Singularity Functions as New Tool for Integrated ... - Science Direct

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 85 (2014) 339 – 350

&UHDWLYH&RQVWUXFWLRQ&RQIHUHQFH&&

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



&RUUHVSRQGLQJDXWKRU7HOID[ E-mail address:OXFNR#FXDHGX

1877-7058 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Diamond Congress Kft. doi:10.1016/j.proeng.2014.10.559

340

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

TXLUHPHQWWKDW³>W@KHSODQVKRXOGSRLQWGLUHFWO\WRWKHGLIILFXOWDQGVLJQLILFDQWDFWLYLWLHV±WKHSUREOHPVRIDFKLHYLQJ WKHREMHFWLYH´>S@&30PD\EHGHVFULEHGDVDRQHDQGDKDOIGLPHQVLRQDOPHWKRGEHFDXVHLWSULPDULO\DS SOLHVDQDOJRULWKPWRVFKHGXOHWLPHZKLOHDVHSDUDWHODWHUWLPHFRVWWUDGHRIIDQDO\VLVFRXOGFRQVLGHUGLUHFWFRVWEXW QRW LQGLUHFW FRVW >@ 0RUH UHFHQWO\ DGGLWLRQDO GLPHQVLRQV RIWHQ WKUHH  DUH EURXJKW LQWR PXOWLREMHFWLYH PRGHOV 7KH\ZHUHVROYHG³XVLQJDYDULHW\RIPHWKRGVLQFOXGLQJOLQHDUSURJUDPPLQJLQWHJHUSURJUDPPLQJG\QDPLFSUR JUDPPLQJDQGJHQHWLFDOJRULWKPV´>S@%XW&30VWLOOGRPLQDWHVDVWKHLUOLPLWLQJIRXQGDWLRQWRWKHGHWULPHQW RIRWKHUGLPHQVLRQVWKH@PRVWLPSRUWDQWREMHFWLYHZKLOHHLWKHUQHJOHFWLQJWKHOHVVLPSRUWDQWFRPSHWLQJ REMHFWLYHV RU LPSRVLQJ WKHP DV NQRZQ FRQVWUDLQWV LQ WKH RSWLPL]DWLRQ IRUPXODWLRQ´ > S @ 6XFK VWXGLHV RQ VLQJOHREMHFWLYHVXVXDOO\H[SORUHDGHWDLOHGsubsystemHJVFKHGXOLQJ>@RUFDVKIORZV>@%XWFRQVWUXFWLRQSUR MHFWVDUHFRPSOH[V\VWHPVDQGWKXVLWLVGHSORUDEOHWKDWWKHUHH[LVWV³DSOHWKRUDRI³FRQWURO´WHFKQLTXHVWKDWFDQQRW SURYLGHDQ\LQVLJKWLQWRWKHLQWHUDFWLRQVDPRQJWKHPDQ\FRPSRQHQWVRIDFRQVWUXFWLRQHQJLQHHULQJSURMHFW´>S @7RPDQDJHPXOWLREMHFWLYHSUREOHPVVWXGLHVVHHNWRFUHDWH³WRROVDQGVWUDWHJLHVWKDWFDQVLPXOWDQHRXVO\LP SURYHSURMHFWSHUIRUPDQFHLQPXOWLSOHGLPHQVLRQV´IRUintegrated systems>S@P@XOWLREMHFWLYHRSWLPL]D WLRQIRUPXODWLRQVKDYHFOHDUWKHRUHWLFDODGYDQWDJHVEXWLQFUHDVHWKHFRPSOH[LW\RIWKHPDWKHPDWLFDOIRUPXODWLRQ´> S@,QPRVWFDVHVUHVHDUFKHUVPDNHDSSUR[LPDWLRQVWRVLPSOLI\SUREOHPV$PPDU>S@IRUDWLPHFRVW WUDGHRIIRSWLPL]DWLRQH[SODLQHGWKDWD³>G@LVFRXQWIDFWRULQWKHH[SRQHQWLDOIRUP«LVWRRFRPSOLFDWHGWREHKDQGOHG LQDPDWKHPDWLFDORSWLPL]DWLRQPRGHO«,QVWHDGDVLPSOLILHGIRUP«ZLOOEHXVHG´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versatile\HWaccurateWRWKHPD[ LPXPH[WHQWWKDWLQSXWGDWDDOORZZLWKRXWLPSRVLQJH[WUDQHRXVUHVWULFWLRQVIURPPRGHOLQJDVVXPSWLRQV3ULRUVWXG LHVKDYHIRFXVHGH[WHQVLYHO\RQRSWLPL]DWLRQDOJRULWKPV>@EXWDSSHDUWRRYHUORRNWKLVPRGHOLQJFKDOOHQJH 2.1. Research Need and Objectives $EULGJHGREMHFWLYHIXQFWLRQVWRPLQLPL]HRUPD[LPL]HGHSHQGHQWYDULDEOHVUDGLFDOO\VLPSOLI\UHDOLW\'XUDWLRQLV GHWHUPLQHGE\IDFWRUVVXFKDVSURGXFWLYLW\FUHZVL]HUHVRXUFHDYDLODELOLW\VKLIWVOHDGODJGXUDWLRQVEXIIHUVHWF PXOWLREMHFWLYHVWXGLHVRPLWPRVWVXFKGHWDLOV&DVKIORZVPXVWFRQVLGHUGLUHFWDQGLQGLUHFWFRVWELOOWRSD\GHOD\ SURPSW SD\PHQW GLVFRXQW FUHGLW OLPLW LQWHUHVW WLPH YDOXH RI PRQH\ HWF 2EMHFWLYH IXQFWLRQV W\SLFDOO\ VLPSOLI\ WKHVHGHWDLOVIRFXVLQJLQVWHDGRQDOJRULWKPVWRLGHQWLI\RUFRPSDUHVROXWLRQV2QHPD\DUJXHWKDWLWLVRYHUO\FRP SOLFDWHGWRPDLQWDLQWKHVDPHOHYHORIGHWDLODVORFDOsubsystemsZKHQPRYLQJWRPRGHOLQJDJOREDOintegrated system%XWSHU2FNKDP¶VUD]RUZKRVHSDUDGLJPDGYRFDWHGµDVVLPSOHDVSRVVLEOHDVFRPSOLFDWHGDVQHFHVVDU\¶IRU PRGHOVRQHVKRXOGQRWUHGXFHUHDOLVPLIDV\VWHPEHFRPHVPRUHFRPSOH[ZKLFKOLPLWVWKHYDOLGLW\RILWVRXWSXWDQG PD\ PLVOHDG GHFLVLRQPDNHUV 7KLV UHVHDUFK UDLVHV WKH IXQGDPHQWDO TXHVWLRQ RI KRZ WR EULGJH ORFDO DQG JOREDO YLHZVZKLOHUHPDLQLQJHIILFLHQWDQGDFFXUDWHDVGHWHUPLQHGE\WKHTXDOLW\RIDYDLODEOHGDWDQRWPRGHODVVXPSWLRQV 6LQJXODULW\ IXQFWLRQVGHILQHG LQ WKHIROORZLQJRIIHU WKH XQLTXHIHDWXUHV RIdetailability FDQ UHIOHFW DQ\ GHVLUHG OHYHO RIGHWDLO ZLWKLQ WKHLU PDWKHPDWLFDO H[SUHVVLRQV  extensibility FDQLQFRUSRUDWH DQ\ QXPEHURI LQWHUDFWLQJGL PHQVLRQDOYDULDEOHV DQGconvertibilityFDQH[WUDFWSDLUZLVHSHUIRUPDQFHSDUDPHWHUVWRH[DPLQHWKHLUUHODWLRQVKLS   7KUHHVHTXHQWLDO5HVHDUFK2EMHFWLYHVZLOOEHDGGUHVVHGE\WKLVUHVHDUFKZKLFKWRJHWKHUFRQWULEXWHWRLWVRYHUDOO JRDORIXOWLPDWHO\JDLQLQJDVLQJOHFRPSUHKHQVLYH\HWFXVWRPL]DEOHDSSURDFKWRFRQVWUXFWLRQSURMHFWPDQDJHPHQW

