scieee Science in your language
[es] (orig)

Planificación conjunta de fabricación y distribución de productos con instantes fijos de entrega.

Abstract

En este artículo se presenta el problema asociado a la planificación conjunta de la fabricación y distribución de pedidos cuando ambos procesos se producen de forma continua sin esperas. Analizamos el caso en el que los pedidos poseen un instante

Read accessible full text

Planificación conjunta de fabricación y distribución de productos con instantes fijos de entrega.

Author: García Sánchez, José Manuel; Villa Caro, Gabriel
Year: 2001
Source: https://idus.us.es/bitstreams/87ff48ba-a420-4bbc-a0de-9483454b1e83/download
3/$1,),&$&,Ï1&21-817$'(/$)$%5,&$&,Ï1<
',675,%8&,Ï1'(352'8&726&21,167$17(6),-26'(
(175(*$
-0*DUF D6HEDVWLiQ/R]DQR)HUQDQGR*XHUUHUR*DEULHO9LOOD
MPJV#HVLXVHV
OR]DQR#FLFDHV
IHUJXH#HVLXVHV
JYLOOD#HVLXVHV
(VFXHOD6XSHULRUGH,QJHQLHURV8QLYHUVLGDGGH6HYLOOD
&DPLQRGHORV'HVFXEULPLHQWRVVQ6HYLOOD
5HVXPHQ
(QHVWHDUW FXORVHSUHVHQWDHOSUREOHPDDVRFLDGRDODSODQLILFDFLyQFRQMXQWDGHODIDEULFDFLyQ 
GLVWULEXFLyQ GH SHGLGRV FXDQGR DPERV SURFHVRV VH SURGXFHQ GH IRUPD FRQWLQXD VLQ HVSHUDV
$QDOL]DPRVHOFDVRHQHOTXHORVSHGLGRVSRVHHQXQLQVWDQWHILMRGHHQWUHJD VHFXHQWDFRQXQD
SODQWDSDUDODIDEULFDFLyQGHORVSHGLGRV(OSUREOHPDHVDQDOL]DGRHQGLIHUHQWHVHVFHQDULRVHQ
IXQFLyQ GH GHWHUPLQDGRV SDUiPHWURV 6H SURSRQHQ HVWUDWHJLDV GH UHVROXFLyQ EDVDGDV HQ OD
DSOLFDFLyQGHXQDOJRULWPRGHIOXMR H[SORUDFLyQGLULJLGD)LQDOPHQWHVHPXHVWUDXQDLOXVWUDFLyQ
GHORVPpWRGRVHQXQHMHPSOR
 ,QWURGXFFLyQ
/DORJ VWLFDDVRFLDGDDODGLVWULEXFLyQGHPHUFDQF DVVXHOHVHUDQDOL]DGDFRPRXQSURFHVR
LQGHSHQGLHQWHGHOSURFHVRGHIDEULFDFLyQGHOSURGXFWRTXHVHGLVWULEX H(OSUREOHPDVXHOH
DVRFLDUVHDOGLVHxRGHUXWDVSDUDYHK FXORVHQGRQGHVHGHWHUPLQDODUXWDTXHUHDOL]DFDGD
YHK FXORGHIRUPDTXHVHDWLHQGDQWRGDVODVSHWLFLRQHVWHQLHQGRHQFXHQWDSRUORJHQHUDO
WLHPSRVGHYLDMH UHVWULFFLRQHVGHFDSDFLGDGHQORVYHK FXORV
5HVSHFWR D OD SODQLILFDFLyQ GH OD IDEULFDFLyQ GH SURGXFWRV QRUPDOPHQWH HVWH SUREOHPD VH
HQFXDGUDHQHOFDPSRGHOD6HFXHQFLDFLyQGHWUDEDMRVGRQGHXQDVHULHGHWUDEDMRVWLHQHQTXH
