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u}= QO xv}y@ ?=wH uDi=} |=Q@ "OW=@ QDl}ORv C}ak=w x@ |tm p@k |=ypOt x@ C@Uv xOWu}= =@ |OOa p=Ft u}OvJ R}v =yDv= QO "CU= xOW xO=iDU= l}DvS sD} Qwor= VwQ R= 'pOtQO u; O}=wi w =yC}r@=k w |O=yvW}B OQm} wQ ?wN |}=Q=m Qou=}@ u; G}=Dv xm xOW pL VwQ
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"OW Oy=wN3�CLSC� xDU@xkrL u}t-=D |xQ}HvR R= |irDNt |=yx@vH Q}N= |=yxyO QO'|OwHwt pQDvm 'O}rwD |R} Qxt=vQ@ '|v}@V}B xrtHR= &CU= xDiQo Q=Qk j}kLD OQwtw CU= xQ}HvR pm OwU |R=Uxv}W}@ hOy j}kLD u}= QO "|@=}u=mt w C} Q}OtpQDvm 'O}rwDR=@/O}rwD |R} Qxt=vQ@ 'ptaDUt CqwYLt |Qw;`tH |=yx@vH 'u; QO"CU= xOw@ Q_v OtCi=} R=@ w R} QQwO '�CWoQ@ 'O}rwDR=@ 'O}rwD� |Q=BUuwQ@ '|OwHwt'OHvo|t xDU@xkrL sDU}U l} QO O}rwDR=@ w O}rwD |=yC}r=ai xm |t=ovy
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[2]"OvQ@|t xQy@ xDU@xkrL u}t-=D|=}=Rt R= |@ wNx@ 1�OEM� |mO} C=a]k u=oOvvmO}rwD '`}=vY R= |Q=}U@ QOC@Uv |QDW}@ Vv=O =yCmQW xvwou}= xm =QJ 'OvQ@|t xQy@ O}rwDR=@ w Ci=} R=@hOy =@ OvQO=k xv}tR u}= QO p=ai |=yCmQW u}vJty "OvQ=O pwYLt w Q=R=@ x@w O}rwD |=yC}r=ai x@ u=tRsy Qw]x@ �xDU@xkrL� xQ}HvR pm VRQ= |R=Uxv}y@xO=iDU= hQYt Q=@l} |=yu}@ QwO 2l =OmCmQW p=Ft u=wvax@ [3]"OvR=OQB@ O}rwDR=@|=y|SD=QDU= [4]"Ovm|t |Qw;`tH �Q=R=@� u=} QDWt R= OOHt |xO=iDU= |=Q@ =Q xOW|m}vwQDmr= |=yu}W=t '=yQoB=J Q}_v ��hrDNt `}=vY QO u=wD|t =Q |Q=}U@ x@=WtuOv=OQoQ@ w xOW xO=iDU= CqwYLt O}rwDR=@ [5w4]"OQmxOy=Wt �� u}W=t C=a]k wQ=m u}= =@ xmr@ 'CU= Qw;OwU u=} QDWt w CU} R \}Lt |=Q@ =yvDxv 'Q=R=@ x@ =yu;
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[3]"OQ=O OwHw xDU@xkrL u}t-=D |xQ}HvR|xQ}HvR |xv}tR QO VywSB 180 R= V}@ 2005 =D 1995 |=yp=U u}@ QO'Ov}=Qi '|OwQw pt=W xDU@xkrL |=ysDU}U [1]"CU= xOW QWDvt xDU@xkrL u}t-=D"CU= xDiQo Q=Qk|UQQ@ OQwt xv=o =OH Qw]x@ =yu;|oty xm OvDUy|HwQN w Q=DN=U|a]kQ}e C=P x@ w xOw@ |a]k 'xv}tR u}= QO OwHwt |[=} Q |=ypOt QFm = |rw|R=Uxv}W}@ |=Q@ [21]"CU= xOWv |i=m xHwD p�=Ut xvwou}= QO CWoQ@ w =[=kDR= "CU= |QwQ[ w sRq `t=H |rOt x@ |UQDUO 'xDU@xkrL u}t-=D |xQ}HvR OwUu; pL 'OvwW|t `}tHD pOt l} QO hrDNt |=yx@vH xm |t=ovy 'Qo}O |wUQ=}U@ `t=H pOt |=Q@ =Q=m pL |xw}W l} |x�=Q= u}=Q@=v@ "OwW|t xO}J}B Q=}U@|rwYLtOvJ O}rwD |R} Qxt=vQ@ |xDU@xkrL pOt l} u}kkLt [3]"CU= |QwQ[C}i}m w u=R}t w 'CU= |a]kQ}e CWoQ@ w =[=kD u=R}t u; QO xm [3]OvOQm x�=Q=pOt u}= QO "CU= xOW xDiQo Q_v QO CWoQ@ Ct}k R= |a@=D |DWoQ@ CqwYLtCqwYLt C}i}m u}vJty w CqwYLt CWoQ@ Ct}k u}}aD |}=v=wD xOvvmO}rwDVwQ xm xOW O=yvW}B Sv=Qo q |R=UO=R; OQm} wQ pOt u}= pL |=Q@ "OQ=O =Q |DWoQ@\UwD QwmPt pOt pL =@ "OUQ|t Q_v x@ xv}y@ x@ l}ORv ?=wH uDi=} |=Q@ |@ wN
"OW xO}WN@ Ow@y@ ?=wH C}i}m 'R}v [22]l}DvS sD} Qwor==@ "CU= xOW x�=Q= xYqN CQwYx@ xRwL u}= C=}@O= R= |}=tv 1 pwOH QO|=yxv}tR QO |}=y<qN Rwvy 'OwW|t xOy=Wt w[wt C=}@O= QO xm xJv; x@ xHwDQo}O |=yxRwL QO xD@r= "OwW|t xOy=Wt =ypOt QO C}a]k sOa w |OwHwt pQDvm|xRwL QO |rw xOW xDN=OQB |OwHwt pQDvm EL@t x@ |@ wNx@ 'u}t-=D |xQ}HvR|OwHwt pQDvm xm|D=k}kLD 'C}a]k sOa uDiQo Q_v QO =@ w xDU@xkrL u}t-=D |xQ}HvR
