Department of Pariaman Hospital). AIP Conference Proceedings 1902, 020002 (2017); 10.1063/1.5010619. Preface: 3rd International Materials, Industrial, and ...
Load allocation of power plant using multi echelon economic dispatch Wahyuda, Budi Santosa, and Ahmad Rusdiansyah
Citation: AIP Conference Proceedings 1902, 020007 (2017); View online: https://doi.org/10.1063/1.5010624 View Table of Contents: http://aip.scitation.org/toc/apc/1902/1 Published by the American Institute of Physics
Articles you may be interested in Sound absorption properties of kenaf bamboo particleboard at various mixing ratio and density AIP Conference Proceedings 1902, 020001 (2017); 10.1063/1.5010618 Joint decision of pricing and order quantity by considering product substitution in dual channel supply chain AIP Conference Proceedings 1902, 020005 (2017); 10.1063/1.5010622 A joint inventory policy under permissible delay in payment and stochastic demand (Case study: Pharmacy Department of Pariaman Hospital) AIP Conference Proceedings 1902, 020002 (2017); 10.1063/1.5010619 Preface: 3rd International Materials, Industrial, and Manufacturing Engineering Conference (MIMEC2017) AIP Conference Proceedings 1902, 010001 (2017); 10.1063/1.5010617 A mixed integer linear programming model for operational planning of a biodiesel supply chain network from used cooking oil AIP Conference Proceedings 1902, 020006 (2017); 10.1063/1.5010623 A supply chain model to improve the beef quality distribution using investment analysis: A case study AIP Conference Proceedings 1902, 020003 (2017); 10.1063/1.5010620
/RDG$OORFDWLRQRI3RZHU3ODQWXVLQJ0XOWL(FKHORQ (FRQRPLF'LVSDWFK :DK\XGDD %XGL6DQWRVDDQG$KPDG5XVGLDQV\DK 1
Industrial Engineering Universitas Mulawarman, Samarinda, Indonesia 2 Industrial Engineering ITS, Surabaya, Indonesia D &RUUHVSRQGLQJDXWKRU:DK\XGD#JPDLOFRP
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
3rd International Materials, Industrial and Manufacturing Engineering Conference (MIMEC2017) AIP Conf. Proc. 1902, 020007-1–020007-9; https://doi.org/10.1063/1.5010624 Published by AIP Publishing. 978-0-7354-1590-4 /$30.00
020007-1