341

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

• ([SORULQJLQWHUDFWLRQVDQGFRQYHUVLRQVDPRQJVLQJXODULW\IXQFWLRQVIRUPHUJLQJVXEV\VWHPVLQWRDJOREDOPRGHO • $OLJQLQJVXEV\VWHPVFKHGXOHFDVKIORZDQGUHVRXUFHPRGHOVLQFXPXODWLYHDQGQRQFXPXODWLYHH[SUHVVLRQV • 9LVXDOL]LQJWKHLQWHJUDWHG'SURMHFWPRGHODQGDVVHVVLQJLWVSRWHQWLDOFRQWULEXWLRQDVDQRYHOPDQDJHPHQWWRRO 6LQJXODULW\)XQFWLRQV 6LQJXODULW\IXQFWLRQVZHUHLQLWLDOO\XVHGLQVWUXFWXUDOHQJLQHHULQJWRDQDO\]HWKHSUREOHPRIEHDPVWKDWDUHORDGHG ZLWKGLYHUVHW\SHVRIORDGVZKLFKDUHORFDWHGDWGLVFUHWHRUGLVWULEXWHGORFDWLRQVRQVDLGEHDPV7KHEDVLFWHUPRI (TXDWLRQZDVKLVWRULFDOO\NQRZQDVWKH)|SSOV\PERO>@RU0DFDXOD\EUDFNHWV>@7KLVRSHUDWRUSHUIRUPVD case distinctionIRUWKHJLYHQFXWRIIYDOXHaRIWKHLQGHSHQGHQWYDULDEOHx7KHIXQFWLRQV\LHOGV]HURLIxLVVPDOOHU WKDQaZKLOHHYDOXDWLQJWKHSRLQWHGEUDFNHWVDVURXQGRQHVLIxLVHTXDOWRRUODUJHUWKDQa7KHVWUHQJWKsDPSOLILHV WKHYDOXHRIWKHIXQFWLRQZKLOHWKHH[SRQHQWn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

 ­ n s⋅ x−a =® n ¯s ⋅ ( x − a )

for x < a for x ≥ a



 