VHUSURFHVDGRVKDFLHQGRXVRGHXQQ~PHUROLPLWDGRGHUHFXUVRVGLVSRQLEOHV
(Q HVWH DUW FXOR VH SUHVHQWD HO SUREOHPD DVRFLDGR FRQ OD SODQLILFDFLyQ FRQMXQWD GH OD
IDEULFDFLyQ GLVWULEXFLyQHQVLVWHPDVHQORVTXHHOVXPLQLVWURGHSURGXFWRVHVWiDFRSODGRFRQ
HOVLVWHPDSURGXFWLYRGHELGRDODDXVHQFLDGHLQYHQWDULRVGHOSURGXFWRILQDO'LFKRSUREOHPD
VXUJH FXDQGR HO SURGXFWR KD GH VHU IDEULFDGR VREUH SHGLGR  VHUYLGR LQPHGLDWDPHQWH
XVXDOPHQWH SRU VX FDUiFWHU SHUHFHGHUR (QHVWRVSUREOHPDVOD GLVWULEXFLyQHVWi OLJDGDD OD
IDEULFDFLyQ SRUWDQWRVXSHGLWDGDDODFDSDFLGDGGHOSURFHVRSURGXFWLYR
6H SRGU D DERUGDU HO HVWXGLR GH OD SODQLILFDFLyQ GH OD GLVWULEXFLyQ  OD IDEULFDFLyQ FRPR
FRQFHSWRVLQGHSHQGLHQWHVVLH[LVWLHUDQLQYHQWDULRVGHOSURGXFWRIDEULFDGR&XDQGRQRHVDV 
KD  TXH VHFXHQFLDU OD GLVWULEXFLyQ HQ IXQFLyQ GH OD FDSDFLGDG GH SURGXFFLyQ GH OD
GLVSRQLELOLGDGGHYHK FXORV GHORVGDWRVGHGHPDQGD
3DUDHOHVWXGLRGHOSUREOHPDQRVHQFXDGUDPRVHQXQDVLWXDFLyQWRWDOPHQWHGHWHUPLQLVWDFRQ
XQ FRQRFLPLHQWR FRPSOHWR GH ORV SHGLGRV TXH GHEHQ DWHQGHUVH HQ XQ KRUL]RQWH WHPSRUDO
GHWHUPLQDGR(ODQiOLVLVVHUHDOL]DFRQXQDVRODSODQWDGHIDEULFDFLyQGHVGHODTXHSDUWHQ 
GRQGHLQLFLDOPHQWHVHHQFXHQWUDQORVYHK FXORV/DIDEULFDFLyQGHXQSHGLGRVHOLPLWDDXQ
~QLFR SURFHVR TXH VH UHDOL]D VLQ LQWHUUXSFLRQHV QR SUHHPSWLRQ /D SODQWD GH IDEULFDFLyQ
PLGHVXFDSDFLGDGGHSURGXFFLyQHQQ~PHURGHSHGLGRVTXHSXHGHQVHUDWHQGLGRVDOPLVPR
WLHPSR&DGDSHGLGRXWLOL]DXQDXQLGDGGHFDSDFLGDGGXUDQWHHOWLHPSRGHIDEULFDFLyQSRUOR
TXHVXSRQLHQGR&XQLGDGHVGHFDSDFLGDGHQODSODQWDQRSXHGHQIDEULFDUVHPiVGH&SHGLGRV
DOPLVPRWLHPSR
/RV SHGLGRV VH DWLHQGHQ GH IRUPD LQGHSHQGLHQWH OR TXH VLJQLILFD TXH XQ SHGLGR HV
WUDQVSRUWDGRSRUXQVRORYHK FXORTXHUHJUHVDDODSODQWDXQDYH]VHUYLGRHOSHGLGR TXHGD
GLVSRQLEOHSDUDRWUDVHQWUHJDV(VWRLPSOLFDXQDQiOLVLVGLIHUHQWHGHOSUREOHPDFRQUHVSHFWRD
XQDSODQLILFDFLyQHQODTXHSXGLHUDQVHUYLUVHYDULRVSHGLGRVSRUXQVRORYHK FXORDVSHFWRTXH
FRQGXFLU D OD IDVH GH GLVWULEXFLyQ DO FOiVLFR SUREOHPD GH GLVHxR GH UXWDV SDUD YHK FXORV
YHKLFOHURXWLQJFRQUHVWULFFLRQHVGHFDSDFLGDG(OSUREOHPDVXSRQHODPLVPDFDSDFLGDGHQ
WRGRVORVYHK FXORV FRQVLGHUDTXHORVSHGLGRVSRVHHQXQDWDPDxRLQIHULRUDODFDSDFLGDGGH
