGHOR76),6~QLFRHV
XQPRGHORJHQHUDOGHOSURFHVRSHURTXHHVGLIHUHQWH
GH XQ PRGHOR 76 ),6 LGHQWLILFDGR FRQ XQ~QLFR
FRQMXQWRGHGDWRVIRUPDGRSRUODVXPDGHORVGDWRV
XVDGRVSDUDREWHQHUORVGRVPRGHORVORFDOHV
6L HO SURFHVR GH LGHQWLILFDFLyQ VH KD UHDOL]DGR HQ
IRUPD FRUUHFWD HQ ODV ]RQDV GRQGH VH KDQ REWHQLGR
ORV PRGHORV ORFDOHV HQWRQFHV VH VDWLVIDUiQ ODV
VLJXLHQWHVFRQGLFLRQHV
I1
Q
Q
[
[
|
w
w
w
w
I1
Q
Q
Q
Q
[
[
[
[
|
SDUD FDGD XQR GH ORV PRGHORV ORFDOHV &RPR HO
PRGHOR VHUi YiOLGR SDUD OD ]RQD GH YDOLGH] ORV
FHQWURVVHHQFXHQWUDQ GHQWURGHOD]RQDGHYDOLGH]
ODVHFXDFLRQHV WDPELpQVHUiQYiOLGDSDUD
ORV FHQWURV GH ORV PRGHORV $O DFRSODU ORV GRV
PRGHORVODVHFV VHJXLUiQPDQWHQLpQGRVH
SDUDORVFHQWURVGHOPRGHORDFRSODGRRIXVLRQDGR
$'$37$&,Ï1 2 6,1721Ë$ '(
3$5È0(7526
(Q HVWD VHFFLyQ VH DQDOL]D OD GLIHUHQFLD HQWUH
DGDSWDFLyQ GH SDUiPHWURV VLQWRQ D GH SDUiPHWURV
(VWH DQiOLVLV HV XQD H[WHQVLyQ GH ODV SURSLHGDGHV
HVWXGLDGDVSUHYLDPHQWH
&XDQGR VH UHDOL]D XQ SURFHVR GH LGHQWLILFDFLyQ FRQ
XQ PRGHOR WLSR FDMD QHJUD FRQ OD FDSDFLGDG GH
DSUR[LPDU IXQFLRQHV FRQ HO JUDGR GH SUHFLVLyQ
QHFHVDULD VREUH XQ VLVWHPD QR OLQHDO HQ HVWDGR GH
IXQFLRQDPLHQWRVHGHEHQGLIHUHQFLDUHOFRQFHSWRGH
DMXVWHGHSDUiPHWURV HOFRQFHSWRGHDGDSWDFLyQ
GH SDUiPHWURV 6H VXSRQH TXH XQ VLVWHPD HQ
IXQFLRQDPLHQWRHVWiVLHQGRLGHQWLILFDGRHQO QHDSRU
XQ PRGHOR WLSR FDMD QHJUD 3DUD FODULGDG HQ OD
H[SOLFDFLyQ VH VXSRQH WDPELpQ TXH HO DOJRULWPR GH
LGHQWLILFDFLyQ DMXVWD ORV SDUiPHWURV GHO PRGHOR
SHULyGLFDPHQWHGH DFXHUGR D XQ ORWH R FRQMXQWR GH
GDWRVGHHQWUDGDVDOLGD$QWHXQ FRQMXQWR QXHYRGH
GDWRVSXHGHQRFXUULUGLVWLQWDVDOWHUQDWLYDV
TXHDOJXQRVGHORVSDUiPHWURVGHOVLVWHPDI VLFR
KD DQ FDPELDGR 'H HVWR VXUJH XQ HUURU HQWUH OD
VDOLGDGHOVLVWHPD GHOPRGHOR
TXHHOVLVWHPDKD DFDPELDGROD]RQDGHWUDEDMR
(VWR WDPELpQ SURYRFD XQ HUURU HQWUH OD VDOLGD GHO
VLVWHPD GHOPRGHOR(VWRVHGHEHDTXHHOPRGHOR
QRVHWLHQHLQIRUPDFLyQGHOVLVWHPDHQHVD]RQD
$QWH OD SULPHUD DOWHUQDWLYD VH GHEH UHDOL]DU XQD
DGDSWDFLyQ GH ORV SDUiPHWURV GHO PRGHOR SDUD
