scieee Open visual document viewer

Planificación conjunta de la fabricación y distribución de productos con ventanas temporales en las entregas.

García Sánchez, José Manuel; Calle Suárez, Marcos

Abstract

En este artículo estudiamos el problema asociado con la planificación conjunta de la fabricación y distribución de productos con ventanas temporales en las entregas de los pedidos. Para la fabricación de pedidos se cuenta con una planta desde la que s

Full text

3/$1,),&$&,Ï1&21-817$'(/$)$%5,&$&,Ï1< ',675,%8&,Ï1'(352'8&726&219(17$1$67(0325$/(6 (1/$6(175(*$6 -0*DUF D6/R]DQR'3pUH]0&DOOH MPJV#HVLXVHV VOR]DQR#FLFDHV GSHUH]#VDGLHOHV PDUFRVFDOOHVXDUH]#ZDQDGRRHV (VFXHOD6XSHULRUGH,QJHQLHURV8QLYHUVLGDGGH6HYLOOD &DPLQR GHORV'HVFXEULPLHQWRVVQ6HYLOOD 5HVXPHQ (QHVWHDUW FXORHVWXGLDPRVHOSUREOHPDDVRFLDGRFRQODSODQLILFDFLyQFRQMXQWDGHODIDEULFDFLyQ  GLVWULEXFLyQ GH SURGXFWRV FRQ YHQWDQDV WHPSRUDOHV HQ ODV HQWUHJDV GH ORV SHGLGRV 3DUD OD IDEULFDFLyQGHSHGLGRVVHFXHQWDFRQXQDSODQWDGHVGHODTXHVHVLUYHQORVSHGLGRVFRQD XGDGH XQDIORWDGHYHK FXORVGHLGpQWLFDVFDUDFWHU VWLFDV(OREMHWLYREiVLFRHVHQFRQWUDUODDVLJQDFLyQ GHYHK FXORVDSHGLGRVTXHPD[LPLFHHOYDORUGHORVSHGLGRVVHUYLGRV(OSUREOHPDVHUHVXHOYHD WUDYpV GH XQ DOJRULWPR GH IOXMR HQ XQ JUDIR FRQVWUXLGR PHGLDQWH WpFQLFDV GH SURJUDPDFLyQ GLQiPLFD 3DODEUDVFODYH)DEULFDFLyQGLVWULEXFLyQYHQWDQDWHPSRUDOSURJUDPDFLyQGLQiPLFD ,QWURGXFFLyQ 'HWHUPLQDGRVSURGXFWRVQRSXHGHQVHUIDEULFDGRVFRQPXFKDDQWHODFLyQDOPRPHQWRH[DFWR GHVHUVHUYLGRVGHELGRIXQGDPHQWDOPHQWHDVXFDUiFWHUSHUHFHGHUR/DIDEULFDFLyQGHHVWRV SURGXFWRVVXHOHVHUSRUHOORXQSURFHVREDVWDQWHEiVLFRTXHDSDUHFHDFRSODGRDODGLVWULEXFLyQ SRVWHULRUGHOSURGXFWR(QRFDVLRQHVLQFOXVRHOYHK FXORHQFDUJDGRGHVHUYLUHOSHGLGRIRUPD SDUWHGHOSURFHVRSURGXFWLYR8Q ILHOUHIOHMRGHHVWHSUREOHPDVHSUHVHQWDHQHOVHFWRUGHOD FRQVWUXFFLyQFRQFUHWDPHQWHHQODIDEULFDFLyQ GLVWULEXFLyQGHOKRUPLJyQ /DIDEULFDFLyQGHOKRUPLJyQVHFRPSRQHGHODPH]FODGHGHWHUPLQDGRVPDWHULDOHVFHPHQWR DJXDDGLWLYRV HQODTXHVHGLVSRQHGHXQWLHPSROLPLWDGRGHVGHTXHVHUHDOL]DODPH]FOD HQODSODQWDKDVWDTXHVHGHVFDUJDHOKRUPLJyQHQODREUD'HELGRDHOORODIDEULFDFLyQGHOD PH]FOD  VX SRVWHULRU GLVWULEXFLyQ D OD REUD VRQ SURFHVRV VHFXHQFLDOHV TXH QR DGPLWHQ GHPRUD (O VRSRUWH HQ OD UHDOL]DFLyQ GH OD PH]FOD VRQ GLUHFWDPHQWH ORV YHK FXORV TXH GLVWULEX HQ HO KRUPLJyQ D ODV GLIHUHQWHV REUDV HV GHFLU HO SURFHVR GH IDEULFDFLyQ GHO KRUPLJyQ  OD FDUJD GHO PLVPR HQ HO YHK FXOR TXH OR GLVWULEX H VH FRQVLGHUD XQ PLVPR SURFHVR/RV SHGLGRVGHEHQDWHQGHUVHFRQFHOHULGDGORTXHVLJQLILFDTXHSRUORJHQHUDOHQ FDGDHQY RVHDWLHQGHXQVRORSHGLGR $WHQGLHQGR D OD ORJ VWLFD UHIOHMDGD HQ OD GLVWULEXFLyQ GHO KRUPLJyQ HQ HVWH DUW FXOR HVWXGLDPRV OD SODQLILFDFLyQ FRQMXQWD SDUD OD IDEULFDFLyQ  GLVWULEXFLyQ VREUH SHGLGR HQ VLVWHPDVHQORVTXHHOVXPLQLVWURGHSURGXFWRVHVWiDFRSODGRDOSURFHVRSURGXFWLYR 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HQFXHQWUDODIORWDGHYHK FXORVIRUPDGDSRU 9YHK FXORVGHLGpQWLFDV FDUDFWHU VWLFDV/DIDEULFDFLyQGHORVSHGLGRVVHOLPLWDDXQ~QLFRSURFHVRTXHVHUHDOL]DVLQ LQWHUUXSFLRQHV /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FDGD XQR GHHOORVHV WUDQVSRUWDGRSRUXQVRORYHK FXORTXHUHJUHVDDODSODQWDXQDYH]VHUYLGRHOSHGLGR TXHGD GLVSRQLEOH SDUD RWUDV HQWUHJDV 6H FRQVLGHUD TXH HO WDPDxR GH ORV SHGLGRV HV LQIHULRU D OD FDSDFLGDG GH ORV YHK FXORV 3DUD FDGD SHGLGR 3LGHILQLPRV HLFRPR HO LQVWDQWH GH HQWUHJD VROLFLWDGR ZLFRPRHOYDORUREHQHILFLRREWHQLGRFRQODHQWUHJDGHOPLVPRHQHOLQVWDQWH HL 3DUD FDGD SHGLGR H[LVWH XQD YHQWDQD WHPSRUDO >DL EL@ FRQ  DLdHLdELGHQWUR GH OD TXH VH FRQVLGHUD DGPLVLEOH OD HQWUHJD GHO SHGLGR (O YDORU GHOSHGLGR VH YH PRGLILFDGR FXDQGR HO LQVWDQWHGHHQWUHJDVHGHVY DUHVSHFWRDOLQVWDQWHGHHQWUHJDVROLFLWDGR VHGHILQHSDUDHOOR XQ FRVWHXQLWDULRGHSHQDOL]DFLyQSRUH[FHVR RWURSRUGHIHFWRTXHUHGXFHQHOYDORUGHOSHGLGR TXHGDQGRpVWHILQDOPHQWHGHILQLGRGHODVLJXLHQWHIRUPD > @        LLLLLL R LLLL LLLLLL ZHROHR 9DORU GHO SHGLGR Z R D E L Q ZRHOHR     ° {  ®   ° ¯ ! RL LQVWDQWHGHHQWUHJDGHOSHGLGROL FRVWHGHSHQDOL]DFLyQSRUGHIHFWRVREUHHOLQVWDQWHGH HQWUHJDVROLFLWDGROL FRVWHGHSHQDOL]DFLyQSRUH[FHVR 5HVSHFWRDORVWLHPSRVDVRFLDGRVFRQODDFWLYLGDGGHOSHGLGRGHILQLPRVWILFRPRHOWLHPSRGH IDEULFDFLyQ WULFRPRHOWLHPSRGHGHVFDUJDGHOSHGLGR/DUXWDTXHUHDOL]DHOYHK FXORKDVWD ODORFDOL]DFLyQGHOSHGLGROOHYDDVRFLDGRXQWLHPSRGHHQY R WLL XQWLHPSRGHUHJUHVRDOD SODQWDWYL(OWLHPSRWRWDOGHODIDVHGHGLVWULEXFLyQYHQGUiGHILQLGGRSRUWDQWRFRPRWGL WLL  WUL WYL 'HULYDGRV GH ORV DQWHULRUHV VH GHILQHQ  DL  DLWLLWILFRPR HO WLHPSR PiV WHPSUDQRGHFRPLHQ]RGHOSURFHVRGHIDEULFDFLyQGHOSHGLGREL ELWLLWILFRPRHOWLHPSR PiVWDUGHGHFRPLHQ]RGHOSURFHVRGHIDEULFDFLyQHL HLWLLWIL FRPRHOWLHPSRVROLFLWDGR GHFRPLHQ]RGHODIDEULFDFLyQGHOSHGLGR IL E¶LWILWGLFRPRHOSHULRGRPiVWDUGHHQ HOTXHSXHGHHVWDUUHDOL]iQGRVHODDFWLYLGDGGHOSHGLGR D¶ L H¶ L E¶ L DL HL EL WIL WLL WUL WYL IL )LJXUD(VTXHPDGHODDFWLYLGDGDVRFLDGDDXQSHGLGR /RV REMHWLYRV TXH VH SHUVLJXHQ HQ SUREOHPDV GH SODQLILFDFLyQ TXH PDQHMDQ YHQWDMDV WHPSRUDOHVVRQQXPHURVRV(OREMHWLYREiVLFRHQHOSUREOHPDHVODPD[LPL]DFLyQGHOYDORUGH ORVSHGLGRVVHUYLGRVDXQTXHGDUHPRVFDELGDWDPELpQDREMHWLYRVSDUHFLGRVFRPRSXHGHQVHU ODPD[LPL]DFLyQGHOQ~PHURGHSHGLGRVVHUYLGRVRODPD[LPL]DFLyQGHOQ~PHURGHSHGLGRV