7\SHRISUREOHP

,QGHSHQGHQW

'HSHQGHQW

/LQHDUVFKHGXOH

x ZRUNXQLW

y WLPHXQLW

&DVKIORZV

y WLPHXQLW

z FRVWXQLW

5HVRXUFHXWLOL]DWLRQ

y WLPHXQLW

r UHVRXUFHXQLW

3.1. Linear Schedule model (cumulative and non-cumulative forms) 0RVW FRQVWUXFWLRQ SURMHFWV ZKHWKHU SLSHOLQHV RU PXOWLIORRU EXLOGLQJV FRQWDLQ PDQ\ UHSHDWLQJ DFWLYLWLHV >@ &30FDQRQO\JXDUDQWHHWKDWVHTXHQWLDOUHODWLRQVEHWZHHQWKRVHUHSHDWLQJDFWLYLWLHVDUHREH\HGEXWFDQQRWGLUHFWO\ UHSUHVHQWFRQVWUDLQWVIRUUHVRXUFHFRQWLQXLW\>@QRUH[SORLWWKHUHSHWLWLYHQDWXUHIRUWKHPRGHOLWVHOI2QWKHRWKHU KDQG WKH /LQHDU 6FKHGXOLQJ 0HWKRG /60  DQG FORVHO\ UHODWHG DSSURDFKHV ZLWK VLPLODU QDPHV HJ UHSHWLWLYH RU ORFDWLRQEDVHG VFKHGXOLQJ ZKLFK ³DQDO\]H SURMHFWV WKDW DUH FKDUDFWHUL]HG DV JHRPHWULFDOO\ OLQHDU RU UHSHWLWLYH LQ WKHLURSHUDWLRQV´>S@DUHDEOHWRWDNHDGYDQWDJHRISUHYDLOLQJUHSHWLWLYHQHVVWRGHULYHDPRUHLQWXLWLYHPRG HO$VVKRZQLQ)LJXUHVXFKVFKHGXOHVFDQLQWXLWLYHO\GLVSOD\KRZSDLUZLVHDFWLYLWLHVRIXQHTXDOSURGXFWLYLWLHVDUH UHODWHGLQUHJDUGVWRWKHLUVWDUWDQGILQLVKFRRUGLQDWHV>@/60ZDVZLGHO\FRQVLGHUHGWREHPHUHO\JUDSKLFDOO\ EDVHGVFKHGXOLQJWKDW³LVSUHVHQWHGJUDSKLFDOO\DVDQXYSORWZKHUHRQHD[LVUHSUHVHQWV>UHSHDWLQJ@XQLWVDQGWKH RWKHUWLPH´>S@6XFKJUDSKLFDOQRQPDWKHPDWLFDOIRFXVZDVDVHYHUHOLPLWDWLRQRI/60DQGKDVKLQGHUHGLWV FRPSXWHUL]DWLRQDQGEURDGHUDSSOLFDWLRQLQWKHFRQVWUXFWLRQLQGXVWU\+RZHYHUWKDWVLWXDWLRQKDVFKDQJHGWKURXJK WKHLQWURGXFWLRQRIWKH3URGXFWLYLW\6FKHGXOLQJ0HWKRG360 ZKLFKHPSOR\VVLQJXODULW\IXQFWLRQV7KH\³SURYLGH D IOH[LEOH DQG SRZHUIXO PDWKHPDWLFDO PRGHO IRU FRQVWUXFWLRQ DFWLYLWLHV DQG WKHLU EXIIHUV WKDW DUH FKDUDFWHUL]HG E\ WKHLU OLQHDU RU UHSHWLWLYH QDWXUH´ > S @ WR DOORZ D FRPSUHKHQVLYH PDWKHPDWLFDOO\ ULJRURXV WUHDWPHQW 7KH\ VXSSRUWFDOHQGDUL]HGWLPHD[HV>@IRUPRUHUHDOLVWLFPRGHOVZKLFKLVGHVLUDEOHDVLWKDVEHHQVKRZQWKDW³GLVUH JDUGLQJ«FDOHQGDUVVHHPVWREHDQRYHUVLPSOLILFDWLRQWKDWFDQGLVWRUWWKHUHVXOWV´>S@  /XFNR >@ GHVFULEHG WKH VWHSV RI 360 DV DFWLYLW\ DQG EXIIHU HTXDWLRQV LQLWLDO VWDFNLQJ PLQLPXP GLIIHUHQFHV DQGGLIIHUHQWLDWLRQIRUFRQVROLGDWLRQZKLFKJHQHUDWHVUHYLVHGDFWLYLW\DQGEXIIHUHTXDWLRQVDQGFULWLFDOLW\DQDO\VLV