"OvOwOat Q=}U@ OvW=@ xOv=Hvo OwN pOt QO R}v =Q?wULt |O}rwD |=yx=ov@ QO =yxv} Ry u} QDsyt R= |m} |OwHwt |=yxv} Ry'|Qw;OwU u=R}t u; `@Dr=@ w VOQo QO x}=tQU u=R}t Ov=wD|t =yu; pQDvm w xOWQO u=wD|tv ,qwtat Qo}O hQ] R= "OyO V}=Ri= =Q CtON K]U w |Q}PBC@=kQ|xty QO q=@ C}iQ_ uDiQo Q_v QO w O=O Q}}eD =Q xv=NQ=m C}iQ_ u=R}t xQwO QyQO OUQ|t Q_v x@ p}rO u}tyx@ "O=O Oy=wN V}=Ri= =Q Q=@ QU |=yxv} Ry R}v =yxQwOuDiQo Q_v QO '=[=kD x@ |} woMU=B |=Q@ =yVwQ u} QDy@ R= |m} |a]k Q}e |=ypOt|=Q@ "OW Oy=wN R}v pOt |oO}J}B V}=Ri= Ea=@ C}r@=k u}= xD@r= "OW=@ |OwHwt|}xQwOlD |=ypOt |=Q@ &OwWZQi |}xQwOOvJ O}=@ pOt '|OwHwt uDiQo Q_v QOsOa p}rOx@ '|a]k Q}e |=ypOt QO u}vJty "OQ=Ov |}=vat |OwHwt |xv} RyV}=Ri= =Q pOt |oO}J}B u; |xv} Ry w |OwHwt u=R}t |x@U=Lt '=[=kD C}a]kVwQ "CUH xQy@ u=wD|t VwQ wO R= |OwHwt |xv} Ry |x@U=Lt |=Q@ "OyO|t
|=Q@ u}kkLt "CU= �O}rwDR=@ w O}rwD |=yOv}=Qi u}@ |ovy=ty� Vr=J u} QD|rY=[7]Ov=xO=O O=yvW}B |rOt xDU@xkrL sDU}U l} |OwHwt pQDvm w O}rwD |R} Qxt=vQ@|t=tD R= w xOW xDiQo Q_v QO u=tRty Qw]x@ O}rwDR=@ w O}rwD |=yC}r=ai u; QO xmOvtxQy@ u=} QDWt |=[=kD |R=UxOQw;Q@ |=Q@ u=wD|t �|O}rwDR=@ w |O}rwD� CqwYLt"1 %Ov=xO=O Q=Qk |UQQ@ OQwt =Q pQDvm |SD=QDU= wO OwN C=ar=]t QO =yu; "OW&OvwW|t O}rwDR=@CYQi u}rw= QO|DWoQ@ CqwYLt|t=tD u; QO xm Q=Wi |SD=QDU=O}rwDR=@ QDQ}O u=mtq=|DL |DWoQ@ CqwYLt |t=tD u; QO xm |WWm |SD=QDU= "2|=y|UQQ@ R= |m} QO "�OvwW|tv O}rwD 'OvW=@ xDW=Ov =[=kD xm |v=tR =D� OvwW|t[8]'O}rwDR=@/O}rwD |O} Q@}y sDU}U l} |xv}y@ |=yCr=L XwYNQO xOWs=Hv=xJv=vJ w OvwW |O}rwDR=@ CqwYLt u} Ro}=H Ow@tm s=ovy Ovv=wD|t wv CqwYLt
"OW Oy=wNv O}rwD wv CqwYLt 'OW=@ O=} R |i=m OL x@ O}rwDR=@ u=R}tR= xO=iDU= =@ [9]'O}rwDR=@ w O}rwD |=Q@ |O=yvW}B |@}mQD |=ysDU}U R= |m} QO"OwW|t p}rLD w x} RHD |@}mQD sDU}U |=} wB OQmrta '|R=Ux}@W w pQDvm |x} Q_v|=y|SD=QDU= p}rLD w x} RHD |=Q@ |R=UpOt ?wJQ=yJ l} u=QoVywSB u}vJty|O} Q@}y sDU}U l} QO O}rwDR=@ w O}rwD u}@ |ovy=ty w �QN-=D w sOkD� |r=wDw |}xQwOOvJ �MIP� K}LY OOa pOt l} Qo}O |wU R= [4]"Ov=xOQm |iQatS=DvwtO O}rwDR=@ |=Q@ |DWoQ@ CqwYLt u; QO xm [5]Ov=xOQm x�=Q= |rwYLtOvJCU=wNQO "1 %OQ=O ?=NDv= wO C=a]k u}t-=D |=Q@ xOvvmO}rwD 'pOt u}= QO "OvwW|tptaDUtCqwYLt |wQ|U=U=C=Q}taD s=Hv= "2 &QDq=@K]U u=oOvvmu}t-=D R= xa]kCq}yUD |@=}=H K}LYOOa pOtl} R}v u}kkLt Qo}O "=yu; R= xQ=@ wO |xO=iDU= w\=@DQ= =yu; pOt Cwk |x]kv [10]"OvO=O \U@ Twmat l}DUHr |xRwL QO =Q
"CU= u=tR =@ CqwYLt Ct}kl} QO |OwHwt pQDvm |=Q@ u}kkLt xm EPQ w EOQ u=t-=wD pOt QOwv CqwYLt O} QN j} Q] R= =Q =[=kD u=wD|t [11]Ov=xO=O x�=Q= xDU@xkrL sDU}UXwYNQO xOt; ptax@ C=ar=]t QO "OQm <=[Q= ptaDUt CqwYLt O}rwDR=@ =}w O}rwD u}@ C}iQ_ |ovy=ty [12]?=v O}rwD \}Lt QO Twmat l}DUHr sDU}Uxv}y@ CU=}U uDi=} |xQ=@ QO w xDiQo Q=Qk p}rLD w x} RHD w |UQQ@ OQwt O}rwDR=@