VHUYLGRV HQ VX LQVWDQWH GH HQWUHJD VROLFLWDGR 6H SXHGHQ SODQWHD LQFOXVR XQ REMHWLYR VHFXQGDULR TXH EXVFD PLQLPL]DU HO Q~PHUR GH YHK FXORV QHFHVDULRV SDUD VDWLVIDFHU XQ FRQMXQWRGHSHGLGRVTXHRSWLPLFHDOJXQRVGHORVREMHWLYRVDQWHULRUHV 3UREOHPDVUHODFLRQDGRV (O SUREOHPD GHVFULWR SXHGH VHU DVRFLDGR D SUREOHPDV GH VHFXHQFLDFLyQ HQ WDOOHUHVGH IOXMR IOH[LEOH)OH[LEOH)ORZVKRS))6(VWRVSUREOHPDVH[LVWHQWHVHQFLHUWDFODVHGHVLVWHPDVGH IDEULFDFLyQVHFDUDFWHUL]DQSRUP~OWLSOHVFHQWURVGHPiTXLQDVFRQYDULDVPiTXLQDVLGpQWLFDV HQFDGDXQRGHHOORV&DGD WHPGHOVLVWHPDWLHQHTXHVHUSURFHVDGRVREUHXQDPiTXLQDHQ FDGD XQR GH ORV FHQWURV (O SUREOHPD SRVHH GLYHUVDV YHUVLRQHV  REMHWLYRV HQWUH ORV TXH GHVWDFDQODPLQLPL]DFLyQGHOWLHPSRILQDOGHSURFHVRPDNHVSDQ WRGRVORTXHFRQFLHUQHQD ODPLQLPL]DFLyQGHUHWUDVRVHQORVWUDEDMRV/DYHUVLyQGHHVWHSUREOHPDTXHPiVVHDMXVWDDO SUREOHPD GH OD IDEULFDFLyQ  GLVWULEXFLyQ FRQMXQWD  HV DTXpOOD HQ OD TXH QR VH SHUPLWHQ HVSHUDVHQHOSURFHVDPLHQWRGHFDGD WHPVREUHORVGLVWLQWRVFHQWURVQRZDLW5DPXGKLQ  5DWOLIIHVWXGLDQHVWHSUREOHPDHQSDUWLFXODU&RQVLGHUDQHOSUREOHPDGHPD[LPL]DUOD VXPDGHSHVRVGHSHGLGRVTXHSXHGHQVHUFRPSOHWDGRVHQXQSHULRGRGHWHUPLQDGRGHWLHPSR SDUDXQWDOOHUFRQFHQWURVGHPiTXLQDV /D VLPLOLWXG HQWUH HVWRV GRV SUREOHPDV VH DOFDQ]D DVRFLDQGR OD IDVH GH IDEULFDFLyQ FRQ XQ SULPHUFHQWURGHPiTXLQDVIRUPDGRSRU&LQVWDQFLDVGRQGH&HVODFDSDFLGDGGHIDEULFDFLyQ GHODSODQWD/DIDVHGHGLVWULEXFLyQVHFRQVLGHUDU DFRPRXQVHJXQGRFHQWURFRQXQQ~PHUR GH PiTXLQDV LJXDO DO Q~PHUR GH YHK FXORV 9 3RU WDQWR OD UHDOL]DFLyQ GH XQ SHGLGR FRQOOHYDU DHQSULPHUOXJDUXQWLHPSRGHSURFHVRWILHQXQDGHODVPiTXLQDVGHOSULPHUWLSR  XQ WLHPSR WGLHQ XQD GH ODV PiTXLQDV GHO VHJXQGR WLSR  $GHPiV FRPR VH FRPHQWy HQ OD LQWURGXFFLyQORVSURFHVRVGHIDEULFDFLyQ  GLVWULEXFLyQVRQFRQWLQXRVHVGHFLUQRDGPLWHQ HVSHUDV /D GLIHUHQFLD IXQGDPHQWDO UDGLFD HQ OD H[LVWHQFLD GH XQD YHQWDQD WHPSRUDOTXH QR SXHGH YLRODUVH HQ QLQJ~Q FDVR (Q ORV VLVWHPDV GH WDOOHU GH IOXMR IOH[LEOH VH HVWDEOHFH XQD IHFKD GH HQWUHJD HTXLYDOHQWH DO LQVWDQWH GH HQWUHJD VROLFLWDGR SDUD HO SHGLGR SHUR QR VH LPSRQH UHVWULFFLyQ DOJXQD VREUH OD IHFKD ILQDO GH ILQDOL]DFLyQ GH FDGD WHP  LQIOX HQGR ~QLFDPHQWHVREUHGLFKDIHFKDHOFULWHULRTXHVHHVWDEOHFHHQODIXQFLyQREMHWLYRPLQLPL]DFLyQ GHUHWUDVRVPLQLPL]DFLyQGHOPi[LPRUHWUDVRPD[LPL]DFLyQGHORVSHVRVGHORVSHGLGRVQR UHWUDVDGRVHWF3RUHOORHOSUREOHPD))6SXHGHVHUYLUGHJX DSDUDHOSUREOHPDREMHWRGH HVWHDUW FXORFXDQGRVHWUDEDMHFRQYHQWDQDVWHPSRUDOHVFRQXQDDPSOLWXGWDOTXHQRLQIOX D HQODVUHVWULFFLRQHVGHOSUREOHPD 3RURWURODGRVLHOQ~PHURGHYHK FXORV9HVORVXILFLHQWHPHQWHJUDQGHGHIRUPDTXHVLHPSUH