FRQWHPSODUORVFDPELRVHQORVSDUiPHWURVI VLFRVGHO
VLVWHPD(VWHDMXVWH VHGHEHUHDOL]DUSDUDUHGXFLUHO
QGLFH GH HUURU $ HVWH FRQFHSWR VH OR SXHGH
LQWHUSUHWDUFRPRDGDSWDFLyQGHORVSDUiPHWURV
(QODVHJXQGDDOWHUQDWLYDHODMXVWHGHORVSDUiPHWURV
SXHGH VHU SHUMXGLFLDO SRUTXH VH FDPELD HO
FRPSRUWDPLHQWRJHQHUDO GHO PRGHORFXDQGROR TXH
RFXUUH HV TXH KD VXUJLGR XQD QXHYD ]RQD GH
RSHUDFLyQ GHO VLVWHPD (Q HVWDV FLUFXQVWDQFLDV VH
GHEH UHDOL]DU XQD H[WHQVLyQ GHO PRGHOR D OD ]RQD
QXHYDGHWUDEDMR
3DUD SRGHU OOHYDU D FDER HVWRV FRQFHSWRV HV
LPSRUWDQWH OD SURSLHGDG GH DFRSODPLHQWR OD
SURSLHGDGGHODGHWHUPLQDFLyQGHOD]RQDGHYDOLGH]
GHO PRGHOR /R TXH VH GHEH KDFHU HV DQDOL]DU VL HO
QXHYR FRQMXQWR GH GDWRV SHUWHQHFH D OD ]RQD GH
YDOLGH]GHOPRGHOR6LHVWHSHUWHQHFHDGLFKD]RQDVH
GHEH DSOLFDU XQ DOJRULWPR SDUD HO DMXVWH GH ORV
SDUiPHWURV GHO PRGHOR D TXH VH HVWDU D DQWH XQ
SUREOHPDGHDGDSWDFLyQGHORVSDUiPHWURV3RUOR
FRQWUDULRVLHOQXHYRFRQMXQWRGHGDWRVQRSHUWHQHFH
DOD]RQDGHYDOLGH]GHOPRGHORVHGHEHREWHQHUXQ
PRGHORORFDO FRQ HVWH FRQMXQWR GH GDWRV D WUDYpV
GHODFRSODPLHQWRGHORVPRGHORVREWHQHUXQPRGHOR
JOREDO
'(3(1'(1&,$ 3$5$0e75,&$ (175(
(/6,67(0$<(/02'(/2
(Q HVWD VHFFLyQ VH DQDOL]D HO FRQFHSWR GH
GHSHQGHQFLDHQWUHORVSDUiPHWURVGHOVLVWHPDUHDO
ORV SDUiPHWURV GHO PRGHOR LGHQWLILFDGR FXDQGR VH
XWLOL]D HO PRGHOR 76 ),6 SURSXHVWR R HQ IRUPD
JHQHUDOXQDSUR[LPDGRUXQLYHUVDOGHIXQFLRQHV
6HVXSRQHTXHDOJXQRVSDUiPHWURVGHOVLVWHPDI VLFR
FDPELDQ FRQ HO WLHPSR TXH ORV SDUiPHWURV GHO
PRGHORVHHVWiQLGHQWLILFDQGRHQIRUPDSHULyGLFD(Q
HVWDVFLUFXQVWDQFLDVVLHOPRGHORXWLOL]DGRVHEDVDHQ
ORV SULQFLSLRV I VLFRV TXH ULJHQ DO SURFHVR PRGHOR
WLSR FDMD EODQFD HO FDPELR HQ XQSDUiPHWUR GHO
VLVWHPD I VLFR SURGXFLUi GHVSXpV GHO SURFHVR GH
LGHQWLILFDFLyQ HO FDPELR HQ XQ SDUiPHWUR HQ HO
PRGHOR 3RU RWUR ODGR FXDQGR HO VLVWHPD HVWi
PRGHODGRSRUXQPpWRGRJHQpULFRFRPRSXHGHVHUXQ
DSUR[LPDGRU XQLYHUVDO GH IXQFLRQHV PRGHORV WLSRV
FDMD QHJUD HO FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD
I VLFR SXHGH SURGXFLU HO FDPELR HQ XQR YDULRV R
WRGRV ORV SDUiPHWURV GHO PRGHOR (Q JHQHUDO XQ
FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD SURGXFH XQ
FDPELRHQPXFKRVSDUiPHWURVGHOPRGHOR
&RPR OD FRPSOHMLGDG GHO SUREOHPD GH FiOFXOR HV
PHQRUFXDQGRHVPHQRUODFDQWLGDGGHSDUiPHWURVD
DMXVWDU HV FRQYHQLHQWH TXH DQWH FDPELRV HQ ORV
SDUiPHWURVGHOVLVWHPDFDPELHQODPHQRUFDQWLGDGGH
SDUiPHWURVGHOPRGHOR/RLGHDOVHU DTXHXQFDPELR
HQHOSDUiPHWURGHOVLVWHPDSURGX]FDXQFDPELRHQHO
SDUiPHWURGHOPRGHOR
(ODQiOLVLVGHODGHSHQGHQFLDHQWUHORVSDUiPHWURVGHO
VLVWHPD I VLFR ORV SDUiPHWURV GHO PRGHOR SXHGHQ
EULQGDU XQD PHMRU LQWHUSUHWDFLyQ GHO VLVWHPD HQ
FRQMXQWR
'DGR XQ VLVWHPD I VLFR GHILQLGR HQ HQWUDGDVDOLGD
FX R FRPSRUWDPLHQWR GHSHQGH GH VXV SDUiPHWURV
I VLFRV TXH VH SXHGH PRGHODU HQ IXQFLyQ GH VXV
SDUiPHWURVI VLFRFRPR
S
[
S
[
Q
Q
I
GRQGH
S
HVHOYHFWRUGHSDUiPHWURVFRQVLJQLILFDGR
I VLFR HVODVDOLGDGHOVLVWHPD [QHVHOYHFWRUGH
HQWUDGDV 'LFKR VLVWHPD VH PRGHOD D WUDYpV GH XQ
PpWRGRGHLGHQWLILFDFLyQFRQ XQPRGHORERUURVRGH
ODIRUPD
¦
/
M
M
Q
7
M
M
I
Q
I
D
Z
[
D
S
[
GRQGH
I
S
HVHOYHFWRUFRQORVSDUiPHWURVGHOPRGHOR
ERUURVR(OREMHWRHVDQDOL]DUHOFRPSRUWDPLHQWRGH
ORV SDUiPHWURV GHO PRGHOR
I
S
HQ IXQFLyQ GHO
FRPSRUWDPLHQWRGHORVSDUiPHWURVGHOVLVWHPD
S
8QD IRUPD GH HYDOXDU HVWH FRPSRUWDPLHQWR HV
HYDOXDQGRODGHULYDGDGHORVSDUiPHWURVGHOPRGHOR
UHVSHFWR GH ORV SDUiPHWURV GHO VLVWHPD R VHD
HYDOXDQGR
S
S
w
w
I
'LFKR FRPSRUWDPLHQWR HV
DQDOL]DGR SDUD XQ PRGHOR ERUURVR REWHQLGR SRU
OLQHDOL]DFLyQHQORVFHQWURVGHORVFRQMXQWRVERUURVRV
GHODQWHFHGHQWHSURSRVLFLyQ
'HELGR D TXH VH FRQVLGHUD TXH HO FHQWUR GH ORV
FRQMXQWRV ERUURVRV GHO DQWHFHGHQWH
L
Y
HV ILMR ORV
SDUiPHWURVGHOFRQVHFXHQWHFRQVWLWX HQHOYHFWRUGH
SDUiPHWURVDDMXVWDU3RUORWDQWR
>
@
/
/
I
D
D
D
D
S
'HELGRDTXHHOPRGHORERUURVRVHVXSRQHTXHVHKD
REWHQLGR SRU OLQHDOL]DFLyQ HQ ORV FHQWURV VHJ~Q OD
SURSRVLFLyQUHVXOWD
O
Q
Q
Q
O
Y
[
[
S
[
D
w
w
O
Q
O
Q
Q
Q
7
O
Q
O
D
Y
[
Y
[
[
S
[
Y
S
[
w