"CU= xOW EL@ =ysDU}U xvwou}= |=Q@'O}rwD Ov}=Qi QO |ovy=ty O=H}= Q@ xwqa xOvvmO}rwD xDU@xkrL sDU}U l} QOxrtHR= "OW=@ xDW=O xHwD R}v CWoQ@ w =[=kD C}a]k sOa QO uR=wD O=H}= x@ O}=@O=H}= x@ u=wD|t 'OvwW|t O}rwDR=@ |=ysDU}U QO |oO}J}B O=H}= Ea=@ xm |OQ=wtCqwYLt C}tm w C}i}m QO C}a]k sOa R}v w 'CWoQ@ w =[=kD u}@ uR=wD|=ysDU}U QO |OwHwt pQDvm |xr�Ut p}rLD w x} RHD QO [13]"OQm xQ=W= |DWoQ@w OvDU}v xDU@=w Qo}Om} x@ CWoQ@ w =[=kD xm OvOQm ZQi u}kkLt [14]xDU@xkrLl}DUHr pOtl} QO |OwHwt pQDvm |xar=]t QO "Ovvm|tC}a@D uwU=wB `} RwD R=|xt=vQ@ Q@ pwYLt CWoQ@ u=R}t Q}F-=D hwmQ=t Ov}=Qi R= xO=iDU= =@ [15]'TwmatQO pwYLt Ci=} R=@ |=yVr=J XwYNQO xar=]t "OW |UQQ@ |OwHwt |xv}y@swOat w Ci=} R=@ 'O}rwD |=yC}r=ai uR=wD xm O=O u=Wv [16]xDU@xkrL sDU}U l}"OQ}o CQwY CWoQ@ w =[=kD C}a]ksOa uDiQo Q_vQO =@ O}=@ CqwYLt uOQm
pair=@ |O=YDk= |=yC}@=PHp}rLD |=Q@|@ wJQ=yJ OwNC=ar=]t QOu}kkLts=ovy CU= QDy@ xm OyO|t u=Wv =yu; C=}@ QHD [6]"OvOQm x�=Q= CqwYLt O}rwDR=@C} Q}Ot R= u=wD|tu}vJty &OwW xHwD =yu;C}i}m x@ptaDUtCqwYLt |Qw;`tHxO=iDU= CWoQ@ u=R}t pQDvm Q=R@= u} QD|rY= u=wvax@ ptaDUt CqwYLt CWoQ@CqwYLt C}tm w C}i}m Ovvm|t O=yvW}B [17]u=v; xm |O}rwDR=@ sDU}U QO "OQm"OQ=O |oDU@ �Q=R=@ R= ptaDUt CqwYLt O} QN Ct}k� CWoQ@ Ct}k x@ |DWoQ@
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Q=}U@ |=y?=wH 'Q_v OQwt pL OQm} wQ =@ xmCU= Qt= u}= R=|m =L xrY=LG}=DvxOvQ}os}tYD Q=}DN= QO |O}it C=aq]= w xOW =O}B |@ wNx@ xv}y@ ?=wH x@ l}ORvOy=wN O}it Q=}U@ COtu=}t Kw]U C=t}tYD |=Q@ C=aq]= u}= "CiQo Oy=wN Q=Qk
"Ow@u; C=}[Qi w pOt Oa@ CtUk QO %CU= CQwY u}= x@ xr=kt u}= Q=DN=U|R=UpOt |]NQ}e |R} Qxt=vQ@ CQwYx@ xOW |iQat pOt TBU "OwW|t |iQats}=xDN=OQB pL OQm} wQ |iQat x@ sQ=yJ VN@ QO 'xt=O= QO "�swU VN@� OwW|tp=Ft l} 'u; |@=} RQ= w pL OQm} wQ 'pOt QDW}@ K}[wD |=Q@ sHvB CtUk QO w|OOa p=Ft 360 'pL VwQ |@=} RQ= |=Q@ sWWCtUk QO "CU= xOW pL |OOaw |Q}oxH}Dv x@ R}v |v=}=B CtUk "CU= xOW pL w O}rwD |iO=YD CQwYx@ |vOW
"CU= xOW xO=O X=YDN= |D; C=k}kLD |=Q@ O=yvW}B
pOt |iQat "2|OwHwt pQDvm w O}rwD |R} Qxt=vQ@ pOt l} Q=DWwv u}= QO xOW O=yvW}B pOt"Ov=|a]kQ}eCWoQ@ w =[=kD u; QO xmCU= xDU@xkrL sDU}Ul} |=Q@ |}xQwOlD|=yu}@ QwO Ovv=t �� sm Qtapw] =@ CqwYLt x@ u=wD|t pOtu}= |=yOQ@ Q=m xrtH R=
95 CtON K]U QO p=Ft u=wvax@ &CU= CtON K]U l} uDiQo Q_v QO pw=95 s} wW u�t]t =D xOW xQ}NP Q=@v= QO u=v}t]= |OwHwt |Q=Okt xW}ty 'OYQO|=[Q= |wQ u=wD|t swO VwQ QO "OW Ovy=wNv xH=wt Ow@tm =@ =y=[=kD OYQO'u; QO xm CU= xOW xO=iDU= swO VwQ R= xar=]t u}= QO "OQm h} QaD w} Q=vU =[=kD|DQwY QO w xOQm =[Q= =Q u; 'OW=@ |i=m |OwHwt xJv=vJ =[=kD Ci=} QO s=ovys}y=wN x[Qa |OwHwt u=R}t |xR=Ov=x@ \ki 'OW=@ |OwHwt R= V}@ =[=kD xm?}DQD u}= x@ "OwW|t xH=wt �xDiQ CUO R= VwQi� Ow@tm =@ =[=kD |k@=t w CW=OK]U h} QaD x@ |R=}v w xOQm |Q=Oxov xv}y@ OL QO =Q |OwHwt u=R}t hOy `@=D