342

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

'HWDLOVRIWKHVHVWHSVDUHRPLWWHGLQWKLVSDSHUIRUEUHYLW\StackinJJHQHUDWHVDIHDVLEOHEXWH[WUHPHO\FRQVHUYDWLYH DQG WKXV OHQJWK\ VFKHGXOH consolidation RYHUODSV DV PDQ\ DFWLYLWLHV DV SRVVLEOH ZLWKLQ WKH VHTXHQFH FRQVWUDLQWV 7KHDSSURDFKRI360LVWRFRQYHUWDOOLQSXWVDERXWDFWLYLW\VHTXHQFHGXUDWLRQVOHDGVRUODJVEHWZHHQDFWLYLWLHVDQG DQ\WLPHRUZRUNEUHDNLQWRWKHPDWKHPDWLFDOPRGHOWKDWLVFRPSRVHGRIVLQJXODULW\IXQFWLRQV7KHVFKHGXOHVWDUW DQGILQLVKRIHDFKDFWLYLW\LQWKHLQLWLDODQGILQDOYHUVLRQV DQGLWVFULWLFDOLW\FKDUDFWHULVWLFVDUHRXWSXWV7LPHy LV WKHLQGHSHQGHQWYDULDEOHLQ360SHU(TXDWLRQx LVZRUNUiLVWKHQXPEHURIUHSHDWLQJZRUNXQLWVDiLVWKHGXUD WLRQRIDFWLYLW\i aSi DQG a Fi DUHLWVVWDUWDQGILQLVKZKRVHDVWHULVNLQGLFDWHVWKDWWKH\PD\LQFOXGHDVKLIWHGVWDUW SULRU GHOD\ d  RU H[WHQGHG GXUDWLRQ QHZ GHOD\ d  1RWH WKDW WLPH LV EHWWHU PHDVXUHG RQ WKH yD[LV EHFDXVH LW VKRXOGEHPLQLPL]HGE\WKHDOJRULWKP$QDQDORJRXVIRUPZLWKWLPHDVWKHGHSHQGHQWYDULDEOHFDQEHGHULYHGE\ VZLWFKLQJWKHD[HV$QH[DPSOHZLWKDFWLYLWLHVSHU7DEOHLVVKRZQLQWKHxy RULHQWHGOLQHDUVFKHGXOHRI)LJXUH  )LJXUHVKRZVWKHVFKHGXOHLQDcumulativeIRUPZKLFKPHDQVWKDWWKHZRUNTXDQWLW\RIHDFKDFWLYLW\YHUWLFDO D[LV LQFUHDVHVZLWKWLPHWKDWSDVVHVKRUL]RQWDOD[LV $FFRUGLQJWRFDOFXOXVFDOFXODWLQJWKHGHULYDWLYHRIDIXQFWLRQ \LHOGVLWVUDWHRIFKDQJH>@7KXVGLIIHUHQWLDWLQJWKHFXPXODWLYH(TXDWLRQUHWXUQVWKHnon-cumulative(TXDWLRQ )LJXUHVKRZVWKLVQRQFXPXODWLYHIRUP,QWHUHVWLQJO\WKHSURILOHRIQRQFXPXODWLYHDFWLYLW\HTXDWLRQVLVVLPLODUWR DWUDGLWLRQDOEDUFKDUW,WGLIIHUVIURPDEDUFKDUWRQO\LQWKDWWKHYHUWLFDOD[LVUHSUHVHQWVSURGXFWLYLW\DQGQRWMXVWDQ DFWLYLW\QDPHRUODEHO,WWKXVGLVSOD\VPRUHLQIRUPDWLRQWKDQDEDUFKDUW7KHDFWLYLW\ZLWKWKHKLJKHVWSURGXFWLYLW\ LVSODFHGDWWKHWRSDQGWKHVPDOOHUWKHSURGXFWLYLW\WKHORZHUWKHKHLJKWZKHUHDFWLYLW\EDUVDUHSODFHG   º    Ui Ui ª ⋅ « y − a Si − y − a Fi »  x( y )i = ⋅ ª y − aSi − y − a Fi − (Di + d i ) ⋅ y − a Fi º    x ′( y )i = »¼ Di + d i ¬ Di + d i «¬ ¼  7DEOH6FKHGXOHFDVKIORZDQGUHVRXUFHLQSXWIRUH[DPSOH 1DPH 6XFFHVVRU 'XUDWLRQ :RUN8QLW 7LPH%XIIHU 6KLIWG 'HOD\G &RVWC 0DUNXSM %LOOWR3D\'HOD\b 5HVRXUFH5DWH >PRQWKV@ >PRQWKV@ >@ >RIFRVW@ >PRQWKV@ >ZRUNHUV@ >@ >@ >PRQWKV@ >FRXQW@ >PRQWKV@ $

%

















%

&

















 

&





















 3URGXFWLYLW\>TXDQWLW\PRQWKV@ x¶y A

:RUN>TXDQWLW\@

xy A

xy B

xy C 7LPH>PRQWKV@

)LJ&XPXODWLYHOLQHDUVFKHGXOHIRUH[DPSOH

x¶y B

x¶y C 7LPH>PRQWKV@

)LJ1RQFXPXODWLYHOLQHDUVFKHGXOHIRUH[DPSOH

 2YHUDOO360ZLWKLWVV\VWHPDWLFDSSOLFDWLRQRIVLQJXODULW\IXQFWLRQVSURYLGHVDPDWKHPDWLFDOPRGHOWKDWXQLILHV FRPSDUWPHQWDOL]HG FRQFHSWV DQG SURMHFW SHUIRUPDQFH SDUDPHWHUV DV XVHG HJ LQ PLQLPL]LQJ WKH SURMHFW GXUDWLRQ DQGGHWHUPLQLQJWKHFULWLFDOLW\RIDFWLYLWLHVXQGHU&30GLVSOD\LQJJUDSKLFDOO\WKHLUVWDUWDQGILQLVKGDWHVDVLQEDU FKDUWVDQGUHSUHVHQWLQJWKHVWDUWVILQLVKHVVHTXHQFHDQGSURGXFWLYLW\RIDFWLYLWLHVDVXQGHU/607KHFXPXODWLYH DQGQRQFXPXODWLYHIRUPVRIWKHHTXDWLRQVHQKDQFHVFKHGXOLQJUHVHDUFKLQWKDWLWEHFRPHVDSSDUHQWWKDWFRQFHSWV ZKRVHUHODWLRQZDVSUHYLRXVO\DUGXRXVWRPRGHOFDQQRZEHH[SOLFLWO\KDQGOHGLQDQLQWHJUDWHGTXDQWLWDWLYHPDQQHU