w
/D GHULYDGD GH ORV SDUiPHWURV GHO PRGHOR
I
S
UHVSHFWRGHORVSDUiPHWURVGHOVLVWHPD
S
UHVXOWD
O
Q
Q
Q
O
Y
[
S
[
S
[
S
D
w
w
w
w
w
O
Q
O
Q
Q
Q
7
O
Q
O
D
Y
[
Y
[
S
[
S
[
Y
S
S
[
S
w
w
w
w
w
w
w
/DVHFXDFLRQHV PXHVWUDQFXDOHVHOHIHFWR
TXH VH SURGXFH HQ ORV SDUiPHWURV GHO FRQVHFXHQWH
FXDQGR H[LVWH XQ FDPELR HQ ORV SDUiPHWURV GHO
VLVWHPD 3DUD DFODUDU HVWH FRQFHSWR VH SUHVHQWD XQ
HMHPSORVHQFLOOR
(MHPSOR
(O VLJXLHQWH VLVWHPD SXHGH LOXVWUDU HO FRQFHSWR
DQWHULRU
'DGRXQVLVWHPDFRQXQDHQWUDGD XQDVDOLGDGHOD
IRUPD
[
[
N
[
[
N
N
[
S
GRQGH
[
HV OD HQWUDGD
HV OD VDOLGD
>
@
7
N
N
N
N
S
HVHOYHFWRUGHORVSDUiPHWURVGHO
VLVWHPD
(QHVWHHMHPSOR
N
[
[
N
[
[
w
w
S
3RUODHYDOXDFLyQUHVSHFWRGHOSDUiPHWUR
N
w
w
N
[
S
w
w
w
N
[
[
S
SRUODVXVWLWXFLyQGHHQ
N
D
O
w
w
N
D
O
w
w
6LVHHYDO~DFRQUHVSHFWRDOSDUiPHWUR
N
[
[
N
[
w
w
S
w
w
w
N
[
[
S
VXVWLWX HQGRHQ
N
D
O
w
w
[
Y
[
[
N
D
O
Y
[
O
O
w
w
(QIRUPDVLPLODUSDUD
N
[
[
N
[
w
w
S
[
[
N
[
[
w
w
w
S
VXVWLWX HQGRHQ
[
Y
[
[
N
D
O
Y
[
O
O
w
w
O
Y
[
O
Y
[
O
Y
[
[
[
Y
[
[
N
D
O
O
w
w
)LQDOPHQWHHYDOXDQGRSDUD
[
N
[
[
N
[
[
w
w
S
N
[
[
[
w
w
w
S
3RUODVXVWLWXFLyQGHHQ
N
N
[
D
O
Y
[
O
w
w
N
[
N
N
Y
N
[
[
N
[
D
O
O
Y
[
O
Y
[
O
w
w
3DUDDQDOL]DUORVUHVXOWDGRVGHHVWHHMHPSORVHKDFH
XQD DQDORJ D FRQ OD DSUR[LPDFLyQ ORFDO SRU XQ
SROLQRPLR GH 7D ORU GH VHJXQGR RUGHQ (VWD
DSUR[LPDFLyQVHREWLHQHFRPR
[
[
G[
[
G
[
[
G[
[
G
[
[
[
[
[
[
|
GRQGHGHVSXpVGHFRQWUDVWDUFRQVHSXHGHQ
FRQWUDVWDUORVSDUiPHWURV
[
N
[
[
G[
[
G
N
[
[
G[
[
G
N
$QDOL]DQGRHVWRVUHVXOWDGRVSDUDXQFRPSRUWDPLHQWR
ORFDOVHSXHGHLQIHULUORVLJXLHQWH
(O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
FDPELH HQ XQD FRQVWDQWH OD HFXDFLyQ GHO VLVWHPD
FDPELR GHO RIIVHW HQ HVWH FDVR
[
HV GHFLU
N
SURGXFLUiTXHORVSDUiPHWURVGHOPRGHOR
O
D
QR FDPELHQ ORV SDUiPHWURV
O
D
FDPELHQ HQ OD
PLVPDSURSRUFLyQTXHHOSDUiPHWURTXHFDPELRHQ
HO VLVWHPD (Q OD )LJ VH REVHUYD HO
FRPSRUWDPLHQWR GH OD IXQFLyQ GH ORV
SDUiPHWURV SDUD GLIHUHQWHV YDORUHV GH
N
(Q OD