ORVYHK FXORV
/RVGDWRVEiVLFRVGHXQSHGLGR3LVRQHOLQVWDQWHGHHQWUHJDVROLFLWDGRHLHOYDORUREHQHILFLR
REWHQLGRFRQODHQWUHJDGHOSHGLGRZLHOWLHPSRGHIDEULFDFLyQWIL HOWLHPSRGHGHVFDUJDGHO
SHGLGR WUL /D UXWD TXH UHDOL]D HO YHK FXOR HV FRQRFLGD GH DQWHPDQR FRQ VyOR FRQRFHU OD
ORFDOL]DFLyQGHOSHGLGR/RVGDWRVHQHOSUREOHPDTXHGHVFULEHQODUXWDGHOYHK FXORVRQHO
WLHPSRGHHQY RKDVWDODORFDOL]DFLyQGHOSHGLGR WLL  HOWLHPSRGHYXHOWDGHOYHK FXORDOD
SODQWDWYL/ODPDUHPRVWGLDOWLHPSRWRWDOGHODIDVHGHGLVWULEXFLyQWGL WLLWULWYL(QHO
WUDEDMRVHVXSRQHQWLHPSRVGLVFUHWRV
/DDFWLYLGDGDVRFLDGDDODIDEULFDFLyQ HQY RGHOSHGLGRFRUUHVSRQGHU DDODVLJXLHQWHILJXUD
'LVWULEXFLyQWGL
)DEULFDFLyQ
WIL
(QY R
WLL
'HVFDUJD
WUL
5HJUHVRGHOYHK FXOR
WYL
)LJXUD&URQRJUDPDGHODDFWLYLGDGGHXQSHGLGR
8QDVSHFWRDWHQHUHQFXHQWDHQHVWHSUREOHPDHVTXHFRQVLGHUDPRVTXHHOYHK FXORSDUWLFLSD
HQHOSURFHVRSURGXFWLYR (QGHWHUPLQDGDVDFWLYLGDGHVLQGXVWULDOHVHOYHK FXORIRUPDSDUWH
GHO SURFHVR GH IDEULFDFLyQ GHO SURGXFWR FRPR VRSRUWH GHO SURFHVR (VWR VH SURGXFH HQ
SURGXFWRVFRQXQDIDEULFDFLyQPX  VLPSOLILFDGDFDUDFWHUL]DGD~QLFDPHQWHSRUODPH]FODGH
GHWHUPLQDGRVFRPSXHVWRVTXHVHUHDOL]DGLUHFWDPHQWHHQHOGHSyVLWRGHFDUJDGHOYHK FXOR(O
HMHPSORPiVFODURVHSUHVHQWDHQODIDEULFDFLyQGHOKRUPLJyQ
3DUD HO DQiOLVLV VH FRQVLGHUD XQ Q~PHUR GH YHK FXORV LOLPLWDGR HV GHFLU VLHPSUH H[LVWHQ
YHK FXORVGLVSRQLEOHVHQOD SODQWD/RV REMHWLYRVEiVLFRVHQHOSUREOHPDVRQPD[LPL]DUHO
EHQHILFLR RYDORU REWHQLGR SRU ORV SHGLGRV VHUYLGRV  PD[LPL]DU HO Q~PHUR GH SHGLGRV
VHUYLGRV(VWHVHJXQGRREMHWLYRVHREWLHQHGHOSULPHURDVLJQDQGRHOPLVPRSHVRZLDWRGRV
ORV SHGLGRV $GHPiV HQ HVH FDVR VH DxDGH XQ VHJXQGR REMHWLYR VHFXQGDULR TXH VHU D
GHWHUPLQDU HO P QLPR Q~PHUR GH YHK FXORV QHFHVDULRV SDUD DWHQGHU HO Pi[LPRQ~PHURGH
SHGLGRVFDOFXODGR
(VFHQDULR0D[LPL]DUHOYDORUGHORVSHGLGRV
/DSODQLILFDFLyQFRQMXQWDGHODIDEULFDFLyQ GLVWULEXFLyQGHSHGLGRVFXDQGRVHGLVSRQHGHXQ
Q~PHURLOLPLWDGRGHYHK FXORVSDUDORVHQY RV HOREMHWLYRHVPD[LPL]DUHOEHQHILFLRGHODV
HQWUHJDVGHSHQGH~QLFDPHQWHGHODVHFXHQFLDFLyQGHORVSHGLGRVTXHVHUHDOLFHHQODSODQWD
$
)
-
%
*
'
,
&
(
+

