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
/,7(5$785(5(9,(: (TXDOLW\DQG,QHTXDOLW\&RQVWUDLQWVLQ(FRQRPLF'LVSDWFK $OORFDWLRQRIWKHHFRQRPLFORDGGLVSDWFKSODQWLQLWLDOO\KDGRQHREMHFWLYHIXQFWLRQDQGLVXVXDOO\LQWKHIRUPRI IXHO FRVW PLQLPL]DWLRQ RU WKH PLQLPL]DWLRQ RI WKH XVH RI FRDO DV FRQWDLQHG LQ >@±>@ 2QH RI WKH FRQVWUDLQWV LQ HFRQRPLFGLVSDWFKLVWKHSRZHUEDODQFHFRQVWUDLQWZKLFKFDQEHZULWWHQDVIROORZV N
¦ Pit
PDt
i
:KHUHܲ௧ WKH.:JHQHUDWHGIURPXQLWLDWWLPHWܲܦ௧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i PLQ d Pi t d Pi PD[ :KHUHܲ LVWKH.:JHQHUDWHGIURPXQLWLܲ LVWKHPLQLPDODQGܲ௫ LVWKHPD[LPDOSRZHU
7KH&RVW)XQFWLRQLQ3RZHU*HQHUDWLRQ 7RREWDLQDFHUWDLQDPRXQWRIHOHFWULFDORXWSXWLWWDNHVDQXPEHURIIXHOLQSXWZLWKDFHUWDLQDPRXQWIXHOLQSXWV FDQ EH PHDVXUHG LQ WRQV KRXU RU 0%WXV KRXU )XHO FRVWV LV GHQRWHG E\ ,'5WRQ DQG LQSXW IRU SRZHU SODQWV LV H[SUHVVHGDV,'5KRXU,IWKHLQSXWRXWSXWFXUYHIRUSODQWLLVDVVXPHGDVDTXDGUDWLFIXQFWLRQWKHQLWFDQEHZULWWHQ DVIROORZV Cit ai Pi t bi Pi t ci ,IWKHLQSXWRXWSXWFKDUDFWHULVWLFVIRUGLIIHUHQWSODQWVDUHLGHQWLFDOWKHQDOOSODQWVFDQEHDVVLJQHGZLWKWKHVDPH ORDG%XWLQIDFWWKHSRZHUSODQWVKDYHGLIIHUHQWFKDUDFWHULVWLFVRILQSXWRXWSXW7KLVPHDQVWKDWZLWKWKHVDPHDPRXQW RIIXHOHDFKSODQWPD\QRWSURGXFHWKHVDPHDPRXQWRISRZHU7KHUHIRUHHDFKSODQWKDVDGLIIHUHQWDOORFDWHGORDGLQ RUGHUWRREWDLQPLQLPXPFRVW
3RZHU/RVVLQ7UDQVPLVVLRQ'LVWULEXWLRQ $FFRUGLQJWR>@RKPLFSRZHUORVVLVIRUPXODWHGDVIROORZV
020007-2
Loss I RkW km phase :KHUHLLVWKHFXUUHQWDORQJWKHWUDQVPLVVLRQQHWZRUNGLVWULEXWLRQDQG5LVWKHUHVLVWDQFHDORQJWKHQHWZRUN ఘ WUDQVPLVVLRQGLVWULEXWLRQܴ ൌ ȡ UHVLVWLYLW\RIOLQHWUDQVPLVVLRQ/ WKHOHQJWKRIWKHOLQH$ WKHFURVVVHFWLRQDO DUHDRIWKHOLQH
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h ik GHPDQGIRUSURGXFWk LQPDUNHWi f j IL[HGFRVWRIORFDWLQJDZDUHKRXVHDWFDQGLGDWHVLWHj k c ijm FRVWRISURGXFLQJRQHXQLWRISURGXFWk DWSODQWm DQGVKLSSLQJLWWRPDUNHWYLDDZDUHKRXVHDWFDQGLGDWH ORFDWLRQj s mk FDSDFLW\RISODQWm IRUSURGXFWLRQRISURGXFWk M FDSDFLW\RISODQWm IRUSURGXFWLRQRISURGXFWk k c ijm IORZRISURGXFWk IURPSODQWm WRPDUNHWYLDZDUHKRXVHj
Xj
^
LI ZHORFDWHDZDUHKRXVHDWFDQGLGDWHVLWH M LI QRW
:LWKWKLVQRWDWLRQZHFDQIRUPXODWHDVLPSOHSURGXFWLRQGLVWULEXWLRQSUREOHPDVIROORZV k k 0LQLPL]H fjX j c ijm Yijm
¦ j
6XEMHFWWR
¦¦¦¦ i
m
k
j
m