"CU}v CtON'�OW xO=O K}[wD ,q@k xm � [3]u=Q=mty w |W\UwD xOW x�=Q= pOt xr=kt u}= QO�CWoQ@ 'O}rwDR=@ 'O}rwD� |Q=BUuwQ@ w |OwHwt pQDvm |=yC}r@=k uOv=Hvo hOy =@xm CU= xOW ZQi [3]u=Q=mty w |W pOt QO u}vJty "CU= xOW xO=O \U@w xOW Zkv ZQi u}= pOt u}= QO |rw OvO}rwDR=@ p@=k |DWoQ@ CqwYLt |t=tD'OvW=@v O}rwDR=@ p@=k |DWoQ@ CqwYLt R= |OYQO CU= umtt xm ZQi u}= =@Ci=} R=@ |=yxv} Ry CLD R}v |}=yxv} Ry p}rO u}tyx@ "CU= xOW s=Hv= |R=UpOtu=wD|t 'ptaDUt CqwYLt Ci=} R=@ R= TB xD@r= "OvwW|t xDiQo Q_v QO R} QQwO w"OQm u=Q@H =Q =yxv} Ry u}= R= |Q=Okt w Ov=UQ VwQi x@ s=N O=wt u=wvax@ =Q =yu;
"CU= xOW xO=iDU= l}DvS sD} Qwor= OQm} wQ R= 'pOt u}= pL |=Q@
43
"""pQDvm
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R}Qxt=vQ@
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x�=Q=pwYLtCWoQ@Ct}k R= QF-=Dt ptaDUt CqwYLt |Qw;`tH |Q=BUuwQ@Ct}ku}= |=yQDt=Q=B "CU= Q=QkQ@ =yu; u}@ Boi = coe � Pri |x]@=Q w CU=
"CU= xOW |iQat swU CtUk QO R}v x]@=Q
|R=UpOt "3%OvwW|t h} QaD Q} R CQwYx@ pOt |=yQDt=Q=B w =yT}Ov=
&=yxQwO T}Ov= %(I; :::; 1) i%=yQDt=Q=B
&xOW O}rwDR=@/O}rwD pwYLt |Q=Oxov |xv} Ry %h&|DWoQ@ pwYLt |Q=Oxov |xv} Ry %hr
&�x}rw= O=wt ?=UDL= =@� wv pwYLt O}rwD |xv} Ry %Cp&�cp R= QDsm � |DWoQ@ pwYLt O}rwDR=@ |xv} Ry %Cr
&�x}rw= O=wt ?=UDL= =@� wv pwYLt O}rwD |Q=BUuwQ@ |xv} Ry %Cop&�Cop R= QDsm � |DWoQ@ pwYLt O}rwDR=@ |Q=BUuwQ@ |xv} Ry %cor
&pwYLt O}rwD |=Q@ R=}v OQwt `@vt Q=Okt %ms
&�ms R= QDsm � pwYLt O}rwDR=@ |=Q@ R=}v OQwt `@vt Q=Okt %rs&`@vt C}iQ_ %PC
&pwYLt |=[=kD |atHD `} RwD `@=D w |r=oJ `@=D %fd(i); F d(i)
&pwYLt |=[=kD Q=}at h=QLv= %�d(i)
&CWoQ@ |iO=YD Q=Okt |atHD `} RwD `@=D w |r=oJ `@=D %fr(i); F r(i)
&pwYLt |=[=kD Q=}at h=QLv= w u}ov=}t %�r(i); �r(i)
&O}rwDR=@ p@=kQ}e |DWoQ@ pwYLt OL=w Qy R} QQwO |xv} Ry %LO}rwDR=@ p@=k Q}e |DWoQ@ pwYLt OL=w QyCi=} R=@ R= pY=L �Xr=N=v� OwU %Re
&s=N O=wt x@&s=N O=wt x@ CqwYLt Ci=} R=@ C}=U C}iQ_ %CaRe
&Ov=OQoQ@ =Q =yu; u=wD|t w OvDUy Q=R=@ QO xm |DqwYLt u=R}t u} QDW}@ %Mar
&�QiY VwQi Ct}k� xv}W}@ |=[=kD %Przi&�QiY =[=kD� xv}W}@ Ct}k %Przi=coee
&Box@ Pr p}O@D ?} Q[ %coe|Q=BUuwQ@ xm|}=y|DWoQ@ |=Q@\ki�|DWoQ@ CqwYLt R= O}rwDR=@p@=k OYQO %rr
&�Ov=xOWv%s}tYD |=yQ}eDt
&wv pwYLt O}rwD %Xpi&pwYLt CWoQ@ Ct}k %Pri&pwYLt VwQi Ct}k %Prsi
&O}rwDR=@ Q=Okt %Xri&wv pwYLt O}rwD |Q=BUuwQ@ u=R}t %Xpoi
&O}rwDR=@ |Q=BUuwQ@ u=R}t %Xroi&|Qw;`tH |Q=BUuwQ@ u=R}t %XBoi
&s=N O=wt x@ Ci=} R=@ u=R}t %Ri
=yQDt=Q=B \UwD w OvDU}v s}tYD Q}eDt OwN |OwN x@ =yQ}eDt xvwou}= %=yQ}eDt Q}=U"OvwW|t x@U=Lt s}tYD |=yQ}eDt w
&�xOW O}rwDR=@/O}rwD� CqwYLt |OwHwt %Ipi
"OQm xQ=W= �� xv=}=Q C=a]k w |Bm x=oDUO w QDv} QB |=yG} QDQ=m 'hQYt Q=@l}O}rwDR=@ =} O}rwD x@ QO=k xOvvmO}rwD w 'Q}PBh=]av= O}rwD Ov}=Qi pOt u}= QO=yu; u=oOvQ=O R= ptaDUt CqwYLt 'O}rwDR=@ Ov}=Qi QO "OwW|t ZQi CqwYLt?