343

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

3.2. Cash Flow Model (cumulative and non-cumulative forms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b IRUHDFKDFWLYLW\:KHUHDVWKHVORSHUHSUHVHQWHGSURGXFWLYLW\LQWKHOLQHDUVFKHGXOHWKHVFDOHIDFWRUC / D + d LQWKHVLQJXODULW\IXQFWLRQSHU(TXDWLRQUHSUHVHQWVWKHUDWHRIFRVWJURZWKZKLFKLVWKHVORSHRIWKHFRVW SURILOH$GGLQJWKHPDUNXSWRWKHFRVW\LHOGVDELOOIXQFWLRQSHU(TXDWLRQ$VELOOVDUHVHQWWRWKHSD\HUDWWKHHQG RIHDFKSHULRGDQRSHUDWRU¬¼WKDWURXQGVGRZQWKHRSHUDQGWRLWVQHDUHVWLQWHJHULVDSSOLHGWRWKHLQGHSHQGHQWYDUL DEOH y6XFKURXQGLQJRSHUDWRUFDQHDVLO\H[SUHVVWKH³SHULRGLFLW\>WKDW@RFFXUVERWKLQFDVKRXWIORZVDQGLQIORZV WKDWKDYHDVSHFLILFIUHTXHQF\DQGDPSOLWXGHHJRYHUKHDGELOOLQJDQGSD\PHQWIXQFWLRQV´>S@7KHSD\ IXQFWLRQSHU(TXDWLRQLVGHULYHGIURPWKHELOOIXQFWLRQEXWVXEWUDFWVWKHELOOWRSD\GHOD\bIURPHDFKyZKLFKKDV WKHHIIHFWRIPRYLQJWKHELOOSURILOHWRWKHULJKWWREHFRPHWKHSD\SURILOHSHU)LJXUH1RWHWKDWWKHFRVWELOOSD\ DQGEDODQFHSURILOHVLQ)LJXUHPRGHOWKHHQWLUHSURMHFWDGGLQJWKHFDVKIORZVRIWKHWKUHHDFWLYLWLHVDFFRUGLQJO\ 7KHEDODQFHLVWKHGLIIHUHQFHEHWZHHQWKHVXPRIWKHFRVWIXQFWLRQVRXWIORZV DQGWKHVXPRIDOOSD\IXQFWLRQVLQ IORZV SHU(TXDWLRQ,QDUHDOSURMHFWbZLOOEHDSSUR[LPDWHO\WRGD\VKHUHLWLVDVVXPHGDVRQHPRQWK,WLV DVVXPHGWKDWWKHEDODQFHIXQFWLRQGRHVQRWFRQVLGHU790,WVYDOXHGHSHQGVRQWKHSHULRGRYHUZKLFKLWLVDVVHVVHG HJIRUILQDQFLQJLQWHUHVWRUDQXQXVHGFUHGLWIHHDVDQDO\]HGLQGHWDLO>@EXWLVH[FOXGHGKHUHIRUEUHYLW\  3UHYLRXVFDVKIORZPRGHOVDUH cumulative\HWWKH non-cumulative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

&RVW>@

&RVW5DWH>PRQWK@ z¶costy zeachBpayy 

zbilly 

zcosty

7LPH>PRQWKV@

zpayy  7LPH>PRQWKV@

zbaly 

zbaly  )LJ&XPXODWLYHFDVKIORZSURILOHIRUH[DPSOH

)LJ1RQFXPXODWLYHFDVKIORZSURILOHIRUH[DPSOH



z cost ( y )i = z pay ( y )i =

Ci Di + d i

ª

⋅ « y − a Si ¬



− y − a Fi

º

»¼ 

  zbill ( y )i =

  Ci ( + M i ) ª

º   ⋅ ¬ y ¼ − aSi − ¬ y ¼ − aFi « »¼ Di + d i ¬

  Ci ( + M i ) ª ⋅ ¬ y − b¼ − aSi − ¬ y − b¼ − a Fi º    z balance ( y ) = ¦ z pay ( y )i − ¦ z cost ( y )i  »¼ Di + d i «¬

′ st ( y )i = z co

Ci Di + d i

ª

⋅ « y − a Si ¬



− y − a Fi

º

»¼ 

  z each B pay ( y ) = ¦

C i ⋅ ( + M i ) ⋅ z pay B signal ( y )  Di + d i

 

344

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

(

z pay B signal ( y ) = §¨ ¬ y ¼ − a s + b ©

)



(

− ¬ y ¼ − a F + b

)



(

)

·¸ − §¨ y − a + b +  ª º s ¹ ©



(

)

 − ª y º − a F + b +  ·¸  ¹

 

3.3. Resource Model (cumulative and non-cumulative forms) 7KHVDPHDSSURDFKDVGHVFULEHGIRUOLQHDUVFKHGXOLQJDQGFDVKIORZVFDQDOVREHDGRSWHGIRUUHVRXUFHXWLOL]DWLRQ ,WVVFDOHIDFWRUSHU(TXDWLRQUHSUHVHQWVWKHUDWHRIUHVRXUFHFRQVXPSWLRQr>@W\SLFDOO\IRUJHQHUDORUVSHFLDO L]HGODERU&RQWLQXLQJWKHSUHYLRXVH[DPSOH7DEOHOLVWVWKHUHVRXUFHUDWHIRUHDFKDFWLYLW\(TXDWLRQVDQG H[SUHVVWKHFXPXODWLYHDQGQRQFXPXODWLYHUHVRXUFHIXQFWLRQVUHVSHFWLYHO\ZKLFKDUHVKRZQLQ)LJXUHVDQG  $OLJQLQJ WKHVH VXEV\VWHPV LQ WKHLU FXPXODWLYH DQG QRQFXPXODWLYH IRUPV IXOILOOV 5HVHDUFK 2EMHFWLYH  1RWH WKDWDGGLWLRQDOUHILQHPHQWVFDQEHDGGHGWRUHIOHFWWKHDIRUHPHQWLRQHGIDFWRUVVXFKDVVKLIWVdWKDWPRYHWKHVWDUW  DQGGHOD\VdWKDWPRYHWKHILQLVKLHH[SDQGGXUDWLRQ >@WRHQKDQFHLWVUHDOLVP7KLVFDQEHDFFRPSOLVKHGE\ DGGLQJWKHPWRWKHFXWRIIRIWKHVLQJXODULW\IXQFWLRQ(TXDWLRQOLQNVVXEV\VWHPVYLDWKHVFDOLQJIDFWRUVRIWKHLU SDLUZLVHYDULDEOHVIRUSURSRUWLRQDOLW\QRWZLWKVWDQGLQJWKDWWKHFXWRIILQELOOHTXDWLRQVLVIXUWKHUPRYHGDQGURXQGHG  5HVRXUFH5DWH>ZRUNHUVPRQWK@ 5HVRXUFHV>ZRUNHUV@ ry tot¶ ry tot ry B ry B¶ ry C ry A¶ ry A ry C¶ 7LPH>PRQWKV@ 7LPH>PRQWKV@