k ijm
d MX j
k
k ijm
t hik
k ijm
t S mk
¦¦ Y i
m
¦¦¦ Y ¦¦ Y i
j
j
k Yijm t
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
020007-3
SRZHU SODQW FDQ EH VHHQ LQ 7DEOH &RVW.: WUDQVPLVVLRQ LQ 7DEOH DQG ORDG EXV LQ WDEOH 7KH FDSDFLWLHV RI WUDQVPLVVLRQDQGGLVWULEXWLRQVXEVWDWLRQVDUHUHVSHFWLYHO\.:OLQH.: DQG.:OLQH.: 7UDQVPLVVLRQQHWZRUNDQGGLVWULEXWLRQQHWZRUNFDSDFLWLHVDUHUHVSHFWLYHO\0:DQG0: 7$%/('LVWDQFH%HWZHHQ3RZHU3ODQWVDQG7UDQVPLVVLRQ6XEVWDWLRQDQG&RVW(DFK.Z.P
3 3 3
*7 NP NP NP
*7 NP NP NP
*7 NP NP NP
7$%/('LVWDQFH%HWZHHQ7UDQVPLVVLRQ6XEVWDWLRQVDQG/RDGDQG&RVWHDFK.Z.P
*7 *7 *7
*' NP NP NP
*' NP NP NP
*' NP NP NP
*' NP NP NP
*' NP NP NP
*7 NP NP NP
7$%/('DWDRI3RZHU3ODQWV
3 3 3
D
E
F
0D[ .:
0LQ .:
85 .:
'5 .:
7$%/(/RDG%XV±,Q.Z
7LPH W
/RDG *'
/RDG *'
/RDG *'
/RDG *'
/RDG *'
/RDG *'
02'(//,1*2)6,1*/(2%-(&7,9(08/7,(&+(/21(&2120,&',63$7&+ 620((' 7KLVGHYHORSPHQWSURFHVVLVEDVLFDOO\GLYLGHGIRXUSDUWVQDPHO\ (VWDEOLVKPHQWRIDFRQFHSWXDOPRGHO ,GHQWLILFDWLRQRIYDULDEOHVDQGSDUDPHWHUV )RUPXODWLRQRIPRGHOV ,QWHUQDOYDOLGDWLRQ
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
020007-4
*HQHUDWRU L
7UDQVPLVVLRQVXEVWDWLRQ M
dƌĂŶƐŵŝƐƐŝŽŶĐŽƐƚ
ŝƐƚƌŝďƵƚŝŽŶŽƐƚ
'LVWULEXWLRQVXEVWDWLRQ N
*HQHUDWRU
7UDQVPLVVLRQ VXEVWDWLRQ
'LVWULEXWLRQ VXEVWDWLRQ
*HQHUDWRU
7UDQVPLVVLRQ VXEVWDWLRQ
'LVWULEXWLRQ VXEVWDWLRQ
&RQVWUDLQW &DSDFLW\RI 7UDQVPLVVLRQ QHWZRUN
&RQVWUDLQW &DSDFLW\RI 'LVWULEXWLRQ QHWZRUN
(QHUJ\LQ HQHUJ\RXW (QHUJ\RXW HQHUJ\LQ
7UDQVPLVVLRQ VXEVWDWLRQM
*HQHUDWRUL
&RQVWUDLQW &DSDFLW\RI WUDQVPLVVLRQ VXEVWDWLRQ
&RQVWUDLQW *HQHUDWRUOLPLW
'LVWULEXWLRQ VXEVWDWLRQN &RQVWUDLQW &DSDFLW\RI GLVWULEXWLRQ VXEVWDWLRQ
3RZHU%DODQFH
),*85(&RQFHSWXDO0RGHOIRU620(('
,GHQWLILFDWLRQRI9DULDEOHVDQG3DUDPHWHUV x 'HFLVLRQVYDULDEOH ܲ 7KH DPRXQW RI HOHFWULF SRZHU JHQHUDWHG E\ SRZHU SODQW L WKDWLV VHQW WKURXJK WUDQVPLVVLRQ M WR PHHW WKH GHPDQGLQGLVWULEXWLRQVXEVWDWLRQN
Yi t Y j t Yij
X jk
^ ^ ^ ^
LI SRZHUSODQWLDVVLJQHGDWVLWHW LI QRW
LI WUDQVPLVVLRQVXEVWDWLRQ MDVVLJQHGDWW LI QRW
LI SRZHUSODQWLWUDQVIHUWR M LI QRW
LI WUDQVPLVVLRQVXEVWDWLRQ MWUDQVIHUWRN LI QRW