}DQDx@ TBU "OW Oy=wN xQ}NP Ci=} R=@ p@=k |=y|OwHwt QO w xOW |Q=O} QNCqwYLt O}rwDC}=U QO "OvwW|t O}rwDC}=U OQ=wptaDUtCqwYLt 'C=WQ=iUOQwt ,=OOHt OvQ=O |@ wN OQmrta xm |}=RH= w 'OvwW|t |UQR=@ w S=DvwtO ptaDUt'OvwW|tZ} waD =} Q}taD QDu}}=BC}i}m =@ <=RH=Cr=L u}= QO "OvQ}o|t Q=Qk xO=iDU=swOat w Ci=} R=@ "OvwW|t swOat =} Ci=} R=@ R}v OvQ=Ov O}rwDR=@ C}r@=k xm |}=RH= wO=wt u=wvax@ Q=R=@ QO u=wD|t =Q |Di=} R=@ C=a]k =t= 'CU= Q@xv} Ry C=a]k uOQmp@=k 'C=a]k |t=tD xm CU= u}= Q@ ZQi Q=DWwv u}= QO "Ov=UQ VwQi x@ s=NCi=} R=@ u=R}t xm CU= Ci=} R=@ OL=w C}iQ_ u}= w OvDUy �s=N O=wt x@� Ci=} R=@wv CqwYLt Ovv=t |DWoQ@ CqwYLt 'O}rwDR=@ Ov}=Qi R= TB "Ovm|t OwOLt =QVwQi p@=k CqwYLt |OwHwt wxOQ QO wv CqwYLt x=Qtyx@ w OvwW|t ZQiw CU=[=kD Q=Okt R= QDsm |O}rwDR=@ CqwYLt Q=Okt ,qwtat "CiQo Ovy=wN Q=QkO}rwD s=N O=wt R= xO=iDU= =@ R}v =Q |DqwYLt CU= Qw@Ht xOvvmO}rwD p}rO u}tyx@pOt C=[wQit "OwW|t ?wULt O}rwDR=@/O}rwD |@}mQD pOt l} pOt u}= "Ovm
%R= CU= CQ=@aCqwYLt u}= w OQ=Ov OwHw |Dw=iD |O}rwDR=@ CqwYLt w wv CqwYLt u}@ �
"OvwW|t x[Qa Ct}k l} =@ w sy=@"OvDU}v O}rwDR=@ p@=k |DWoQ@ CqwYLt |t=tD �
|rw "OQm Oy=wN Q}}eDhrDNt |=yxQwO QO wCU= |r=tDL= CqwYLt |=[=kD �"CU}v xDU@=w Qo}Om} x@ hrDNt |=yxQwO |=[=kD
Q=Okt u}@ |x]@=Q u}vJty "CU= |r=tDL= w Ct}k x@ xDU@=w CWoQ@ Q=Okt �x]@=Q u}= R= wCU= swrat |Q=Okt 'ptaDUt CqwYLtCWoQ@Ct}k wCWoQ@QO pwYLt CWoQ@ Ct}k Pri u; QO xm a + bPri + u %O};|t CUOx@xR=@ QO xDUUo CN=wvm} `} RwD R= xm CU= |iO=YD |OOa u w xOw@ i xQwO
[3]"CU= b > 0 w a � 0 xwqax@ &Ovm|t C}a@D [ar; br]|rw "CU}v CqwYLtCWoQ@ |=Q@ xOW hQY |xv} Ry pt=W O}rwDR=@ |xv} Ry �xm |D=a]k |xv} Ry 'O}rwDR=@ 'Q}taD 'C}i}m u}t[D '|UQR=@ 'S=DvwtO |=yxv} Ry
[3]"OwW|t pt=W =Q |D} Q}Ot |=yxv} Ry Q}=U w OvwW Z} waD O}=@Q}=U w S=Dvwt 'C=a]k w s=N O=wt 'O}rwD |=yxv} Ry O}OH pwYLt O}rwD |xv} Ry �
[3]"OwW|t pt=W =Q |D} Q}Ot |=yxv} RyhqNQ@ 'OvQ}o|t Q=Qk Q_v Ot R}v |OwHwt |=yxv} Ry pOt u}= QO xm =Hv; R= �R=HtQ}e |OwHwt Ow@tm w CU= |}xQwOOvJ pOt u}= [3]'u=Q=mty w |W pOt
"OwW|t ZQiR= V}@ |oO}J}B R= ?=vDH= |=Q@ w |}xQwOOvJ Cr=L QO pOt |oO}J}B Crax@ �|rwYLtOvJ pOt x@ p}O@DC}r@=k |rw 'xOWZQi |rwYLtlD pOt u}= 'OL
"OQ=O =Qw xOw@ s}tYD |=yQ}eDt <RH R}v |O}rwD CqwYLt |Q=PoCt}k pOt u}= QO ��di = �Prsi � coee + Przi CQwYx@ pwYLt |=[=kD =@ u; |x]@=Q
"CU= xOW |iQat |R=UpOt CtUk QO u; |=yQDt=Q=B xm 'OwW|t ZQiCU= QO=k xOvvmO}rwD OwW|t ZQi 'pOt u}= QO Ow@tm uOw@ R=HtQ}e p}rOx@ �"OR=U u=Q@H =Q Ow@tm u=R}t j} Q] u}= x@ =D Ovm |Q=BUuwQ@ =Q CWoQ@ R= |DtUk
44
u=}�=QLY
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=[Q}ra C}OwOLt 3 C}OwOLt "CU= O}rwDR=@ w O}rwD |=Q@ xOvvmO}rwD C}iQ_ C}OwOLt
O}rwD pwYLt |OwHwt u=R}t |x@U=Lt |=Q@ 4 C}OwOLt "CU= Ci=} R=@ C}iQ_QO CqwYLt |OwHwt Qo = xm |}xvwox@ 'OwW|t xO=iDU= xQwO Qy QO O}rwDR=@/QO w =[=kD u=R}t x@ 'OW=@ xQwO u; QO =[=kD Q=Okt |w=Ut QDnQR@ xQwO l}|=Q@ 5 C}OwOLt R= "OW Oy=wN p=UQ= Q=R=@ x@ |OwHwt xR=Ov=x@ CQwYu}= Q}e|=Q@ 6 C}OwOLt R= w 'xQwO Qy QO |DWoQ@ CqwYLt |OwHwt u=R}t |x@U=Lt'VwQi Ct}k uOQm OwOLt u}vJty w VwQi Ct}k w =[=kD u=}t |x]@=Q p=ta=Qy QO |DWoQ@ CqwYLt u=R}t xm Ovm|t u}t[D 7 C}OwOLt "OwW|t xO=iDU=CqwYLt |Qw;`tH |Q=BUuwQ@ |xv} Ry 8 C}OwOLt "OwQv QD=Qi OwN OL R= xQwOR= |=y|OwHwt u=R}t Ovm|t u}t[D 9 C}OwOLt "Ovm|t x@U=Lt =Q ptaDUtO=Oa= |xawtHt <RH =yQ}eDt |t=tD xm OwW|t Qw;O=} u}vJty "OwWv QDsm QiY|k}kL O=Oa= |xawtHt <RH wO Qy xm Prsi w Pri |=yQ}eDt RHx@ 'Ov=|@=UL
"Ov=|ivt Q}e w
pL OQm}wQ "4p}rO u}tyx@ [3]"CU= NP-hard |]N Q}e |R} Qxt=vQ@ pOt l} xOW x�=Q= pOtu}kkLt "CU= |Q=mD@==Qi w |Q=mD@= |=ysD} Qwor= OvtR=}v w CU= pmWt u; pLSv=Qo q |R=UO=R; VwQ �pOt u}= R= |Y=N Cr=L� QDxO=U ,=D@Uv pOt l} |=Q@l}DvS sD} Qwor= pOt u=ty |=Q@ [22]|Oa@ C=ar=]t QO =t= [3]"Ov=xO=O O=yvW}B =Qp}rO u}tyx@ "O}WN@ Ow@y@ =Q [3]Sv=Qo q |R=UO=R; pOt ?=wH C}i}m xm OW O=yvW}B"OwW|t xO=iDU= l}DvS sD} Qwor= OQm} wQ R= Q=DWwv u}= QO xOW x�=Q= pOt pL |=Q@pOt pL |=Q@ u; |=yQDt=Q=B u}}aD w |O=yvW}B l}DvS sD} Qwor= OQm} wQ xt=O= QO
"OW Oy=wN K} QWD QwmPt&CU4=y?=wH V}=tv RQ] |Q=mD@==Qi w |Q=mD@= |=ysD} Qwor= QO sOk u}rw=sD} Qwor= QO "OwW|t xO=iDU= swRwtwQm R= =y?=wH V}=tv |=Q@ l}DvS sD} Qwor= QO`@=D Q=Okt hQat pw= |x}=QO xm OvO=Oa= R= |Q=OQ@ CQwYx@ =yswRwtwQm |O=yvW}B'Prsi Pri 'Xpi ?}DQDx@ |Oa@ |=yx}=QO w CU= Q_v OQwt ?=wH |=R=x@ hOysD} Qwor= u}= QO x}rw= C}atH O=OaD "OvDUy Ri w XBoi 'Xroi 'Xpoi 'XriO}rwD |iO=YD CQwYx@ |vOW ?=wH 10 O=OaD =OD@= |va} "CU= xOW ?=NDv= 10Qw@a xrLQt xU R= QDy@ |=y?=wH uDi=} w x}rw= C}atH Q}}eD |=Q@ TBU "OwW|t
"OwW|tQ_v QO u}Or=w u=wvax@ wO x@ wO =Q x}rw= ?=wH |=yswRwtwQm pw= |xrLQt QOCQ=@ax@ "OvwW|tZ} waD Qo}Om} =@ =yu; |=yx}=QO R=l} Qy 0 5 p=tDL= =@ w xDiQo0 5 |RwQ}B p=tDL= w |rwvQ@ `} RwD =@ |iO=YD OOa l} Q=@ l} x}=QO Qy |=Q@ Qo}O=Hx@=H u}Or=w QO =Q Q_v OQwt |x}=QO 'Ow@ 1 =@ Q@=Q@ OOa u}= Qo = &OwW|t O}rwDu}= QO "�OwW x@U=Lt O}=@ w CU= hOy `@=D Q=Okt xm pw= |x}=QO RH� s}vm|t
"OwW|t O}rwD OvRQi 10 ,=k}kO xrLQtOOa l} 'pw= |xrLQt QO xOWO}rwD u=OvRQi R= l} Qy |=R=x@ swO |xrLQt QO|=yx}=QO R= |m} 'Ow@ 1 u; Q=Okt Qo = xm 'OwW|t O}rwD p = 0 3 =@ |rwvQ@ |iO=YD|vOW ?=wH l} xm s}vm|t Z} waD |Qw] |iO=YD OOa l} =@ =Q Q_v OQwt OvRQi
"OW Oy=wN O}rwD Qo}O OvRQi 10 QFm =OL xrLQt u}= QO "OwW pY=Lu=OvRQi QO =Q TvHty |=yx}=QO |t=tD 0 3 p=tDL= =@ swU |xrLQt QOO}rwD |vOW ?=wH l} xm s}yO|t Q}}eD |Qw] |iO=YD CQwYx@ 'pw= |xrLQt
&|DWoQ@ CqwYLt |OwHwt %Iri&pwYLt |=[=kD u}ov=}t %�d(i)
"ptaDUt pwYLt OL=w Qy |Qw;`tH |Q=BUuwQ@ |xv} Ry %Boiu}vJ =Q Q_v OQwt |xr�Ut u=wD|t 'xOW h} QaD |=yQ}eDt w =yQDt=Q=B x@ xHwD =@
%OQm |R=UpOt
Maxz =IX
i=18>>>>>>>>>>>>>><>>>>>>>>>>>>>>:
�1s0Prsi � fdi (Di) dDi
�+Ri �Re
� [(Xpi � Cp) + (Xpoi � Cop)]
� [Xri � Cr +Xroi � cor]
��1s0(a+b� Pri+U)�Pri�fri (u) du+XBoi�Boi
�� [Ipi � h+ Iri � hr]
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0(1� rr)(a+ b� Pri + U)fri (u) du�Ri
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9>>>>>>>>>>>>>>=>>>>>>>>>>>>>>;(1)
Subject to
Xpi �ms+Xri � rs � PC (2)Ri �MinfCaRe; (1� rr) (a+ b� Pri + U)g (3)Ipi = [Xri +Xroi] + [Xpi +Xpoi] + Ipi�1�
Xri+Xroi+Xpi+Xpoi+Ipi�1Z0
Difdi (Di)dDi�
(Xri +Xroi +Xpi +Xpoi + Ipi�1)�1Z
Xri+Xroi+Xpi+Xpoi+Ipi�1