H[LVWDQYHK FXORVGLVSRQLEOHVHOSUREOHPDSXHGHYHUVHFRPRXQSUREOHPDGHVHFXHQFLDFLyQ GHWUDEDMRVFRQWLHPSRVYDULDEOHV9DULDEOH-RE6FKHGXLQJ3UREOHP963TXHFRUUHVSRQGHD ODVLJXLHQWH VLWXDFLyQ'DGRVQWUDEDMRVFRQWLHPSRVGHSURFHVRILMR XQLQWHUYDORGHWLHPSR GH FRPLHQ]R GRQGH FDGD WUDEDMR GHEH VHU SURFHVDGR VLQ LQWHUUXSFLyQ VREUH DOJXQD GH ODV PiTXLQDVGLVSRQLEOHVVHWUDWDHQFRQWUDUODDVLJQDFLyQGHPiTXLQDVDWUDEDMRVTXHPD[LPLFHHO Q~PHURGHWUDEDMRVSURFHVDGRV6XUJHQGLYHUVDVYHUVLRQHVDWHQGLHQGRDOQ~PHURGHYHK FXORV GLVSRQLEOHV R D OD FODVH GH WUDEDMRV  PiTXLQDV *HUWVEDNK  6WHUQ SURSRQHQ XQD IRUPXODFLyQGLVFUHWDGHOSUREOHPDTXHXVDUHPRVGHEDVHSDUDQXHVWUDIRUPXODFLyQ )RUPXODFLyQ 'LVFUHWL]DPRVHO WLHPSR PHGLDQWHXQFRQMXQWRGH 7LQWHUYDORVRSHULRGRV LQGH[DGRVSRUHO QGLFHM 7FRQHOMpVLPRLQWHUYDORUHSUHVHQWDQGRODVXQLGDGHVGHWLHPSRHQWUH>MM 3DUDFDGDSHGLGR3LFRQYHQWDQD WHPSRUDO GHFRPLHQ]R>D¶LE¶L@VHGHILQHHOFRQMXQWR 7L  ^D¶LIL` FRPR HO FRQMXQWR WRWDO GH LQVWDQWHV HQ ORV FXiOHV GHEH UHDOL]DUVH OD DFWLYLGDG FRPSOHWDIDEULFDFLyQ  GLVWULEXFLyQ DVRFLDGD DO SHGLGR 3L 'HILQLPRV %L  ^DL  EL` FRPRHOFRQMXQWRGHLQVWDQWHVHQORVFXiOHVGHEHFRPHQ]DUHOSHGLGR3L6HGHILQHWDPELpQ-M FRPRHOFRQMXQWRGHSHGLGRVTXHSXHGDQHVWDUHQFXUVRHQHO MpVLPRLQVWDQWHGHWLHPSR(O WLHPSRWRWDOGHDFWLYLGDGGHXQSHGLGRVHGHILQHFRPRWWL WILWGL 6HGHILQHQYDULDEOHV[LM L QM7LELQDULDVTXHWRPDQYDORUVL3LVHSURFHVDHQHO LQVWDQWHM HQRWURFDVR'HULYDGDVGHpVWDVVHGHILQHQYDULDEOHVELQDULDV LML QM%L TXHWRPDQYDORUVL3LFRPLHQ]DHQHOLQVWDQWHM(VQHFHVDULRGHILQLUWDPELpQXQFRQMXQWRGH YDULDEOHV]LM L QM>D¶LE¶LWIL±@SDUDFRQWURODUTXHHQORVVRODSDPLHQWRVHQIiEULFD VyOR SXHGDQ UHDOL]DUVH XQ Pi[LPR GH &SHGLGRV $V  ]LM WRPD YDORU  VL HO 3LVH IDEULFD GXUDQWHHOLQVWDQWHM6HGHILQHQYDULDEOHVSLL QTXHGHWHUPLQDQVLHOSHGLGRVHDWLHQGHR QR8VDUHPRVYDULDEOHVQL QLTXHUHFRMDQHODGHODQWRRHOUHWUDVRVREUHODIHFKDVROLFLWDGD SDUDHOSHGLGR (OPRGHORTXHPD[LPL]DHOYDORUGHORVSHGLGRVDWHQGHU DDODVLJXLHQWHH[SUHVLyQ  Q ) LL L 0D[ Z S ¦  VD  L LM L L M7 [WWSL Q  ¦ !   M LM L- [9 M 7  d ¦ !     L I LLM LLM LN L L NM WW [ WW [ [ WW L Q M 7    d  ¦ !     LM LM LM L L [[ L QM%MD    z !    L MWI LLM LN L NM WI ] L Q M %  d  ¦ !    7 LM L ]& M 7 d ¦ !    L LM L L L M% W H Q Q L Q    ¦ !   ) L L LL LL ZZQOQO L Q    !    ^`   LM L LM LM L L [S ] QQ   /DV UHVWULFFLRQHV  DVHJXUDQ TXH FDGD SHGLGR VH UHDOL]D H[DFWDPHQWH HQ HO Q~PHUR GH LQVWDQWHV GH WLHPSR D TXH FRUUHVSRQGH VX DFWLYLGDG FRPSOHWD WWL /DV UHVWULFFLRQHV  FRQWURODQTXHQRPiVGH9YHK FXORVHVWpQDFWLYRVHQFXDOTXLHUSHU RGRGHWLHPSR(QVH DVHJXUDTXHFDGDSHGLGRVHDDVLJQDGRDXQFRQMXQWRDG DFHQWHGHSHU RGRV(QVHREWLHQH HO SHULRGR GH FRPLHQ]R GH FDGD SHGLGR (Q  VH FRQWUROD TXH VH IDEULTXH FDGD SHGLGR GXUDQWHORVLQVWDQWHVGHWLHPSRTXHGXUDVXSURFHVRGHIDEULFDFLyQ3DUDFRQWURODUTXHQRVH IDEULTXHQPiVGH&SHGLGRVHQFDGDXQRGHORVSHULRGRVVHGHILQHHOFRQMXQWRGHUHVWULFFLRQHV PRVWUDGRHQ/DVUHVWULFFLRQHV QRVVLUYHQSDUDREWHQHUHOYDORUGHFDGDSHGLGR/D IXQFLyQREMHWLYRGHILQLGDHQHVGHFDUiFWHUQROLQHDODXQTXHQRLQIOX HHVWHKHFKRDODKRUD GHUHVROYHUHOSUREOHPD 6L SUHWHQGHPRV PD[LPL]DU HO Q~PHUR GH SHGLGRV TXH VH DWLHQGHQ HO SUREOHPD SXHGH SUHVFLQGLUGHODVUHVWULFFLRQHV SDVDQGRODIXQFLyQREMHWLYRDVHU6LTXHUHPRV PD[LPL]DUHOQ~PHURGHSHGLGRVHQWUHJDGRVHQODIHFKDVROLFLWDGDODIXQFLyQREMHWLYRSDVDD VHUSUHVFLQGLHQGRWDPELpQGHODVUHVWULFFLRQHV  (VWUDWHJLDGHUHVROXFLyQJUDIRGHHVWDGRV (O PpWRGR GH UHVROXFLyQ TXH SURSRQHPRV VH EDVD HQ OD LGHD SODQWHDGD SRU $UNLQJ  6LOEHUJHUJ SDUD OD UHVROXFLyQ GH XQ SUREOHPD GH VHFXHQFLDFLyQ GH WUDEDMRV FRQ GLIHUHQWHVFODVHVGHPiTXLQDVHQODFXiOVHSODQWHDXQJUDIRGRQGHORVFDPLQRVGHOPLVPR GHILQHQODVSODQLILFDFLRQHVDGPLVLEOHVSDUDORVWUDEDMRV3ODQWHDPRVSRUWDQWRODFRQVWUXFFLyQ GHXQJUDIR*1$PHGLDQWHWpFQLFDVGHSURJUDPDFLyQGLQiPLFDGRQGHYDQDHVWDUUHFRJLGDV WRGDVODVSODQLILFDFLRQHVDGPLVLEOHVGHORVSHGLGRV3RVWHULRUPHQWH DWUDYpVGHXQDOJRULWPR GH IOXMR VREUH * VH REWHQGUi HO ySWLPR GHO SUREOHPD (O JUDIR SHUPLWH OD UHVROXFLyQ GHO SUREOHPDVREUHFXDOTXLHUDGHORVFULWHULRVGHHOHFFLyQGHVROXFLRQHVSODQWHDGRPD[LPL]DUHO YDORU GH ORV SHGLGRV PD[LPL]DU HO Q~PHUR GH SHGLGRV PD[LPL]DU HO Q~PHUR GH SHGLGRV SXQWXDOHV VLPSOHPHQWH YDULDQGR ORV SHVRV GH ORV DUFRV GHO JUDIR &DGD QRGR GHO JUDIR UHSUHVHQWD XQ HVWDGR SRVLEOH HQ TXH SXHGH HQFRQWUDVH OD VHFXHQFLDFLyQ GH ORV SHGLGRV /D IRUPDFLyQGHXQHVWDGRVHSURGXFHDOFRPLHQ]RGHOSURFHVDPLHQWRGHXQSHGLGRSHURQXQFD  L LH L ¦ L L S ¦ SRUILQDOL]DFLyQGHORVPLVPRV$TX VHLQWURGXFHXQDYDULDFLyQLPSRUWDQWHUHVSHFWRDOJUDIR SURSXHVWRSRU$UNLQJ6LOYHUEHUJ HQHOTXHH[LVWHXQQRGRSDUDHOFRPLHQ]R RWUR SDUDOD ILQDOL]DFLyQGHFDGDWUDEDMRHQFDGDFDPLQRGHOJUDIR 3DUDODFRQVWUXFFLyQGHOJUDIRHVQHFHVDULRSDUWLUGHORVSHGLGRVRUGHQDGRVSRUHOLQVWDQWHPiV WHPSUDQRGHFRPLHQ]RD¶L(OJUDIRVHHVWUXFWXUDHQQLYHOHVFRQXQQLYHOSDUDFDGDSHGLGR (QFDGDQLYHOVHHQFXHQWUDQORVQRGRVDVRFLDGRVDODUHDOL]DFLyQGHOSHGLGR(OFRQMXQWR 1GH QRGRV VRQ FDGD XQR GH ORV HVWDGRV HQ ORV TXH SXHGH HQFRQWUDVH FXDOTXLHU SODQLILFDFLyQ DGPLVLEOHGHOFRQMXQWR GHSHGLGRVDGHPiVGHDxDGLUXQQRGR VLQLFLDOVLQDFWLYLGDG  XQ QRGR HGH ILQDOL]DFLyQ GH OD SODQLILFDFLyQ &DGD FDPLQR GH VD HGHILQH XQDSODQLILFDFLyQ DGPLVLEOH  FDGDQRGRGHOFDPLQRGHILQHTXHSHGLGRVVRQORVTXHHVWiQHQFXUVR  HQTXH LQVWDQWH GH OD YHQWDQD WHPSRUDO FRPHQ]DURQ (VWD LQIRUPDFLyQ VH DOPDFHQD HQ HO QRGR PHGLDQWH OD QRWDFLyQ 3LKL FRQ KL  RLH¶LVLJQLILFiQGRVH HO SHGLGR HQ FXUVR  HQWUH SDUpQWHVLV OD GLIHUHQFLD HQWUH HO LQVWDQWH GH FRPLHQ]R GHO SHGLGR  HO LQVWDQWH VROLFLWDGR WRPDQGR FRPR SRVLWLYRV ORV UHWUDVRV  FRPR QHJDWLYRV ORV DGHODQWRV (Q HO JUDIR VH FRQWHPSODUi WDPELpQ HVWDGRV TXH FRUUHVSRQGDQ FRQ QR UHDOL]DU HO SHGLGR ILJXUD 6HJ~Q HOORODHVWUXFWXUDJHQHUDOGHOJUDIRFRUUHVSRQGHU DFRQODGHXQiUEROTXHVHYDUDPLILFDQGRD PHGLGDTXHYDQDSDUHFLHQGRSHGLGRVFRPRVHPXHVWUDHQODILJXUD )LJXUD(VWUXFWXUDJHQHUDOGHOJUDIR 6LQHPEDUJR OD H[SDQVLyQ GHO JUDIR VH YH WUXQFDGD SRU OD ILQDOL]DFLyQ GH ORV SHGLGRVD OR ODUJR GHO WLHPSR &DGD SHGLGR TXH ILQDOL]D GLVPLQX H HO JUDGR GH UDPLILFDFLyQ GHO JUDIR &XDQGROD DFWLYLGDG GH ORV SHGLGRV DSDUHFH PX  VRODSDGD HQ HO WLHPSR VH SURGXFHXQ DOWR JUDGRGHUDPLILFDFLyQHQHOJUDIR$GHPiVHVQHFHVDULRGHVFDUWDUHQODSODQLILFDFLyQDTXHOORV HVWDGRV TXH JHQHUDQ SODQLILFDFLRQHV QR DGPLVLEOHV HV GHFLU HVWDGRV HQ ORV TXH VH YLROH OD FDSDFLGDGGHIDEULFDFLyQHQSODQWDRHOQ~PHURGHYHK FXORVGLVSRQLEOHV &DGDQLYHOGHOJUDIRYHQGUiGHWHUPLQDGRSRUORVQRGRVTXHVHRULJLQDQWUDVODUHDOL]DFLyQGH FDGDSHGLGR  TXHGHQRWDPRVSRUHOFRQMXQWRGHQRGRV 1LL Q3DUDXQSHGLGR3LFRQ YHQWDQDWHPSRUDOGHFRPLHQ]R>D¶LE¶L@SRGUiQHVWDEOHFHUVHXQPi[LPRGHE¶LD¶L_1L_ HVWDGRV'HXQQRGRFXDOTXLHUDGHOQLYHO LSXHGHQJHQHUDUVHXQPi[LPRGHE¶LD¶L HVWDGRVHQHOQLYHOL 6HJ~QORYLVWRHOQ~PHURGHQRGRVGHOJUDIRFRUUHVSRQGHU DD FX RRUGHQHV GH2(ORUGHQHQHOQ~PHURGHDUFRVFRLQFLGHFRQHOGHORVQRGRV $SHVDUGHORUGHQHVWDEOHFLGRHVSRFRSUREDEOHODREWHQFLyQGHHVHQ~PHURGHQRGRVHQHO JUDIRGHELGRDODVSURSLDVUHVWULFFLRQHVGHOPRGHORUHVSHFWRDODFDSDFLGDGGHIDEULFDFLyQ DO Q~PHUR GH YHK FXORV $GHPiV FRPR SRGUi YHUVH HQ OD LOXVWUDFLyQ TXH VH H[SRQH D FRQWLQXDFLyQODILQDOL]DFLyQGHSHGLGRVOLPLWDODH[SDQVLyQGHOJUDIR 1RGRDVRFLDGRFRQQRUHDOL]DU3 1RGRDVRFLDGRFRQQRUHDOL]DU3   Q M M 11  ¦  PD[    Q LL L ED   (Q OD ILJXUD  VH PXHVWUD XQ GLDJUDPD WHPSRUDO VREUH OD GHPDQGD GH  SHGLGRV TXH VH GLVWLQJXHQSRUODIDVHGHIDEULFDFLyQUHSUHVHQWDGDHQRVFXURODSRVWHULRUIDVHGHGLVWULEXFLyQ  XQD YHQWDQD WHPSRUDO GH FRPLHQ]R UHSUHVHQWDGD HQWUH EDUUDV SDUDOHODV    (O HVTXHPD JHQHUDOGHXQSHGLGRVHU DHOVLJXLHQWH D¶L E¶L H¶L 3L )LJXUD(VTXHPDJHQHUDOGHXQSHGLGR                         $ % ' & )LJXUD(MHPSOR /RVGDWRVGHFDGDSHGLGRVRQORVVLJXLHQWHV 3HGLGRV D¶L H¶L E¶L WIL WGL ZL $       %       &       '       7DEOD 6XSRQGUHPRVXQDFDSDFLGDGGHIDEULFDFLyQGHXQLGDG YHK FXORVGLVSRQLEOHV $ FRQWLQXDFLyQ VH PXHVWUD OD IRUPDFLyQ GHO JUDIR HQ GRV IDVHV (Q OD SULPHUD VH IRUPD HO JUDIR SDUD ORV GRV