)LJXUD'LDJUDPDFURQROyJLFRGHXQDGHPDQGDGHSHGLGRV
WLHPSR
HL
/D SULPHUD FXHVWLyQ TXH GHEH SODQWHDUVH HV VL SXHGHQ DWHQGHUVH WRGRV ORV SHGLGRV /D
FDSDFLGDGGHIDEULFDFLyQHQSODQWD&HVHOSDUiPHWURTXHLQIOX HDODKRUDGHUHVSRQGHUDHVD
SUHJXQWD(QODILJXUDVHSODQWHDXQDVLWXDFLyQVREUHXQDGHPDQGDGHSHGLGRVH[SUHVDGD
PHGLDQWHXQGLDJUDPDWHPSRUDOTXHUHIOHMDORVLQVWDQWHVGHFRPLHQ]R HL_ORVWLHPSRVGH
IDEULFDFLyQWIL  GLVWULEXFLyQWGL_GHFDGDSHGLGR6XSXHVWDXQDFDSDFLGDGGHXQLGDG
QRSRGU DQIDEULFDUVHPiVGHSHGLGRDOPLVPRWLHPSRSRUORTXHORVSDUHVGHSHGLGRV$ %
DV FRPRHOSDU% & RWURVVHYHU DQDIHFWDGRV'HELGRDTXHQRVHSHUPLWHQLQWHUUXSFLRQHV
HQORVSURFHVRV DGHPiVHOSOD]RGHHQWUHJDHVILMRKDEU DTXHGHVFDUWDUODIDEULFDFLyQGH
DOJXQRGHHOORV
3DUD GHWHUPLQDU VL HV SRVLEOH SURFHVDU WRGRV ORV WUDEDMRV EDVWDU D FRQ FRPSUREDU VL OD
FDSDFLGDGGHIDEULFDFLyQ&HVPHQRUTXHHOPD RUJUDGRGHVLPXOWDQHLGDGGHORVSHGLGRVHQ
IiEULFD&XDQGRHOJUDGRGHVLPXOWDQHLGDGPH[FHGHGH&HOSUREOHPDWUDWDU DGHHQFRQWUDUHO
VXEFRQMXQWRGHWUDEDMRVFRQPi[LPRYDORUWRWDO(QFDPELRVLGLVSRQHPRVGHXQDFDSDFLGDG
& PWRGRVORVSHGLGRVSRGU DQVHU SURFHVDGRV
(OSUREOHPDGHGHWHUPLQDUTXHVXEFRQMXQWRGHSHGLGRVPD[LPL]DQHOYDORUWRWDOSXHGHVHU
HVWXGLDGR FRPR OD SODQLILFDFLyQ GH WUDEDMRV VREUH PiTXLQDV LGpQWLFDV HQ SDUDOHOR FRQ XQ
Q~PHURGHPiTXLQDVLJXDODODFDSDFLGDGGHODSODQWD/DIDVHGHGLVWULEXFLyQQRLQWHUYHQGU D
HQHODQiOLVLVSXHVVLHPSUHH[LVWHQYHK FXORVGLVSRQLEOHV(QFRQFUHWRODVLWXDFLyQSODQWHDGD
UHVSRQGH DO SUREOHPD GH OD 6HFXHQFLDFLyQ GH WUDEDMRV FRQ WLHPSRV ILMRV )L[HG -RE
6FKHGXOLQJ3UREOHP)63GHVFULWRHQ)LVFKHWWL>@
(QHOSUREOHPD)63VHGLVSRQHQGHQWUDEDMRVFRQWLHPSRGHLQLFLR WLHPSRGHSURFHVDGR
GDGRV 6H GHILQH SDUD XQ WUDEDMR L VLFRPR HO LQVWDQWH GH FRPLHQ]R ILHO LQVWDQWH GH
ILQDOL]DFLyQ GL VLILODGXUDFLyQGHOPLVPR &RQFDGDWUDEDMRVHDVRFLDXQYDORUZLTXH
H[SUHVDHOEHQHILFLRSRUODUHDOL]DFLyQGHOPLVPR/RVWUDEDMRVGHEHQVHUSURFHVDGRVVREUHXQ
FRQMXQWR ILQLWR GH PiTXLQDV SDUDOHODV 6H WUDWD GH HQFRQWUDU OD DVLJQDFLyQ GH WUDEDMRV D
PiTXLQDVGHIRUPDTXHVHPD[LPLFHHOYDORUGHORVWUDEDMRV SURFHVDGRVWHQLHQGRHQFXHQWD
TXHFDGDWUDEDMRVHSURFHVDGHIRUPDLQLQWHUUXPSLGDVREUHDOJXQDGHODVPiTXLQDVGHOVLVWHPD
FDGDPiTXLQDQRSXHGHSURFHVDUPiVGHXQWUDEDMRDOPLVPRWLHPSR(QQXHVWURFDVRFDGD
WUDEDMRFRUUHVSRQGHU DFRQFDGDXQDGHODV IDVHVGHIDEULFDFLyQGHORVSHGLGRV/DFDSDFLGDG
GHIDEULFDFLyQ&FRUUHVSRQGHU DFRQHOQ~PHURGHPiTXLQDV
 )RUPXODFLyQ
&XDQGRHOQ~PHURGHYHK FXORVHVLOLPLWDGRSRGHPRVDVXPLUXQQ~PHURPGHYHK FXORVFRQ
PLJXDODOPD RUJUDGRGHVLPXOWDQHLGDGGHOWLHPSRGHDFWLYLGDGGHORVSHGLGRV/LPLWDPRV
GHHVWDIRUPDHOQ~PHURGHYDULDEOHVGHOSUREOHPD PDQWHQHPRVHOKHFKRGHTXHVLHPSUH
H[LVWHQYHK FXORVGLVSRQLEOHVHQSODQWD
'HILQLPRVHOLQVWDQWHGHFRPLHQ]RGHOSURFHVRSURGXFWLYRFRPRVL HLWILWLL HOLQVWDQWHGH
FRPLHQ]RGHOHQY RFRPROL VLWIL(OYHK FXORGHEHHQFRQWUDUVHGLVSRQLEOHHQSODQWDHQHO
LQVWDQWHOL(OLQVWDQWHHQTXHILQDOL]DODDFWLYLGDGDVRFLDGDDXQSHGLGRVHGHILQHFRPRIL HL
WULWYL
(OPD RUJUDGRGHVLPXOWDQHLGDGYHQGU DGHILQLGRFRPRP Pi[LPR^PWWRdWd7`FRQ
PW ^LVLdWdIL`JUDGRGHVLPXOWDQHLGDGHQFDGDLQVWDQWHWWR 7VHU DQORVLQVWDQWHVHQWUHORV
FXDOHVVHDWLHQGHQWRGRVORVSHGLGRV
'HILQLPRVODVYDULDEOHV
VLHOYHK FXOR GLVWULEX HHOSHGLGR