fdi (Di)dDi (4)
Iri = Iri�1 + [rr � (a+ b� Pri + U)
+XBoi � (Xri +Xroi)] (5)�di = �Prsi � coee+ Przi (6)(a+ b� Pri + U) +XBoi �Mar (7)Boi = coe� Pri (8)Iri � 0; Ipi � 0 (9)pw= CQ=@a u; QO xm 'CU= xOW |L=Q] pm OwU |R=Uxv}W}@ |=Q@ hOy `@=DO}t= swO CQ=@a "CqwYLt VwQi R= |W=v |O}=a pm |[=} Q O}t= =@ CU= Q@=Q@CQ=@a "CU= Ci=} R=@ R= pY=L s=N O=wt VwQi R= |W=v |O}=a pm |[=} Q|x@U=Lt |=Q@ sQ=yJ CQ=@a "OwW|t pt=W =Q wv CqwYLt O}rwD |=yxv} Ry swU"Ovm|t x@U=Lt =Q |Qw;`tH |=yxv} Ry sHvB CQ=@a "OwQ|t Q=mx@ O}rwDR=@ |=yxv} RyCqwYLt R} QQwO |xv} Ry "CU= Q=@v= w |OwHwt |=yxv} Ry pt=W sWW CQ=@aC=Q=@a R= l} Qy "OwW|t x@U=Lt sDiy CQ=@a\UwD R}v xO=iDU= p@=k Q}e |DWoQ@|t=tD Cra u}tyx@ w Ovm|t x@U=Lt =Q xQwO l} R= pY=L |xv} Ry =} |O}=a
"OvwW|t `tH Qo}Om} =@ w x@U=Lt =yxQwO |t=tD |=R=x@ 'C=Q=@a'2 C}OwOLt "OW=@ Q=QkQ@ =yxQwO |t=tD |=R=x@ O}=@ =yC}OwOLt |t=tD
45
"""pQDvm
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x�=Q="xr�Ut |=yQDt=Q=B Q}=U "2 pwOH(i) xQwO QDt=Q=B
5 4 3 2 11 1 5 2 2 �d(i)
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QwmPt |xr�Ut "CU= xOW x�=Q= 3 w 2 |=ypwOH QO xr�Ut |=yQDt=Q=B Q}=U "CU=|@=} RQ= |=Q@ "CU= xOW x�=Q= 4 pwOH QO u; G}=Dv w xOW pL |O=yvW}B OQm} wQ =@=Q u; w xOQm hPL pOt R= |ov}y@ |=DU=Q QO =Q =yC}OwOLt R= |m} 'xr�Ut ?=wH|QDy@ ?=wH xH}DvQO w xOW QDxOQDUo ?=wH |=[i Q=m u}= =@ "s}vm|t pL xQ=@ wO'OW=@v |vOWv |rY= |xr�Ut |=Q@ pY=L ?=wH xm|DQwY QO "O};|t CUO x@hPL |ov}y@ |=DU=Q QO =Q |Qo}O C}OwOLt w xOv=OQoQ@ =Q xOW hPL C}OwOLt|rY= |xr�Ut |=Q@ xOt; CUO x@ ?=wH xm =Hv; R= "s}vm|t pL xQ=@ wO =Q xr�Ut w|=]N xv}W}@ x@ '?=wH wO u}= |xU}=kt j} Q] R= u}=Q@=v@ 'CU= |vOWv |rw xv}y@j} Q] u}= R= w OQ@ |B u=wD|t OW=@ xO=O MQ pL VwQ QO CU= umtt xm |r=tDL=
"OQm |@=} RQ= =Q OQm} wQp}rO "OwW|t ?=NDv= �3 C}OwOLt� Ci=} R=@ C}iQ_ C}OwOLt 'Q=m u}= |=Q@l}ORv OwN OL x@ Qo}O |=yC}OwOLt R= QDW}@ C}OwOLt u}= xm CU= u}= Q=m u}=u}= hPL =@ u}=Q@=v@ "CU= C}OwOLt u}= RQt |wQ xv}y@ ?=wH ,q=tDL= w xOW|vOWv |q=@ OL =Q u; u=wD|t xm 'O}UQ s}y=wN |vOWv w xv}y@ ?=wH x@ 'C}OwOLt=@ Q@=Q@ xv}y@ ?=wH 'C}OwOLt u}= hPL R= TB "CiQo Q_v QO |rY= |xr�Ut |=Q@5 pwOH QO u; =@ Q_=vDt s}tYD |=yQ}eDt Q}O=kt xm Ot;CUO x@ 373385 8378|=R=x@ 3 C}OwOLt 'QwmPt ?=wH QO 'OwW|t xOy=Wt xm u=vJ "CU= xOW x�=Q=
"CU= |vOWv ?=wH l} '?=wH u}= u}=Q@=v@ "CU}v Q=QkQ@ swO w pw= |=yxQwOu=wD|t =Q QwmPt |xr�Ut |vOWv |q=@ OL 'xOW xO=O K}[wD xm u=vJ|@ wNx@ pL OQm} wQ CiQo xH}Dv u=wD|t u}=Q@=v@ "CiQo Q_v QO 373385 8378|xv}y@ ?=wH =@ OYQO 2 7 QFm =OL OQm} wQ u}= R= pY=L ?=wH w xOQm pta
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"Ov=xDiQo Q=Qk |UQQ@CQwYx@|vOW |OOa p=Ft 30 '=yxR=Ov= R=l} Qy QO pL OQm} wQ|@=} RQ= |=Q@R}=U� |}xQwOlD |xr�Ut QO p=Ft u=wvax@ "CU= xOW pL QwmPt pOt =@ |iO=YDl}DvS sD} Qwor= pw= s=o w xOW O}rwD |iO=YD |xr�Ut l} =OD@= �1 =@ Q@=Q@ xr�UtxJv=vJ 'pw= s=o Q=QmD Q=@ 100 R=TB "OwW|t R=e; �|vOW |x}rw= ?=wH 10 uDi=}�|xr�Ut w xOW ZQi |vOWv xr�Ut u; OwWv Ci=} xr�Ut |=Q@ |vOW ?=wH I}y|vOW ?=wH xr�Ut |=Q@ xJv=vJ =t= "OW Oy=wN O}rwD 1 R}=U =@ |Qo}O |iO=YDxv}y@ l}ORv ?=wH uDi=} =D |O=yvW}B l}DvS sD} Qwor= |=ys=o |x}k@ 'OwW Ci=}