SULPHURV QLYHOHV SHGLGRV $  % (Q OD VHJXQGD VH PXHVWUD HO JUDIR FRPSOHWR )LJXUD)RUPDFLyQGHXQJUDIRGHHVWDGRV /RVQRGRVPDUFDGRVFRQVHFRUUHVSRQGHQFRQHVWDGRVQRDGPLVLEOHV TXHSRUWDQWRQR DSDUHFHUiQ HQ HO JUDIR ILQDO /D FRQGLFLyQ GH DGPLVLELOLGDG GH XQ HVWDGR LPSOLFD TXH HO Q~PHURGHSHGLGRVHQFXUVRVHDPHQRURLJXDODOQ~PHURGHYHK FXORVGLVSRQLEOHVRTXH HO Q~PHUR GH SHGLGRV TXH VH SURFHVDQ HQ IiEULFD QR VXSHUH OD FDSDFLGDG GH IDEULFDFLyQ /RV QRGRVTXHQRWLHQHQLQIRUPDFLyQVREUHHOSHGLGRGHVXQLYHOVHFRUUHVSRQGHQFRQQRUHDOL]DU HO SHGLGR (Q HO JUDIR ILQDO ILJXUD GHUHFKD VH REVHUYD FRPR OD ILQDOL]DFLyQ GHO SHGLGR % DQWHVGHFRPHQ]DU'HLQFOXVRODILQDOL]DFLyQGH&DQWHVGH E¶'SURYRFDXQDUHGXFFLyQGHO Q~PHUR GH HVWDGRV HQ HO QLYHO ' (OOR SURYRFD TXH PXFKRV FDPLQRVSODQLILFDFLRQHV DGPLVLEOHVHVWpQIRUPDGRVSRUHVWDGRVFRPXQHV 5HGXFFLyQGHO*UDIR (VSRVLEOHODUHGXFFLyQGHOQ~PHURGHQRGRVGHOJUDIR(OORVHFRQVLJXHHOLPLQDGRORVQRGRV TXHQRLPSOLTXHQXQDYDULDFLyQHQHOVLVWHPDHVGHFLUTXHQRLPSOLTXHQHOFRPLHQ]RGHXQ SHGLGR/RVDUFRVFRQGHVWLQRHQXQQRGRLDHOLPLQDUMLM1 ORVDUFRVFRQRULJHQHQL LNN1VHVXVWLWX HQSRUDUFRVMNMN(OORSURYRFDTXHHQHOJUDIRUHGXFLGRSXHGDQ H[LVWLUDUFRVHQWUHQLYHOHVQRFRQVHFXWLYRV $GHPiV HV SRVLEOH HOLPLQDU GHWHUPLQDGRV DUFRV TXH D SULRUL VH VDEH TXH QR YDQ D IRUPDU SDUWHGHQLQJXQDSODQLILFDFLyQySWLPD(VHHOFDVRGHDTXHOORVDUFRVTXHFRQHFWDQQRGRVQR WHUPLQDOHVDO QRGR HHQWHQGLHQGRFRPRQRGRVQRWHUPLQDOHVDTXHOORVGHVGHORVTXHSDUWHQ DUFRVKDFLDQRGRVTXHQRVRQHOQRGRH (OJUDIRGHOHMHPSORXQDYH]UHGXFLGRTXHGDU DGHODVLJXLHQWHIRUPD )LJXUD*UDIRGHHVWDGRVUHGXFLGR (OREMHWLYRTXHVHSHUVLJDYDDGHILQLUORVSHVRVTXHDVLJQHPRVDORVDUFRVGHOJUDIR9HDPRV FXDOHVVHU DQHVRVSHVRVSLMHQIXQFLyQGHOWLSRGHREMHWLYR 0D[LPL]DUHOYDORUGHORVSHGLGRVVHUYLGRVLM$L1PL1QSLM ZWR R LQVWDQWH GH FRPLHQ]R GH 3QHQ HO QRGR M 8Q DOJRULWPR GH UXWD P QLPD REWHQGU D HO ySWLPR GHO SUREOHPD$TXHOORVDUFRVSHUWHQHFLHQWHVDOFDPLQRGHILQLU DQORVSHGLGRVUHDOL]DGRV HQTXH LQVWDQWHV )LJXUD5XWDP QLPDSDUDHOFiOFXORGHOPi[LPRYDORUGHSHGLGRVVHUYLGRV (QODILJXUDVHLOXVWUDHOFiOFXORGHOPi[LPRYDORUSDUDHOHMHPSOR/DUXWDP QLPDPDUFDGD HQJUXHVRPXHVWUDTXHHOySWLPRFRUUHVSRQGHFRQUHDOL]DUHOSHGLGR& HO'HQHOLQVWDQWH VROLFLWDGR HO$FRQXQDXQLGDGGHWLHPSRGHUHWUDVR(OYDORUWRWDOHVGH 0D[LPL]DUHOQ~PHURGHSHGLGRVVHUYLGRV 6HU DHTXLYDOHQWHDOFDVRDQWHULRUSHURDVLJQDQGR SHVRV LM$SLM   8Q DOJRULWPR GH UXWD P QLPD REWHQGU D HO Q~PHUR Pi[LPR GH SHGLGRV 0D[LPL]DU HO Q~PHUR GH SHGLGRV VHUYLGRV HQ VX LQVWDQWH GH HQWUHJD VROLFLWDGR &RUUHVSRQGHU DDDVLJQDUSHVRDDTXHOORVDUFRVFX RQRGRGHVWLQRLPSOLFDODLQLFLDFLyQGH XQSHGLGRHQVXLQVWDQWHVROLFLWDGRH¶L 2EWHQFLyQGHOQ~PHURP QLPRGHYHK