VLQR
L
LM
M3
[LQMP

®
¯
!!
'HELGRDODSRVLELOLGDGGHTXHQR VHUHDOLFHQWRGRVORVSHGLGRVGHILQLPRVXQQXHYRFRQMXQWR
GHYDULDEOHVGHULYDGDVGHOFRQMXQWRGHYDULDEOHV[LM
6XSRQGUHPRVXQDRUGHQDFLyQGHORVQSHGLGRVVHJ~QVXWLHPSRGHFRPLHQ]RGHIDEULFDFLyQ
WDOTXHVdVd dVQ
3DUDFDGDXQRGHORVSHGLGRVGHILQLPRVXQFRQMXQWR6L ^NVLdVNdOL`6LTXHUHFRJHORV
SHGLGRVTXHVHSURFHVDQHQIiEULFDVLPXOWiQHDPHQWHDOSHGLGRLHQDOJ~QLQVWDQWHGHWLHPSR
'HQWURGHFDGDFRQMXQWRLQFOXLUHPRVDOSURSLRSHGLGR
(OPRGHORTXHGDU DFRPR
(Q VHDFWLYDQODVYDULDEOHVTXHUHFRJHQODUHDOL]DFLyQGHXQSHGLGR(QVHLPSRQHTXH
GRVSHGLGRVFX DDFWLYLGDGFRLQFLGHHQDOJ~QLQVWDQWHGHWLHPSRQRSXHGDQVHUGLVWULEXLGRV
SRUHOPLVPRYHK FXOR(QVHDVHJXUDTXHQRH[LVWHQPiVGH&SHGLGRVSURFHViQGRVHDO
PLVPRWLHPSR(OPRGHORPD[LPL]DHOYDORUWRWDOGHORVSHGLGRVVHUYLGRV
(VWUDWHJLDGH5HVROXFLyQ
$TX SURSRQHPRVXQDPRGLILFDFLyQHQHOPpWRGRSURSXHVWRSRU.URRQHWDO>@EDVDGRHQ
HOFiOFXORGHIOXMRP QLPRDXQJUDIR(OPpWRGRVHEDVDWDPELpQHQXQFiOFXORGHIOXMRGH
FRVWHP QLPRSHURHQHVWHFDVRVREUHXQJUDIR*1$TXHUHGXFHHOQ~PHURGHQRGRVDQ
3DUDFDGDSHGLGR3LVHFDOFXOD3RVWHULRULFRPRHOSULPHUSHGLGRFX RSURFHVRGHIDEULFDFLyQ
FRPLHQ]DGHVSXpVGH ILQDOL]DU HOSURFHVRGH IDEULFDFLyQGH3L6LPDQWHQHPRVORVSHGLGRV
RUGHQDGRVSRUWLHPSRGHFRPLHQ]RVL3RVWHULRUL ^3NN 0 QLPRVN OL`6HDxDGHXQ
SHGLGR ILFWLFLR 3Q TXH VHUi HO SRVWHULRU GH WRGRV ORV SHGLGRV TXH QR SRVHDQ SHGLGRV
SRVWHULRUHV
3RUFDGDSHGLGRDVRFLDPRVXQQRGRHQHOJUDIR1 ^QQ`FRQHOQRGRFRPRQRGR
IXHQWHGHOJUDIR3RUFDGDSHGLGR3LL QH[LVWHXQDUFRGHVGHHOQRGRLKDVWDHOQRGR
3RVWHULRULFRQXQDXQLGDGGHIOXMRGHFDSDFLGDG XQFRVWHLJXDODYL'HQRPLQDPRVHVWRV
DUFRVFRPRHOFRQMXQWR$3$GHPiVVHDxDGHXQDUFRGHFRVWHFHUR FDSDFLGDGLOLPLWDGD
GHVGHHOQRGRLDOQRGRLSDUDL QUHIHUHQFLDGRVFRPRHOFRQMXQWR$0(OIOXMRGH
HQWUDGDHQHOJUDIRHV&ODFDSDFLGDGGHIDEULFDFLyQHQSODQWD
^
`

P
M

VXMHWRD

   

^` ^`
Q
LL
L
LM L
LMNM N L
N
N6L
LM M
0D[ Y S
[SL Q
[[LQMPNLVI
S&L Q
[S

d  ! 
d

¦
¦
¦
!
!!
!
¯
®

QR
VL

UHDOL]DGR
HV
3
SHGLGR
HO
VL

L
L
S
(OJUDIRSDUDHOHMHPSORGHODILJXUDTXHGDU DFRPRVLJXH
$Y
$

%Y
%

&Y
&

'Y
'

)Y
)

(Y
'

0
0
0
0
0
*Y
*

+Y
+

,Y
,

0
0
0
0
>
F@
>F@
3HGLGR&RVWH
&DSDFLGDG
0
-Y
-

)LJXUD(MHPSORGHJUDIR*1$0  
(VSRVLEOHUHGXFLUHOWDPDxRGHOJUDIR*DSDUWLUGHODDSOLFDFLyQGHODOJRULWPRGHVFULWRHQ
.URRQHWDO
(QODILJXUDVHSUHVHQWDHOJUDIRUHGXFLGRVREUHHOJUDIRGHODILJXUD
$
%
&
'
)
(
*
+
,
-
)LJXUD*UDIRUHGXFLGRGH)LJXUD
(OySWLPRFRUUHVSRQGHU DFRQ
3
L
L
S 3L3L $L3L UXWDGHF
RVWHP QLPR

