Procedia Engineering 89 ( 2014 ) 565 – 572
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 Organizing Committee of WDSA 2014 doi: 10.1016/j.proeng.2014.11.479
ScienceDirect
WK&RQIHUHQFHRQ:DWHU'LVWULEXWLRQ6\VWHP$QDO\VLV:'6$
6FHQDULR$QDO\VLVIRU2SWLPL]DWLRQRI3XPSLQJ6FKHGXOHVLQ
&RPSOH[:DWHU6XSSO\6\VWHPV&RQVLGHULQJD&RVW5LVN%DODQFLQJ
3UREOHP
-1DSROLWDQR
D*06HFKL
D3=XGGDV
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
&RUUHVSRQGLQJDXWKRU7HOID[ (PDLODGGUHVVVHFKL#XQLFDLW
© 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/).
WUDGLWLRQDOSODQQLQJIUDPHZRUNLVJHQHUDOO\DVLQJOHIXWXUHGHWHUPLQLVWLFDSSURDFK7RDYRLGWKHULVNRIV\VWHPIDLOXUH XQGHUFRQGLWLRQVWKDWFDQVLJQLILFDQWO\FKDQJHRYHUWLPHDPXOWLSOHVFHQDULRDSSURDFKKDVSURYHQWRKDYHDGYDQWDJHV IRU PDNLQJ UREXVW PDQDJHPHQW GHFLVLRQV &RQVLGHULQJ WKH LQQHU VWUXFWXUH RI VFHQDULRV WHPSRUDO HYROXWLRQ LW LV SRVVLEOHWRREWDLQD³UREXVW´GHFLVLRQSROLF\PLQLPL]LQJWKHULVNRIZURQJIXWXUHGHFLVLRQV8VLQJDVFHQDULRWUHH EDVHGRSWLPL]DWLRQPRGHODPXOWLVWDJHGHFLVLRQPDNLQJDSSURDFKKDVEHHQGHYHORSHGLQSUHYLRXVSDSHUV>@WR GHWHUPLQHUREXVWPDQDJHPHQWRIZDWHUUHVRXUFHVV\VWHPVXQGHUXQFHUWDLQW\FRQGLWLRQV
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¶ DFWLYLWLHV LUULJDWLRQDO FLYLO LQGXVWULDO HWF 7KH FRQFHSW RI ³DGHTXDWH OHYHO´ RI IXOILOOPHQW PXVW EH GHILQHGFRQVLGHULQJERWKWKHULVNRIVKRUWDJHRFFXUUHQFHVDQGFRVWRIHDUO\ZDUQLQJDQGWKHFRQVHTXHQWO\DFWLYDWLRQ RI HPHUJHQF\ DQG FRVWO\ ZDWHU WUDQVIHUV ,Q WKH FDVH RI D ³EHWWHU VFHQDULR´ RFFXUUHQFH LH LQ WHUPV RI KLJKHU K\GURORJLFLQSXWWRUHVHUYRLUV2 0UHJUHWFRVWVVKRXOGEHPDGHDVDFRQVHTXHQFHWKDWIXWXUHVFHQDULRVVKRXOGQRW UHTXLUHSXPSLQJWKHZDWHU
6FHQDULRDQDO\VLVDSSURDFK