SDUWH VXSHULRU L]TXLHUGD VH REVHUYD OD IXQFLyQ
O QHD GH SXQWRV VX DSUR[LPDFLyQ O QHD
FRQWLQXDSDUDGLVWLQWRVYDORUHVGH
N
(QODSDUWH
VXSHULRUGHUHFKDVHPXHVWUDQ ORV GLVWLQWRVYDORUHV
GHORVSDUiPHWURV(QSDUWHLQIHULRUVHREVHUYDORV
YDORUHV TXH WRPDQ ORV SDUiPHWURV
O
D
O
D
HQ
IXQFLyQGHORVYDORUHVGHORVFHQWURV
O
Y
SDUDORV
GLIHUHQWHVYDORUHVGH
N
(O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
PRGLILTXHODSHQGLHQWHGHODHFXDFLyQGHOVLVWHPD
FDPELR GH OD GHULYDGD SULPHUD
G[
[
G
HV GHFLU
N
SURGXFLUiTXHORVSDUiPHWURVGHOPRGHOR
O
D
FDPELHQHQODPLVPDSURSRUFLyQTXHHOSDUiPHWUR
TXHFDPELyHQHOVLVWHPD/RVSDUiPHWURV
O
D
VH
PRGLILFDQ HQ XQD IXQFLyQ FRQVWDQWH TXH GHSHQGH
GH
[
(Q OD )LJ VH REVHUYD OD LQIOXHQFLD GHO
FDPELRGH
N
HQHOYDORUHVGHORVSDUiPHWURV
O
D
O
D
(O FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
PRGLILFD OD FXUYDWXUD FRQFDYLGDG R FRQYH[LGDG
GHODHFXDFLyQGHOVLVWHPDFDPELRGHODGHULYDGD
VHJXQGD
G[
[
G
HV GHFLU
N
SURGXFLUi XQ
FDPELR HQ IRUPD OLQHDO HQ ORV SDUiPHWURV GHO
PRGHOR
O
D
UHVSHFWRD OD SRVLFLyQ GH ORV FHQWUR
O
Y
DO TXH FRUUHVSRQGH HO SDUiPHWUR /RV
FDPELRV HQ ORV SDUiPHWURV
O
D
VHUiQ IXQFLyQ
FXDGUiWLFDUHVSHFWRDODSRVLFLyQGHORVFHQWUR
O
Y
(QOD)LJVHREVHUYDODLQIOXHQFLDGHOFDPELRGH
N
HQORVYDORUHVGHORVSDUiPHWURV
O
D
O
D
8Q FDPELR HQ XQ SDUiPHWUR GHO VLVWHPD TXH
SURGX]FD XQ GHVSOD]DPLHQWR HQ
[
HV GHFLU XQ
FDPELRHQ
[
GHODHFXDFLyQGHOVLVWHPDSURGXFH
XQ FDPELR HQ ORV SDUiPHWURV
O
D
IXQFLyQ GH OD
FXUYDWXUD GH OD IXQFLyQ GH OD GHULYDGD VHJXQGD
G[
[
G
HVGHFLU
N
(OFDPELRHQORVSDUiPHWURV
O
D
VHUiIXQFLyQOLQHDOGHOFDPELRHQ
[
GHORV
SDUiPHWURV
N
FXUYDWXUD
N
SHQGLHQWH(QOD
)LJVHREVHUYDODLQIOXHQFLDGHOFDPELRGH
[
HQ
ORVYDORUHVGHORVSDUiPHWURV
O
D
O
D
&21&/86,21(6
(Q HVWH DUW FXOR VH DQDOL]DURQ GLVWLQWDV SURSLHGDGHV
GH XQ PRGHOR ERUURVR GHO WLSR 7DNDJL6XJHQR $
PRGR GH LQWURGXFFLyQ VH UHSDVDURQ SURSLHGDGHV
SUHYLDPHQWHHVWXGLDGDV(QWUHpVWDVVHUHVXPLHURQOD
]RQD GH YDOLGH] GHO PRGHOR OD FDSDFLGDG GH
OLQHDOL]DFLyQHQORVFHQWURVGHORVFRQMXQWRVERUURVRV