¦
(VFHQDULR0LQLPL]DUHOQ~PHURGHYHK FXORVSDUDHOQ~PHURPi[LPRGHSHGLGRV
(QHVWHHVFHQDULRVHEXVFDPD[LPL]DUHOQ~PHURGHSHGLGRVVHUYLGRVDxDGLHQGRDGHPiVXQ
VHJXQGR REMHWLYR TXH PLQLPL]D HO Q~PHUR GH YHK FXORV QHFHVDULRV /D SDUWLFXODULGDG GH
HVWDEOHFHU XQ GREOH FULWHULR  HQ HVWH HVFHQDULR UDGLFD HQ OD SRVLELOLGDG GH TXH H[LVWDQ
VROXFLRQHVDOWHUQDWLYDVDOLPSRQHUHOFULWHULRGHPD[LPL]DUHOQ~PHURGHSHGLGRV3RUHOOR
GLYLGLPRV HO DQiOLVLV HQ GRV IDVHV (Q OD SULPHUD IDVH VH FDOFXOD HO Q~PHUR  Pi[LPR GH
SHGLGRVTXHSXHGHQVHUDWHQGLGRV HQODVHJXQGDVHEXVFDPLQLPL]DUHOQ~PHURGHYHK FXORV
QHFHVDULRVSDUDDWHQGHUHOQ~PHURGHSHGLGRVFDOFXODGRHQODSULPHUD
)DVH,0D[LPL]DUHOQ~PHURGHSHGLGRV
/DSULPHUD IDVH FRUUHVSRQGHFRQ HO(VFHQDULRGHO SUREOHPDFXDQGRHOYDORU ZLGHFDGD
SHGLGRHV LJXDOD3RUHOORODUHVROXFLyQGHHVWDIDVHFRQVLVWHHQHPSOHDUODPLVPDHVWUDWHJLD
GHVFULWDHQHOSXQWR%DVWDU DFRQPRGLILFDUORVSHVRVGHORVDUFRVDVLJQDQGRDFDGDDUFR
L3L$3XQFRVWHGH'HQRWDUHPRVSRUS HOQ~PHURPi[LPRGHSHGLGRVFDOFXODGR
)DVH,,0LQLPL]DUHOQ~PHURGHYHK FXORV
3DUD OD IRUPXODFLyQ GH OD IDVH ,, DxDGLPRV YDULDEOHV MTXH UHFRJHQ OD XWLOL]DFLyQ GH ORV
YHK FXORV M [LM LM FRQM PPLJXDODOPD RUJUDGRGHVLPXOWDQHLGDG(OUHVWRGH
UHVWULFFLRQHVQR YDU D&RQYHUWLPRVODIXQFLyQREMHWLYRGHODIDVHHQXQDUHVWULFFLyQPiVGHO
SUREOHPDDVLJQDQGRYL L/DIXQFLyQREMHWLYRSDVDDVHUDKRUDODPLQLPL]DFLyQGHOD
VXPDGHYDULDEOHVTXHUHSUHVHQWDQHOXVRGHORVYHK FXORV

&iOFXORGHOQ~PHURP QLPRGHYHK FXORV
3DUDODUHVROXFLyQGHODIDVH,,DSOLFDPRVXQPpWRGRGHH[SORUDFLyQGLULJLGDGHVROXFLRQHV
DGPLVLEOHV IRUPDGDV SRU S SHGLGRV /D REWHQFLyQ GHO Q~PHUR GH YHK FXORV SDUD HVDV
VROXFLRQHV VH REWLHQH FRQ XQ DOJRULWPR GH DVLJQDFLyQ GH YHK FXORV EDVDGR HQ XQ VHQFLOOR
SURFHGLPLHQWR GH DVLJQDFLyQ GH PiTXLQDV D WUDEDMRV )LVFKHWWL  (O DOJRULWPR GH
FDUiFWHUDYDULFLRVRREWLHQHHOP QLPRQ~PHURGHYHK FXORVQHFHVDULRVSDUDVHUYLUHOFRQMXQWR
GHSHGLGRVVHOHFFLRQDGRV/DHVWUDWHJLDFRQVLVWHHQH[SORUDUSULPHURORVYHK FXORVTXH DKDQ
UHDOL]DGR DOJ~Q VHUYLFLR 8QD YH] RUGHQDGRV ORV SHGLGRV SHUWHQHFLHQWHV D 3,SHGLGRV
VHOHFFLRQDGRV SRU HO WLHPSR GH LQLFLR GH DFWLYLGDG VL YDQ VLHQGR DVLJQDGRV GH IRUPD
RUGHQDGD DO SULPHU YHK FXOR OLEUH GH ORV TXH D UHDOL]DURQ DOJ~Q WUDEDMR 6L WRGRV HVWRV
YHK FXORVHVWXYLHUDQRFXSDGRVVHDFWLYDU DXQRQXHYR
(OPpWRGRGHH[SORUDFLyQSODQWHDXQiUEROTXHSDUWHFRPRVROXFLyQLQLFLDOGHOFRQMXQWRGH
SHGLGRV3,XQWRWDOGHSREWHQLGRVHQODIDVH ,(OQ~PHURGHYHK FXORVQHFHVDULRVSDUD
GLVWULEXLUHVRVS SHGLGRVORGHQRWDPRVSRU9TXHHQSULQFLSLRVHFRUUHVSRQGHFRQODPHMRU
VROXFLyQHQFRQWUDGDTXHGHQRWDPRVSRU9'LVWLQJXLPRVSRU3)HOFRQMXQWRGHSHGLGRVQR
VHOHFFLRQDGRVHQODIDVH,IRUPDGRSRUQS SHGLGRV
/DH[SORUDFLyQHQHOiUEROFRQVLVWHHQODIRUPDFLyQGHVROXFLRQHVTXHUHFRJDQODUHDOL]DFLyQ
GHSHGLGRV SHUWHQHFLHQWHVD 3)(QFDGDQLYHOGHOiUEROVHHVWDEOHFHODLQWURGXFFLyQGHXQ
SHGLGR3M3)(QFDGDQRGRGHOiUEROVHGLVWLQJXH XQFRQMXQWR.TXHUHFRJHORVSHGLGRVGH
3)TXHSHUWHQHFHQDODVROXFLyQGHHVHQRGR. ^3M3M3)SM `
/ODPDPRV/3. DOPRGHORSDUDHOFiOFXORGHOQ~PHURP QLPRGHYHK FXORVHQFDGDQRGR/D
VROXFLyQySWLPDGH/3.FRUUHVSRQGHU DFRQ9/3.
/3.
^
`
`