x 3DUDPHWHUV 7KHGHPDQGIRUHOHFWULFLW\LQORDGEXVNDWWLPHW ୩୲ ܲ௫ 7KHPD[LPDO.:JHQHUDWHGIURPXQLWL ܲ WKHPLQLPDO.:JHQHUDWHGIURPXQLWL WKH.:JHQHUDWHGSRZHUSODQWLDWWLPHW ܲ௧ WKH.:HQHUJ\GHOLYHUHGIURPSRZHUSODQWLWRWUDQVPLVVLRQVXEVWDWLRQMDWWLPHW ܲ௧ WKH.:HQHUJ\GHOLYHUHGIURPVXEVWDWLRQMWRORDGEXVNDWWLPHW ܲ௧ WKH.:GHOLYHUHGIURPSRZHUSODQWLWRORDGEXVNYLDWUDQVPLVVLRQVXEVWDWLRQMDWWLPHW ܲ௧ &DSDFLW\RIOLQHWUDQVPLVVLRQIURPSRZHUSODQWLWRWUDQVPLVVLRQVXEVWDWLRQMDWWLPHW ܮ௧ &DSDFLW\RIOLQHGLVWULEXWLRQIURPWUDQVPLVVLRQVXEVWDWLRQMWRORDGEXVNDWWLPHW ܮ௧ ܶ௫ 0D[FDSDFLW\RIWUDQVPLVVLRQVXEVWDWLRQ ܦ௫ 0D[FDSDFLW\RIGLVWULEXWLRQVXEVWDWLRQ 8SZDUGDQGGRZQZDUGUDPSOLPLWVRILWKSRZHUSODQWUHVSHFWLYHO\.: 85L'5L
020007-5
0RGHO)RUPXODWLRQ 7KHREMHFWLYHIXQFWLRQLVWRPLQLPL]HWKHWRWDOFRVW&RVWLQWKLVFDVHLVWKHSRZHUJHQHUDWLRQFRVWVWUDQVPLVVLRQ FRVWVDQGGLVWULEXWLRQFRVWV7KHREMHFWLYHIXQFWLRQLVIRUPXODWHGDVIROORZV t T j J i I
t T i I
0LQLPL]H Z
¦¦
Cit
t i
&LW
t T k K j J
¦¦¦
f ij Pijt
t j i
¦¦¦ g
jk P jkt
t k j
WKHJHQHUDWLRQFRVWIRUWKHSODQWW\SHLDWWLPHW,'5 C it &RQVWDQWD
a i Pi t bi Pi t c i
DLELFL WUDQVPLVVLRQFRVWVLQOLQHLM,'5.: ILM GLVWULEXWLRQFRVWVLQOLQHMN,'5.: JMN WKH.:IURPSRZHUSODQWLWRWUDQVPLVVLRQVXEVWDWLRQMDWWLPHW.: 3LMW WKHDPRXQWRIHOHFWULFLW\VXSSOLHGWRWKHORDGEXVMNIURPWUDQVPLVVLRQVXEVWDWLRQMDWWLPHW.: 3MNW &RQVWUDLQWV *HQHUDWLRQ/LPLW Pi PLQ Yi d Pi t d Pi PD[ Yi
&DSDFLW\7UDQVPLVVLRQDQG'LVWULEXWLRQ1HWZRUN Pijt d Lij X ij P jkt d L jk X
jk
&DSDFLW\RI7UDQVPLVVLRQ6XEVWDWLRQDQG'LVWULEXWLRQ6XEVWDWLRQ Pijt d T jPD[ Y j P jkt d D kPD[ Yk
3RZHU%DODQFH Pijkt
Lk Tloss ijt Dloss jkt T
K
J
¦¦¦¦ P
Pit
I
ijkt
t k j i
T
Pijt
K
J
¦¦¦ P
jkt
Tloss ijt
t k j
T
P jkt
K
¦¦ L
kt
Dloss jkt
t k
5DPS5DWH
Pi t Pi t d URi
Pi t Pi t d DRi
(FKHORQQHWZRUN
X ij d Yi
X
d Yj
jk
020007-6
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±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
7$%/(2SWLPDO/RDG$OORFDWLRQZKHQ*7GRHVQRW:RUNZLWK7RWDO&RVW,'5
*7
*7
3NZ
3NZ
3NZ
*7
7RWDO
*'
*'
*'
*'
*'
*' 7RWDO
*7
*7
*7
7ORVVNZ
'ORVV
3NZ
3NZ
3NZ
*7
*7
*7
7ORVVNZ
'ORVV
3NZ
*7
3NZ
*7
3NZ
*7
7ORVVNZ
'ORVV
020007-7
7$%/(2SWLPDO/RDG$OORFDWLRQZKHQ3,PSDLUHGZLWKD7RWDO&RVWRI,'5
W
*7
*'
*'
*7
*7
*7
3NZ
3NZ 7ORVVNZ 3NZ 3NZ
7RWDO
*7
*7
*7
3NZ
*7
*7
*7
3NZ
7RWDO
*'
7ORVVNZ
*'
'ORVV
*'
3NZ
*'
7ORVVNZ
*7
3NZ
*7
3NZ
'ORVV
'ORVV
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
5()(5(1&(6