)LJ&XPXODWLYHUHVRXUFHSURILOHIRUH[DPSOH

)LJ1RQFXPXODWLYHUHVRXUFHSURILOHIRUH[DPSOH

 r ( y )i = si ⋅ ª y − aS − y − aF «¬ 



 − ( + d i ) ⋅ y − aF º  »¼

­ C Ci Ui f ( x y  z ) = ® z = i x z = y x = y Di + d i Di + d i ¯ Ui

 r ′( y )i = si ⋅ ª y − a S «¬



− y − a F



º »¼



 

,QWHUDFWLRQV

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

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

345

4.1. Integrated Model for Multi-Objective Research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fxyzbal  fxyzpay ±fxyzcost DWDQ\WLPH1RWHWKDWLQ)LJXUHWKHFXUYHV fAfBDQGfCDUHWKHWUDMHFWRULHVRILQGLYLGXDODFWLYLWLHVLQWKH'FRRUGLQDWHV\VWHPZKLOHSURMHFWLQJWKHPHJRQWR WKH'WLPHFRVWSODQH\LHOGVWKHFRVWSURILOHRIHDFKDFWLYLW\7KHLUVXPLVWKHWUDMHFWRU\RIFRVWfcostIRUWKHHQWLUH SURMHFW7KHSD\DQGEDODQFHWUDMHFWRULHVfpayDQGfbalanceLQ)LJXUHDUHVKRZQIRUWKHHQWLUHSURMHFWIRUFODULW\  7DEOH)XQFWLRQVDQGSURMHFWLRQVRIZRUNTXDQWLW\WLPHFRVWDQGUHVRXUFHUHODWLRQVKLSV )LJXUH5HIHUHQFH )XQFWLRQ 'LIIHUHQWLDWHG  >@

          

3URMHFWLRQRQWR[]3ODQH >YDULHV@

C f (x y z cost ) zcost = i ⋅ x   Ui C f (x y  z pay ) z pay = i ⋅ x  Ui s (D + d  i ) ⋅x f ( x y  r )  r = i i Ui s (D + d  i ) f (z cost  y  r ) r = i i ⋅ zcost  Ci s (D + d  i ) f (x z cost  r ) r = i i ⋅x  Ui

3URMHFWLRQRQWR\]3ODQH >YDULHV@

Ci ⋅y Di + d i Ci = ⋅y Di + d i

z cost = z pay

r = si ⋅ y  r = si ⋅ y 

r=

si (Di + d i ) ⋅ zcost Ci

3URMHFWLRQRQWR[\3ODQH >YDULHV@

Ui ⋅y Di + d i  Ui x= ⋅y Di + d i  Ui x= ⋅y Di + d i  Ci zcost = ⋅y Di + d i  C zcost = i ⋅ x Ui  x=

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µGUDJJLQJHIIHFW¶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growth pathRIWKHSURMHFWRQZKLFKHDFKSRLQWLQIRUPVKRZPXFKZRUNTXDQWLW\

346

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

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µJURZQ¶±RUUDWKHUDVVHPEOHG±IURPVXEV\VWHP PRGHOVDOOGHWDLOVIURPWKHVHVXEV\VWHPVFDQEHSUHVHUYHG%\PRGLI\LQJSDUDPHWHUVLQDQ\VXEV\VWHPLWDOORZV WR PRQLWRU WKH JOREDO HIIHFWV GLUHFWO\ 6HQVLWLYLW\ DQDO\VHV DQG RSWLPL]DWLRQ DOJRULWKPV ZRXOG JHQHUDWH RU KDQGOH JURZWKSDWKVLQIRUPRIDWUDMHFWRU\EXQGOHWKURXJKWKHSURMHFWVSDFHLQWKH'FRRUGLQDWHV\VWHP7KLVDSSURDFK ILOOVWKHPRGHOLQJJDSEHWZHHQWKHWZRDIRUHPHQWLRQHGVWHSVZKLFKPD\LPSURYHWKHHIILFLHQF\RIVXFKDOJRULWKPV  fpay

&RVW>N@

ftotal

5HVRXUFH>ZRUNHUV@





fcost









fB



fB









fbal

fA

fC

fC



 

 

fA



  