^
`



^
`



^














[
D
VXMHWR



P

M
LM




d

!

d

d
¦
¦
¦
¦

M
L
LM
L
6
N
N
M
N
NM
LM
Q
L
L
L
LM
M
P
M
M
S
[
Q
L
&
S
I
V
L
N
P
M
Q
L
[
[
S
S
Q
L
S
[
P
M
Q
L
0LQ
!
!
!
!
!
!
^
`
^
`
^
`
^
`

LM
P
M

VXMHWRD
[


  

  
,
P
M
M
M
L
LM
N
N3
LM NM N M
N
N6L
LM M N
0LQ
L QM P
SL.
[
L.
SS .
[[ L Q M PNLV I
S&L Q
[ S N.


d


®

¯

d  ! 
d

¦
¦
¦
¦
!!
!!
!
/D UHVROXFLyQ GHO PRGHOR /3.VH UHDOL]D HQ GRV HWDSDV (Q OD SULPHUD VH HYDO~D OD
DGPLVLELOLGDG GHO PRGHOR HV GHFLU VH HYDO~D VL HV SRVLEOH HQFRQWUDU S_._ SHGLGRV TXH
VDWLVIDJDQODVUHVWULFFLRQHVGHOSUREOHPD(QFDVRDILUPDWLYRHQXQDVHJXQGDHWDSDVHFDOFXOD
HO Q~PHUR GH YHK FXORV 9/3. D SDUWLU GHO SURFHGLPLHQWR DYDULFLRVR GHVFULWR FRQ
DQWHULRULGDG6L9/3.9DFWXDOL]DPRV9FRQ9/3.
3DUDGHWHUPLQDUHQODHWDSDODDGPLVLELOLGDGGHODVROXFLyQVHSODQWHDHOJUDIR*.1$.GH
OD IDVH , DVLJQDQGR D ORV DUFRV TXH UHSUHVHQWDQ ORV SHGLGRV SHUWHQHFLHQWHV DO FRQMXQWR .
M3M$3FRQ3M. XQGpILFLWGHFDSDFLGDGLJXDODHQHOQRGRRULJHQ XQGpILFLWLJXDOD
HQHOQRGRGHVWLQR&RQHOORLPSRQHPRVODUHDOL]DFLyQGHHVHSHGLGR DTXHXQDXQLGDGGH
FDSDFLGDG HV HPSOHDGD SDUD VX IDEULFDFLyQ $GHPiV VH DVLJQD XQ FRVWH GH ±0  0 OR
VXILFLHQWHPHQWHJUDQGHDDTXHOORVDUFRVTXHIRUPDEDQSDUWHGHODVROXFLyQLQLFLDOGHOiUERO
L3L FRQ L3, &RQ HOOR VH JDUDQWL]D TXH HOUHVWR GH SHGLGRV VHOHFFLRQDGRV SDUD VHU
UHDOL]DGRVHQHVHQRGRVHDQ SHGLGRVSHUWHQHFLHQWHVDODVROXFLyQLQLFLDO3,SL o3L3,
3U
3L0
3V0
3M
>F@
>@
>@
>
F@
)LJXUD*UDIR*.
(QODILJXUD3L3V3,3M.(OSHGLGR3U. 3U3,(QFDVRGHREWHQHUFRPRVROXFLyQ
ySWLPDHQHOFiOFXORGHIOXMRD*.XQQ~PHURGHSHGLGRV_3,/3._LJXDODS_._IRUPDQGR
SDUWH GHOD UXWD GH FRVWH P QLPR OD VROXFLyQSURSRUFLRQDGDHV DGPLVLEOH(QFDVRGHTXH
_3,/3._S _._ODVROXFLyQHVLQDGPLVLEOH D TXH_3,/3.__._S(OiUEROVHSRGDUi
HQDTXHOORVQRGRVQRDGPLVLEOHV$GHPiVVLJQLILFDUiTXHORVSHGLGRV3M.GHHVHQRGRQR
SRGUiQIRUPDUSDUWHFRQMXQWDPHQWHGHXQDVROXFLyQDGPLVLEOHTXHVLUYDS SHGLGRV
,OXVWUDFLyQ
3DUDHOHMHPSORGHODILJXUDLOXVWUDPRVORVPpWRGRVSURSXHVWRVHQORVGRVHVFHQDULRVGHO
SUREOHPD6XSRQHPRVXQDFDSDFLGDGGHIDEULFDFLyQGH& 
(VFHQDULR
3HGLGRV
$
%
&
'
(
)
*
+
,
-
ZL