OD FDSDFLGDG GH DFRSODPLHQWR R IXVLyQ GH ORV
PRGHORVERUURVRV
$ FRQWLQXDFLyQ VH DQDOL]y HO FRPSRUWDPLHQWR GHO
PRGHORDQWHODSUHVHQFLDGHGDWRVQXHYRV FXDQWRVH
HVWiQ DMXVWDQGR ORV SDUiPHWURV HQ O QHD 6H
GLIHUHQFLDURQ ORV FRQFHSWRV GH DGDSWDFLyQ GH
SDUiPHWURV HO FXDO RFXUUH FRQ XQ FDPELR HQ ORV
SDUiPHWURV I VLFRV GHO VLVWHPD FRQ HO GH DMXVWH GH
SDUiPHWURVHOFXDORFXUUHSRUXQFDPELRHQOD]RQD
GHWUDEDMRGHOPRGHOR
[
&DPELRHQ
N
R
[
N
R[
N
N
[
Y
O
D
Y
O
D
)LJ&DPELRHQ
O
D
O
D
FRPRFRQVHFXHQFLDGH
XQFDPELRHQN
[
&DPELRHQ
N
R
[
N
N
R[
N
[
Y
O
D
Y
O
D
)LJ&DPELRVHQ
O
D
O
D
FRPRFRQVHFXHQFLDGH
XQFDPELRHQN
(QHVWHWUDEDMRWDPELpQ VHDQDOL]DFXDOHVHO HIHFWR
TXHVHSURGXFHHQORVSDUiPHWURVGHOPRGHORFXDQGR
VHSURGXFHXQFDPELRHQORVSDUiPHWURVGHOVLVWHPD
6HREVHUYDTXHGHELGRDODHVWUXFWXUDHOHJLGDHQHO
PRGHOR ERUURVR VH SXHGHQ GHWHUPLQDU SDUWH GHO
FRPSRUWDPLHQWR GH ORV SDUiPHWURV GHO VLVWHPD
REVHUYDQGRHOFRPSRUWDPLHQWRGHORVSDUiPHWURVGHO
PRGHOR
5()(5(1&,$6
>@ %H]GHN - & 3DWWHUQ 5HFRJQLWLRQ ZKLW
)X]] 2EMHFWLYH )XQFWLRQ $OJRULWKPV 6HFRQG
3ULQWLQJ3OHQXP3UHVV1HZ<RUN
>@ /DXNRQHQ ( DQG 3DVVLQR . 7UDLQLQJ
IX]] V VWHPV WR SHUIRUP HVWLPDWLRQ DQG
LGHQWLILFDWLRQ(QJ$SSOLF$UWLI,QWHOO9RO1R
SS
>@3HxD0&DUHOOL5DQGGL6FLDVFLR)D
6 VWHPV ,GHQWLILFDWLRQ XVLQJ D 7 SH RI 7DNDJL
6XJHQR )X]] 0RGHO 6,&,&$ %XHQRV
$LUHV$UJHQWLQD
>@3HxD0ÈOYDUH]+&DUHOOL5DQGGL6FLDVFLR
)E 9DOLGLW /LQHDUL]DWLRQ DQG&RXSOLQJ
3URSHUWLHV RI D 7DNDJL6XJHQR )X]] 0RGHO ,;
&RQJUHVR/DWLQRDPHULFDQRGH&RQWURO$XWRPiWLFR
&RORPELD
>@ 3HxD 0 &RQWURO %DVDGR HQ 0RGHORV
%RUURVR 7HVLV GH GRFWRUDGR ,QVWLWXWR GH
$XWRPiWLFD )DF GH ,QJHQLHU D 816- ,6%1
()86DQ-XDQ$UJHQWLQD
>@ 7DNDJL 7 DQG 6XJHQR 0 )X]]
,GHQWLILFDWLRQ RI V VWHPV DQG LWV DSSOLFDWLRQ WR
PRGHOLQJ DQ FRQWURO ,((( 7UDQVDFWLRQV RQ
6 VWHPV0DQDQG& EHUQHWLFV9RO1R3DJ
[
&DPELRHQ
N
R
[
N
N
N
R[
[
Y
O
D
Y
O
D
)LJ&DPELRHQ
O
D
O
D
FRPRFRQVHFXHQFLDGHO
FDPELRHQN
[
&DPELRHQ
[
R
[
N
N
N
[
R[
Y
O
D
Y
O
D
)LJ &DPELRV HQ
O
D
O
D
FRPR FRQVHFXHQFLD
GHOFDPELRHQ[