:RUN>TXDQWLW\@



ftotal

5HVRXUFH>ZRUNHUV@













7LPH>PRQWKV@

)LJ&XPXODWLYHZRUNWLPHUHVRXUFHWUDMHFWRU\

ftotal

5HVRXUFH>ZRUNHUV@





:RUN>TXDQWLW\@



)LJ&XPXODWLYHZRUNWLPHFRVWWUDMHFWRU\



fB









fC

fB



 

fC

 

fA 



 



)LJ&XPXODWLYHWLPHFRVWUHVRXUFHWUDMHFWRU\

 



&RVW>N@

 







fA





7LPH>PRQWKV@





7LPH>PRQWKV@







 

&RVW>N@



 

:RUN>TXDQWLW\@

)LJ&XPXODWLYHZRUNFRVWUHVRXUFHWUDMHFWRU\

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

347

'LIIHUHQWLDWLQJWKHFXPXODWLYHHTXDWLRQVRI7DEOH\LHOGVQRQFXPXODWLYHRQHVZKLFKDUHSORWWHGLQ)LJXUHV WKURXJKDVLQGLYLGXDODQGWRWDOFXUYHV$JDLQWKH\FDQEHSURMHFWHGRQWR'SODQHVZKLFK\LHOGV)LJXUHVDQG 1RWHWKDWVSLNHVZLWKLQ)LJXUHDUHVHSDUDWHSD\PHQWVZKLFKUHDFKDERYHWKHSODQHWKDWLVGHILQHGE\cost  DQGWKDWQRQFXPXODWLYHEDODQFHVFDQEHQHJDWLYHRUSRVLWLYH$JDLQGUDJJLQJD'SURILOHLQWRWKHWKLUGGLPHQVLRQ UHYHDOVWKHUHODWLYHLQIOXHQFHRIWKDWQHZSHUIRUPDQFHSDUDPHWHU)LJXUHGLVSOD\VWKUHHDFWLYLWLHVEDUVfAfBDQGfC E\XVLQJWKHGLIIHUHQWLDWHGIRUPRIWKHUHVSHFWLYHIXQFWLRQSHU7DEOH$GGLQJWKHP\LHOGVWKHWRWDOWUDMHFWRU\ftotal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time $QH[FHSWLRQLV )LJXUHZKLFKRPLWVWKHWLPHGLPHQVLRQWRSORWDSURGXFWLYLW\FRVWUDWHUHVRXUFHUDWHFRRUGLQDWHV\VWHP,WVWKUHH WUDMHFWRULHVGLVSOD\WKHGLIIHUHQWLDWHGIRUPRIWKHUHVSHFWLYHIXQFWLRQSHU7DEOH7KH\WUDFNKRZPXFKSURGXFWLYLW\ LVDFKLHYHGIRUVSHFLILFUHVRXUFHUDWHVDQGFRVWUDWHV6LPLODUWR)LJXUHZKLFKLPSOLHGWKHWLPHGLPHQVLRQWKH JURZWKSDWKLQ)LJXUHFDQEHGHWHUPLQHGE\WKHVHTXHQFHRIDFWLYLWLHV,WVWDUWVIURPWKHHQGRIfAresource rate   FOLPEVWRresource rate GURSVWRWKHHQGRIfBresource rate  WKHQFOLPEVDJDLQWRresource rate  GURSVWRWKHHQGRIfCresource rate  DQGILQDOO\UHWXUQVWRWKHRULJLQ7KLVXQGXODWLRQRIWKHJURZWKSDWKFDQ EHYHULILHGYLD)LJXUHVDQG1RQFXPXODWLYHWUDMHFWRULHVFDQWKXVSURYLGHYDOXDEOHLQIRUPDWLRQDERXWDSURMHFW 4.2. Singularity Functions Enabling nD Models $QLQWULJXLQJWKHRUHWLFDOSRVVLELOLW\H[LVWVWKDWDGGLQJIXUWKHUGLPHQVLRQVWRWKHDIRUHPHQWLRQHGLQWHJUDWHGPRGHO ZLOOJHQHUDWH'DQGHYHQWXDOO\n'PRGHOV7KLVZLOOFUHDWHDGGLWLRQDOLQWHUIDFHVWRUHIOHFWWKHLQWHUDFWLRQVEHWZHHQ SURMHFWSHUIRUPDQFHSDUDPHWHUV:KLOHVXFKPRGHOVDUHLPSRVVLEOHWRGLVSOD\JUDSKLFDOO\WKH\DUHHDVLO\H[SUHVVHG PDWKHPDWLFDOO\6LQJXODULW\IXQFWLRQVFDQEHXVHGWRPRGHODQGH[SORUHFRPSOH[EHKDYLRUVLQPXOWLSOHGLPHQVLRQV ZKLFKIXOILOOV5HVHDUFK2EMHFWLYHDQGRIIHUVDQRYHODYHQXHWRZDUGKROLVWLFTXDQWLWDWLYHSURMHFWPDQDJHPHQW &RQWULEXWLRQVDQG5HFRPPHQGDWLRQV

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¶VUD]RUZKRFDQEHSDUDSKUDVHGDVKDYLQJDGYRFDWHGLQFOXGLQJµDVPXFKDVQHFHVVDU\ DVOLWWOHDVSRVVLEOH¶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