7DEOD9DORUHVGHORVSHGLGRV
$

%

&

'

)

(

0
0
0
0
0
*

+

,

0
0
0
0
>@
>@
-

0
5XWDFRVWHP QLPR
)LJXUD)OXMRDFRVWHP QLPRSDUDHOHVFHQDULR,
/RVSHGLGRVTXHIRUPDQSDUWHGHODUXWDGHFRVWHP QLPRKDFHQPi[LPRHOEHQHILFLRFRQXQ
YDORUWRWDOGHXQLGDGHV
(VFHQDULR
(Q OD IDVH , VH REWLHQH HO Q~PHUR Pi[LPR GH SHGLGRV 3DUD HOOR VH KDOOD HO IOXMR D FRVWH
P QLPRFRPRVHPXHVWUDHQODILJXUD
$

%

&

'

)

(

0
0
0
0
0
*

+

,

0
0
0
0


-

0
)LJXUD)OXMRDFRVWHP QLPRSDUDODIDVH,
6HJ~QODILJXUDODUXWDP QLPDHVWiIRUPDGDSRUS SHGLGRVGRQGH3, ^$&')*
+-`3RUWDQWR3) ^%(,`
3DUDODREWHQFLyQGHOQ~PHURP QLPRGHYHK FXORVDSOLFDPRVHOSURFHGLPLHQWRGHDVLJQDFLyQ
9HK FXOR
$
'
+
9HK FXOR
&
)
-
9HK FXOR
*
)LJXUD$VLJQDFLyQGH9HK FXORVDSHGLGRV
6HQHFHVLWDQXQWRWDOGHYHK FXORVHQODVROXFLyQySWLPDGHODIDVH,(OiUEROGHH[SORUDFLyQ
GHODIDVH,,VHU D
)LJXUDÈUEROGHH[SORUDFLyQGLULJLGD
9HDPRVHOFiOFXORHQGRVGHORVQRGRV. ^%` . ^(`
$
0
%

&0

'0

)0

(

0
0
0
0
0
*0

+0

,

0
0
0
0


-0

0


_3,3/.__._ So6ROXFLyQQRDGPLVLEOH
)LJXUD)OXMRDFRVWHP QLPRGHOQRGR. ^%`
$
0
%

&0

'0

)0

(

0
0
0
0
0
*0

+0

,

0
0
0
0


-0

0


_3,3/.__._  So6ROXFLyQ$GPLVLEOHo3URFHGLPLHQWR$VLJQDFLyQ9HK FXORV
9HK FXOR
$
'
+
9HK FXOR
&
(
*
-
Y3/. 9o9 
)LJXUD)OXMRDFRVWHP QLPRGHOQRGR. ^(`
. ^
`
S 
9 9 
. ^,`
_3,3/._  S
,QDGPLVLEOH
. ^(,`
,QDGPLVLEOH
. ^%`
_3,3/._ S
,QDGPLVLEOH
. ^(`
_3,3/._  S
93/. 
9 
5HIHUHQFLDV
>@ )LVFKHWWL00DUWHOOR67RWK3 ³$SSUR[LPDWLRQDOJRULWKPVIRUIL[HGMREVFKHGXOHSUREOHPV´
2SHUDWLRQV5HVHDUFKSS66
>@ .ROHQ :- .URRQ /*  ³2Q WKH FRPSXWDWLRQDO FRPSOH[LW  RI PD[LPXP FODVV VFKHGXOLQJ´
(XURSHDQ-RXUQDORI2SHUDWLRQV5HVHDUFKSS
>@.URRQ/* 6DORPRQ09DQ:DVVHQKRYH/1³([DFWDQGDSSUR[LPDWLRQDOJRULWKPVIRUWKH
RSHUDWLRQDOIL[HGLQWHUYDOVFKHGXOLQJSUREOHP´(XURSHDQ-RXUQDORI 2SHUDWLRQDO5HVHDUFKSS