FXORV 3DUD REWHQHU HO P QLPR Q~PHUR GH YHK FXORV QHFHVDULRV FRPR VHJXQGR REMHWLYR VREUH FXDOTXLHUDGHORVDQWHULRUHVHVQHFHVDULRFDOFXODUODUXWDP QLPDHQWUHV HTXHKDFHP QLPR HOQRGRFRQPi[LPDXWLOL]DFLyQGHYHK FXORVHVGHFLUHOQRGRFRQPD RUQ~PHURGHSHGLGRV HQSURFHVR(VWHSUREOHPDSRGU DVHUWUDWDGRFRPRXQSUREOHPDPXOWLREMHWLYRHQHOFXiOORV REMHWLYRV VRQ OD PLQLPL]DFLyQ GH OD ORQJLWXG GH OD UXWD  OD PLQLPL]DFLyQ GH OD Pi[LPD XWLOL]DFLyQ GH YHK FXORV 6LQ HPEDUJR XQD DOWHUQDWLYD PXFKR PiV VLPSOH  SUiFWLFD HV FDOFXODU WRGDV ODV UXWDV P QLPDV GH VD HD WUDYpV GH XQ DOJRULWPR GHVFULWR HQ &KULVWRILGHV  HVFRJHU DTXHOOD TXH PLQLPL]D HO QRGR FRQ Pi[LPD RFXSDFLyQ GH YHK FXORV (QODVLJXLHQWHILJXUDVHPXHVWUDODLOXVWUDFLyQSDUDHOFDVRGHREWHQHUHOPi[LPRQ~PHURGH SHGLGRVVHUYLGRVFRQSXQWXDOLGDGKDFLHQGRXVRGHOPHQRUQ~PHURSRVLEOHGHYHK FXORV&RQ IOHFKD JUXHVD     DSDUHFHQ VREUH HO JUDIR WRGDV ODV UXWDV TXH KDFHQ P QLPR HO REMHWLYR SULPDULRPD[LPL]DUHOQ~PHURGHSHGLGRVPLHQWUDVTXHFRQIOHFKDUD DGDVHVHxDOD GHHQWUHHOODVODUXWDTXHKDFHP QLPRHOQ~PHURGYHK FXORV6HREVHUYDFRPRHOySWLPRGHO SULPHUREMHWLYRVRQSHGLGRVVHUYLGRVGHPDQHUDSXQWXDO HOQ~PHURP QLPRGHYHK FXORV QHFHVDULRVHV &RQFOXVLRQHV (Q HVWH DUW FXOR KHPRV SUHVHQWDGR HO SUREOHPD DVRFLDGR D OD IDEULFDFLyQ  GLVWULEXFLyQ FRQMXQWDPHGLDQWHSHGLGRQRWUDWDGRFRPRWDOHQODELEOLRJUDI DDXQTXHVLPX DVRFLDGRFRQ SUREOHPDVFRPXQHVGHVHFXHQFLDFLyQGHWUDEDMRV 6H KD GHVFULWR FRPR HVWUDWHJLD GH UHVROXFLyQ XQD IRUPD FOiVLFD GH UHVROYHU SUREOHPDV FRPSOHMRVHQHOFDPSRGHODVHFXHQFLDFLyQODFRQVWUXFFLyQGHXQJUDIRTXHDOPDFHQHWRGDV ODVSRVLEOHVSODQLILFDFLRQHVGHOVLVWHPD(OFiOFXORGHVROXFLRQHVySWLPDVFRQHOXVRGHHVWRV JUDIRVVHPXHVWUDHILFLHQWHHQIXQFLyQGHODGLVSRVLFLyQGHORVSHGLGRVHQHOWLHPSR&XDQGR HO JUDGR GH VLPXOWDQHLGDG GH ORV SHGLGRV HV HOHYDGR OD H[SDQVLyQ GHO JUDIR DGTXLHUH XQ FDUiFWHUSRFRHILFLHQWHSDUDODUHVROXFLyQGHOSUREOHPD6LQHPEDUJRHOXVRGHHVWHWLSRGH JUDIRVWUDQVPLWHXQDYLVLyQFODUDGHWRGDVODVVROXFLRQHVDGPLVLEOHVGHOSUREOHPD 5HIHUHQFLDV >@ $UNLQJ(06LOYHUEHUJ(%³6FKHGXOLQJMREVZLWK IL[HGVWDUWDQGHQGWLPHV´'LVFUHWH$SSOLHG 0DWKHPDWLFVSS >@ *HUWVEDNK , 6WHUQ +,  ³0LQLPDO UHVRXUFHV IRU IL[HG DQG YDULDEOH MRE VFKHGXOHV´ 2SHUDWLRQV 5HVHDUFK9ROSS >@ *DEUHO9³6FKHGXOLQJMREVZLWKLQWLPHZLQGRZVRQLGHQWLFDOSDUDOOHOPDFKLQHV1HZPRGHODQG DOJRULWKPV´(XURSHDQ-RXUQDORI2SHUDWLRQV5HVHDUFKSS >@ 1LFKRODV*+DOO&KHOOLDK6ULVNDQGDUDMDK³$VXUYH RIPDFKLQHVFKHGXOLQJSUREOHPVZLWK EORFNLQJDQGQRZDLWLQSURFHVV´2SHUDWLRQV5HVHDUFK9RO1R0D -XQH >@ &KULVWRILGHV1³*UDSK7KHRU $Q$OJRULWKPLF$SSURDFK´(G:HUQHU5KHLQEROGW8QLYHUVLW  RI0DU ODQG$&$'(0,&35(66,1&/21'21/7'/RQGRQ8.SS