348

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

,QWHJUDWLQJ IDPLOLDU JUDSKLFDO UHSUHVHQWDWLRQV WKDW DUH XVHG LQ FRQVWUXFWLRQ PDQDJHPHQW OLNH EDU FKDUWV OLQHDU VFKHGXOHVFDVKIORZSURILOHVDQGUHVRXUFHKLVWRJUDPVLVOLNHO\WRIDFLOLWDWHLWVDGRSWLRQLQWRSURIHVVLRQDOSUDFWLFH 7KHYHUVDWLOLW\RIWKHQHZDSSURDFKLVHYLGHQWLQWKDWFRPELQDWLRQVRIWKUHHRXWRIIRXUGLPHQVLRQVZRUNWLPHFRVW DQGUHVRXUFHV LQWKHFXPXODWLYHRUQRQFXPXODWLYHIRUPVDOOFRPPXQLFDWHPDQDJHULDOO\UHOHYDQWLQIRUPDWLRQDQG DOORZDµGHSWK¶RIH[SORUDWLRQWKDWKDVEHHQODFNLQJWRGDWH7KLVDSSURDFKIRVWHUVSHUFHLYLQJDSURMHFWDVDPXOWL GLPHQVLRQDOJURZLQJHQGHDYRUZKRVHWUDMHFWRU\PRYHVIURPWKHRULJLQWKURXJKWKHSURMHFWVSDFHLQWKHFRRUGLQDWH V\VWHP$WDQ\SRLQWWKHEHKDYLRULQHDFKRILWVYDULRXVGLPHQVLRQVLVSUHVHUYHGLQGHWDLODQGWKHLULQWHUDFWLRQVFDQ EHH[SORUHGDVQHHGHG)XUWKHUUHVHDUFKLVUHFRPPHQGHGWRH[SORUHVHYHUDODVSHFWVWKDWZLOOHQKDQFHWKHQHZPRGHO • 'HULYLQJDQDOJRULWKPWRWUDQVIRUPWKHXELTXLWRXVQHWZRUNEDVHG&30VFKHGXOHVZKLFKDUHZLGHO\XVHGLQWKH FRQVWUXFWLRQLQGXVWU\LQWROLQHDUVFKHGXOHVZLWKVLQJXODULW\IXQFWLRQVIRUGLUHFWLQWHJUDWLRQLQWRWKHQHZPRGHO • ,QFRUSRUDWLQJDGGLWLRQDOIHDWXUHVDQGFRQVWUDLQWVHJLQWHUUXSWLEOHDFWLYLWLHVWRH[WHQGLWVDQDO\WLFDOFDSDELOLWLHV • 4XDQWLI\LQJWKHEHQHILWRIQRWGLOXWLQJLWVOHYHORIGHWDLOZKHQDGGLQJGLPHQVLRQVWRWKHPRGHODQGPHDVXULQJWKH FRPSXWDWLRQDOHIILFLHQF\RIPXOWLREMHFWLYHRSWLPL]DWLRQDOJRULWKPVWKDWDUHDSSOLHGWRVLQJXODULW\IXQFWLRQV  &RVWUDWH >NPRQWK@

5HVRXUFHUDWH >ZRUNHUVPRQWK@



 

 

fB



fpay

ftotal

ftotal



fB



fC

fA









 

  

fbal

 

7LPH>PRQWKV@

 

 



3URGXFWLYLW\ >TXDQWLW\PRQWK@

)LJ1RQFXPXODWLYHZRUNWLPHFRVWWUDMHFWRU\

fC fA 



 

7LPH>PRQWKV@

 



 3URGXFWLYLW\ >TXDQWLW\PRQWK@

)LJ1RQFXPXODWLYHZRUNWLPHUHVRXUFHWUDMHFWRU\

349

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 – 350

5HVRXUFHUDWH >ZRUNHUVPRQWK@

5HVRXUFHUDWH >ZRUNHUVPRQWK@ 

ftotal



ftotal





fB













fC



fA



fA

 



 









&RVWUDWH >NPRQWK@

)LJ1RQFXPXODWLYHWLPHFRVWUHVRXUFHWUDMHFWRU\

fC

  



7LPH>PRQWKV@

fB



 



&RVWUDWH>NPRQWKV@

3URGXFWLYLW\ >TXDQWLW\PRQWK@

 

)LJ1RQFXPXODWLYHZRUNFRVWUHVRXUFHWUDMHFWRU\

$FNQRZOHGJHPHQWV

The support of the National Science Foundation (Grant CMMI-0927455) for portions of the work presented here is gratefully acknowledged. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily represent the views of the National Science Foundation.

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|SSO9RUOHVXQJHQEHU7HFKQLVFKH0HFKDQLN'ULWWHU%DQG)HVWLJNHLWVOHKUH>/HFWXUHVRQWHFKQLFDOPHFKDQLFV7KLUGYROXPH 6WUHQJWKRIPDWHULDOV@WKHG%*7HXEQHU/HLS]LJ*HUPDQ\ >@:+0DFDXOD\1RWHRQWKHGHIOHFWLRQRIEHDPV0HVVHQJHU0DWK  >@*/XFNR3URGXFWLYLW\VFKHGXOLQJPHWKRGFRPSDUHGWROLQHDUDQGUHSHWLWLYHSURMHFWVFKHGXOLQJPHWKRGV-&RQ(QJ0JPW   >@0+DMGX,PSDFWVRIULVNVRQSURMHFWVFKHGXOLQJ&DQRSWLPLVWLFSURMHFWGXUDWLRQEHJUHDWHUWKDQWKHSHVVLPLVWLFRQH"3URF&UHDW&RQVWU &RQI6]HQW,VWYiQ8QLYHUVLW\%XGDSHVW+XQJDU\

350

Gunnar Lucko and Yi Su / Procedia Engineering 85 (2014) 339 –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