6FHQDULRDQDO\VLVDSSURDFKDULVHVIURPFRQVLGHULQJWKDWWKHIXWXUHHYHQWVFDQHYROYHZLWKDVHWRIGLIIHUHQWDQG VWDWLVWLFDOO\LQGHSHQGHQWVFHQDULRV7KHVLQJOHVFHQDULRGHVFULEHVDSRVVLEOHUHDOL]DWLRQRIVRPHVHWVRIXQFHUWDLQGDWHV LQ WKH H[DPLQHG WLPHKRUL]RQ ,Q D ILUVW VWHS LW LV SRVVLEOH WR ZRUN XVLQJ D FRQILJXUDWLRQ ZLWK SDUDOOHO VFHQDULRV IROORZHGE\DVLPXODWLRQDLPHGWRFRQILUPWKHUHOLDELOLW\RIHDFKVROXWLRQ(YHU\VROXWLRQLVFRPSRVHGE\DVHWRI GHFLVLRQ VHTXHQFHV WKDW VKRXOG EH WDNHQ RQ HDFK VFHQDULR DQG LW LV LQGHSHQGHQW IURP WKRVH FRQFHUQLQJ WKH RWKHUV VFHQDULRV>@,QDVHFRQGVWHSDPRGHOWKDWH[DPLQHVFRQWH[WXDOO\DVHWRIGLIIHUHQWVFHQDULRVFDQEHHODERUDWHG,W UHVSRQGVWRWKHSRVVLEOHWHPSRUDOHYROXWLRQVRIVRPHFUXFLDOGDWHVSURYLGLQJD³EDU\FHQWULFVROXWLRQ´WRWKHPXOWL SHULRGGHFLVLRQSUREOHP7RFRQVLGHUWKHPXOWLSHULRGSUREOHPWKHVFHQDULRWUHHPXVWEHEXLOWLQRUGHUWRDJJUHJDWH DOOVFHQDULRVLQRQHPRGHO7KLVDSSURDFKFDQEHUHSUHVHQWHGDVD³WUHHJUDSK´DFFRUGLQJWRDSSURSULDWHDJJUHJDWLRQ UXOHV7KHIRUPXODWLRQRIWKHVHDJJUHJDWLRQUXOHV>@JXDUDQWHHWKDWWKHVROXWLRQLQDQ\JLYHQSHULRGLVLQGHSHQGHQW RIWKHLQIRUPDWLRQQRW\HWDYDLODEOHLQRWKHUZRUGVWKH\FDQEHFRQVLGHUHGDVQRQDQWLFLSDWLYHGHFLVLRQFRQVWUDLQWV 7ZRVFHQDULRVVKDULQJDFRPPRQLQLWLDOSRUWLRQRIGDWDPXVWEHFRQVLGHUHGWRJHWKHUDQGSDUWLDOO\DJJUHJDWHGZLWKWKH VDPH GHFLVLRQ YDULDEOHV IRU WKH DJJUHJDWHG SDUW LQ RUGHU WR WDNH LQWR DFFRXQW WKH WZR SRVVLEOH HYROXWLRQV LQ WKH VXEVHTXHQWGLYHUVHSDUWV,QWKLVZD\WKHVHWRISDUDOOHOVFHQDULRVLVDJJUHJDWHGE\SURGXFLQJWKHWUHHVWUXFWXUH7KH URRWQRGHRIWKHWUHHFRUUHVSRQGVWRWKHEHJLQQLQJRIWLPHSHULRGW )URPWKLVQRGHQVFHQDULRVVWDUWDQGFRQWLQXH
LQSDUDOOHOIRU7SHULRGV$WW 7HDFKRIQVFHQDULRVLVVSOLWLQWRQVFHQDULRVDQGDOOWKHREWDLQHGVFHQDULRVQQ
FRQWLQXHLQSDUDOOHOIRUDIXUWKHU7SHULRGVXQWLOW 7ZKHQHDFKRIWKHPLVVSOLWLQWRQDGGLWLRQDOVFHQDULRV
$QH[DPSOHRIVXFKDWUHHZLWK7 7 . Q QL DQGL LVVKRZQLQ)LJ,QSODQQLQJ
SUREOHPVFRQVLGHULQJPXOWLUHVHUYRLUVXSSO\V\VWHPRQHWLPHSHULRGFRXOGFRUUHVSRQGVWRRQHPRQWKDQGZHWDNH7
ZKLFKFRUUHVSRQGVWRRQH\HDU7KLVPHDQVWKDWVSOLWWLQJRFFXUVDWWKHHQGRIHDFK\HDUZKLFKFRQIRUPVWRWKH FRPPRQVHDVRQDOSDWWHUQVRILQIORZVDQGGHPDQGV
)LJ6FHQDULRWUHH
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d d
¦
ZKHUH[JUHSUHVHQWVWKHYHFWRURIGHFLVLRQYDULDEOHVLQVFHQDULRJWKHYHFWRUFJGHVFULEHVWKHXQLWFRVWRIGLIIHUHQW
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±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¶VGHPDQGGXHWRLQKHUHQWVFDUFLW\RIWKHUHVRXUFH7KH GLIIHUHQFHEHWZHHQRULJLQDOGHPDQGVDQGUHGXFHGWDUJHW[EZLOOUHSUHVHQWWKHSODQQHGVKRUWDJHV ZKLFKWKHXVHULV DVNHGWRDFFHSWXQGHUGURXJKWFRQGLWLRQV%HVLGHVWKLVSODQQHGVKRUWDJHWKHUHFDQDOVREHXQSODQQHGVKRUWDJHVZKHQ
GXHWRVHYHUHODFNRIUHVRXUFHVXQGHUVRPHVFHQDULRVLQWKLVFDVHVXSSO\LVOHVVWKHQWKDQUHGXFHGWDUJHW,QRUGHUWR IDFHWKLVVLWXDWLRQDQGGHYHORSDQDSSURSULDWHHPHUJHQF\SROLF\WKHSURSRVHGPHWKRGRORJ\WULHVWRUHDFKD³UREXVW´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Ö PLQ J J J J> J J E @ J * S F [ J *S Z [ [ O O
¦
¦
+HUHFJLVWKHFRVWDVVRFLDWHG ZLWKIORZYDOXHV [JLQSXPSLQJ VWDWLRQV XQGHUVFHQDULRJ* Ö[J[ELVWKH
(XFOLGHDQPHDVXUHRIGLVWDQFHEHWZHHQWKHWDUJHWGHOLYHU\DQGDFWXDOGHOLYHU\WRGHPDQGVDQGZJLVWKHFRVWRIUHODWHG
XQSODQQHGGHILFLWV
7KHILUVWLWHPRIWKHREMHFWLYHIXQFWLRQLVD³FRVWIXQFWLRQ³DQGLWWULHVWRORRNIRUWKHV\VWHPIORZVFRQILJXUDWLRQ WKDW DOORZV PLQLPL]LQJ WKH FRVWV VXSSRUWHG E\ ZDWHU V\VWHP¶V PDQDJHU 7KH TXDGUDWLF VHFRQG LWHP LV WKH ³ULVN IXQFWLRQ´ LW FRXOG EH FRQVLGHUHG OLNH D QRQOLQHDU ³VRFLDO IXQFWLRQ´ LQ RUGHU WR JXDUDQWHH XVHUV¶ PDMRU SULRULW\ IXOILOOPHQWVUHIHUULQJWRIXWXUHVFHQDULRV,QWKLVZD\JLYLQJDZHLJKWWRERWKIXQFWLRQVZHFDQILQGWKHVROXWLRQRID FRVWULVNEDODQFLQJSUREOHP7KHUHODWLRQVKLSEHWZHHQFRVWIXQFWLRQDQGULVNIXQFWLRQLVUHJXODWHGE\WKHSDUDPHWHUO FDOOHG ³ZHLJKW IDFWRU´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
2SWLPL]DWLRQRI3XPSLQJ6FKHGXOHVXVLQJWKHPXOWLSHULRGQHWZRUN
3XPSVWDWLRQVDOORZWRVXSSO\VRPHGHPDQGFHQWHUVLQFULWLFDOVFHQDULRVZLWKDQLQFUHDVLQJ2 0HFRQRPLFEXUGHQ WKDW PXVW EH HYDOXDWHG DQG DFFHSWHG E\ V\VWHP PDQDJHU 7KH DLPRI WKLV SDSHU LV WR GHILQH WKH RSWLPDOSXPSLQJ VWDWLRQVDFWLYDWLRQWKUHVKROGV PDLQO\ XVLQJUHVHUYRLUV¶VWRUDJH YROXPHVOLNHWULJJHU YDOXHV7KHUHIRUH ZHKDYH WR GHILQH WKHVH YDOXHV E\ D FRVWULVNEDODQFLQJ SURFHVV FRQVLGHULQJ SXPSLQJ HQHUJ\ DQG PDQDJHPHQW FRVWV FRVW HOHPHQW DQG ZDWHU GHILFLWV IRU XVHUV ULVN HOHPHQW PLQLPL]DWLRQ 0RUHRYHU LQ WKH FDVH RI D ³EHWWHU VFHQDULR´ RFFXUUHQFHLHLQWHUPVRIKLJKHUK\GURORJLFLQSXWWRUHVHUYRLUVDULVNHOHPHQWFRXOGEHJLYHQE\WKH2 0SXPSLQJ UHJUHWFRVWVWKHPDQDJHUVKRXOGPDGHLQWKHSDVWDVDFRQVHTXHQFHWKDWIXWXUHVFHQDULRVVKRXOGQRWUHTXLUHSXPSLQJ WKHZDWHU7KHSXPSDFWLYDWLRQFDQEHGRQHRQWKHVLQJOHVFHQDULRDQGRQGLIIHUHQWVFHQDULRVWRJHWKHULQWKLVZD\ZH FDQGHILQHWKHEDU\FHQWULFDFWLYDWLRQYDOXH,QRXUPXOWLUHVHUYRLUVV\VWHPVWKUHVKROGVOHYHOVDUHPDLQO\UHIHUUHGWR UHVHUYRLU¶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¶
FRQQHFWLRQVEHWZHHQWKHP$UFVDUHGLYLGHGLQWZRW\SHVSK\VLFDODUFVGHVFULELQJVSDWLDOIORZWUDQVIHUVDQGLQWHU SHULRG DUFV GHVFULELQJ LQWLPH IORZ WUDQVIHUV 7KH PXOWLSHULRG JUDSK LV FRPSOHWHG E\ D GXPP\ QRGH ZKLFK FDQ UHSUHVHQWDQ³H[WHUQDOV\VWHP´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Ö PLQ J J J J> J J E @ L L J * S F [ J *S Z [ [ L 3K &0 O O
¦
¦
¦
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¶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
7KUHVKROGV OHYHOV IRU SXPSV DFWLYDWLRQ DUH UHIHUUHG WR VWRUHG YROXPH LQ UHVHUYRLUV WKDW VXSSO\ E\ JUDYLW\ WKH GRZQVWUHDPGHPDQGQRGH7KLVFRXOGEHUHODWHGLQVRPHFDVHVWRDVLQJOHUHVHUYRLURUWRRIWKHPLQWKHVHFRQGFDVH WKHWKUHVKROGYDOXHGHULYHVIURPWKHYROXPHVLQERWKUHVHUYRLUV7KXVLQRUGHUWRPDQDJHWKHOLIWLQJUXOH7DEOH VXPPDUL]HVWKHIXQFWLRQDOGHSHQGHQFHV
7DEOH'HPDQGFHQWHUVUHTXLUHPHQWVDQGGHILFLWFRVWV &RGH 'HPDQGFHQWUHV 'HPDQG>P\HDU@ 'HILFLWFRVW>¼P@ ' &LYLO6DUFLGDQR
' ,UULJDWLRQ2ULVWDQR ' ,QGXVWULDO&DPSLGDQR ' ,UULJDWLRQ&DPSLGDQR ' &LYLO&DPSLGDQR ' &LYLO%DX3UHVVLX 7DEOH3XPSVWDWLRQVIHDWXUHV &RGH 3XPSVWDWLRQQDPH &DSDFLW\>0PPRQWK@ 3XPSLQJFRVW>¼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¼\HDU@LQWKHFRQVLGHUHGVFHQDULRVDUHWKHIROORZLQJ3 3 3 3
6FHQDULRDQDO\VLVRSWLPL]DWLRQFRQILUPVLWVSRWHQWLDOLW\DOVRFRQVLGHULQJWKLVSUREOHPZKLOHUHDFKLQJEDU\FHQWULF YDOXHVDPRQJWKHDQDO\]HGK\GURORJLFDOVFHQDULRV7KHFRVWULVNEDODQFLQJKDVFRQWH[WXDOO\UHVWULFWHGGHILFLWULVNV IRU WKH XVHUV DQG PLQLPL]HG WKH FRVWV RI WKH V\VWHP LQ VKRUWDJH FRQGLWLRQV 7KLV PHWKRG JXDUDQWHHV DOPRVW WKH FRPSOHWHIXOILOOPHQWRIWKHZDWHUGHPDQGWKURXJKXQSODQQHGGHILFLWVPLQLPL]DWLRQDQGUDWLRQDOL]LQJHQHUJ\FRVWV
)LJ3XPSHGYROXPHVE\3DQGVWRUDJHYROXPHV>0P@PLQXVWKUHVKROGYDOXH6 5HIHUHQFHV >@63DOORWWLQR*06HFKL3=XGGDV$'66IRUZDWHUUHVRXUFHVPDQDJHPHQWXQGHUXQFHUWDLQW\E\VFHQDULRDQDO\VLV(QYLURQPHQWDO 0RGHOOLQJ 6RIWZDUH± >@'.DQJDQG./DQVH\0XOWLSHULRG3ODQQLQJRI:DWHU6XSSO\,QIUDVWUXFWXUH%DVHGRQ6FHQDULR$QDO\VLV-RI:DWHU5HVRXUFHV3ODQQLQJ DQG0DQDJHPHQW± >@$*DLYRURQVNL*06HFKL3=XGGDV&RVWULVNEDODQFHGPDQDJHPHQWRIVFDUFHUHVRXUFHVXVLQJVWRFKDVWLFSURJUDPPLQJ(XURSHDQ-RXUQDO RI2SHUDWLRQDO5HVHDUFK± >@$*DLYRURQVNL*06HFKL3=XGGDV%DODQFLQJFRVWULVNLQPDQDJHPHQWRSWLPL]DWLRQRIZDWHUUHVRXUFHV\VWHPVXQGHUXQFHUWDLQW\3K\VLFV DQG&KHPLVWU\RIWKH(DUWK±± >@575RFNDIHOODU5-%:HWV6FHQDULRVDQGSROLF\DJJUHJDWLRQLQRSWLPL]DWLRQXQGHUXQFHUWDLQW\0DWKHPDWLFVRI2SHUDWLRQ5HVHDUFK ± >@5'HPER$UREXVWDSSURDFKIRUZDWHUUHVRXUFHVSODQQLQJXQGHUXQFHUWDLQW\$QQDOVRI2SHUDWLRQV5HVHDUFK± >@*06HFKLDQG$6XOLV:DWHUV\VWHPPDQDJHPHQWWKURXJKDPL[HGRSWLPL]DWLRQVLPXODWLRQDSSURDFK$6&(-RI:DWHU5HVRXUFHV 3ODQQLQJDQG0DQDJHPHQW >@*06HFKLDQG3=XGGDV0XOWLSHULRGK\SHUJUDSKPRGHOVIRUZDWHUV\VWHPVRSWLPL]DWLRQ:DWHU5HVRXUFH0DQDJHPHQW± >@*$06'HYHORSPHQW&RUSRUDWLRQ$8VHU¶*XLGH:DVKLQJWRQ'&86$