u}= QO �"s}yO|t Q}}eD u=OvRQi R= |m} |=Q@ =Q =yXpi |t=tD p=Ft u=wvax@� "OwW"OwW|t O}rwD O}OH ?=wH 10 QFm =OL R}v xrLQt
|xR=Ov= x@ w xOQm O}rwD B �10w0 2� |iO=YD OOa l} QN; |xrLQt QO|iO=YD Q}eDt Qo = p=Ft u=wvax@ "OwW|t O}rwD |vOW |iO=YD C}atH 'OOa u;Q=Qk u=OvRQi |xawtHt QO w xOQm O}rwD |iO=YD ?=wH 2 'OW 2 =@ Q@=Q@ Q_v OQwt
"OwW|t O}rwD O}OH ?=wH 10 QFm =OL R}v xrLQt u}= QO "s}yO|t'x@U=Lt xOW O}rwD u=OvRQi |t=tD |=Q@ =Q hOy `@=D Q=Okt 'u=OvRQi O}rwD R=TB`@=D Q=Okt 'Ow@ |vOWv |@=wH Qo = "s}vm|t |UQQ@ =Q =y?=wH uOw@|vOW TBU wx@ ?=wH u} QDy@ R= ?}DQDx@ =Q =y?=wH TBU "s} Q}o|t Q_v QO QiY =Q u; hOyhPL C}atH |xawtHt R= =Q |Q=QmD |=y?=wH w s}vm|t ?DQt ?=wH u} QDO@u}ty w xDiQo Q_v QO x}rw= C}atH u=wvax@ =Q QDQ@ ?=wH 10 u; R= TB "s}vm|t1 pmW QO |O=yvW}B l}DvS sD} Qwor= Om x@W "s}vm|t Q=QmD Q=@ 100 =Q pL=Qt
"CU= xOy=Wt p@=kC}atH xR=Ov= %CU= QDt=Q=B 5 |=Q=O |O=yvW}B sD} Qwor= xm CU= QmP x@ sRql} Qy Z} waD p=tDL= x@ \w@ Qt `k=w QO xm 5`]=kD Qorta x@ \w@ Qt QDt=Q=B '�10�\w@ Qt |=yQDt=Q=B '�0 5� CU= O}OH u=OvRQi O}rwD |=Q@ u}Or=w QO =yswRwtwQm R=p=tDL= 'CU= xOW h} QaD u; |=Q@ QDt=Q=B wO |O=yvW}B sD} Qwor= QO xm 6VyH x@|x}rm VyH p=tDL= w �0 3� u=OvRQi R= l} Qy |=yswRwtwQm R= |m} VyHxm CQH=yt u=R}t QDt=Q=B xQNq=@ w '�0 3� u=OvRQi R= |m} TvHty |=yswRwtwQm|iO=YD CQwYx@ Q=QmD Qy QO xm |D}atH O=OaD xm CU= |iO=YD |OOa `k=w QO"Ovm|t C}a@D B �10w0 2� |r=oJ `@=D R= xm Ovm|t XNWt =Q OvwW|t O}rwD=]N w uwtR; VwQ R= |O=yvW}B sD} Qwor= |=yQDt=Q=B uOQw; CUO x@ |=Q@xOW xDiQo Q_v QO =yQDt=Q=B u}= R= CWo}=H 130 xm |}xvwox@ 'CU= xOW xO=iDU=6 |iO=YD |xr�Ut 10 w |}xQwO 3 |iO=YD |xr�Ut 10 CWo}=H Qy |=Q@ w"CU= xOW x@U=Lt xv}W}@ |=]N u=R}t w pL u=tR u}ov=}t w xOW pL |}xQwO=yQDt=Q=B R= CWo}=H u} QDy@ '10 |x]@=Q R= xO=iDU= =@ w QDt=Q=B wO u}= x@ xHwD =@CU= CWo}=H Qy VHvU Q=}at u=ty CHt '10 |x]@=Q QO "CU= xOW ?=NDv=u}ov=}t Et "CU= CWo}=H uOw@ QDy@ Qou=Wv OW=@ QDl}ORv QiY x@ xJQy xm=Q pL u=tR u}ov=}t Tt "Ovm|t XNWt CWo}=H Qy QO =Q =]N OYQO u} QDW}@pL u=tR w =]N OYQO =OD@= |Q}os}tYD u}= QO "Ovm|t XNWt CWo}=H Qy QO|@=} RQ= =Q hrDNt |=yCWo}=H TBU w �l} w QiY xR=@ QO� xOQm T=}ktsy =Q
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"Ov=xOW |U} wvOm MATLAB R2010ap=tQv CqwYLt |t=tD |=[=kD w CU= |}xQwO 5 QwmPt |iO=YD |xr�UtC}a@D [ar; br] xR=@ QO xDUUo CN=wvm} `} RwD R= ui u}vJty "OwW|t ZQixOW xDiQo Q_v QO PC = 20090 =@ Q@=Q@ |O}rwD OL=w `@=vt C}iQ_ "Ovm|t
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"u; =@ Q_=vDt s}tYD |=yQ}eDt Q}O=kt w xOt; CUO x@ |xv}y@ |x]kv QO hOy `@=D Q=Okt "4 pwOHPrsi Pri Xpi
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"u; =@ Q_=vDt s}tYD |=yQ}eDt Q}O=kt w xOt; CUO x@ |vOWv w xv}y@ |x]kv QO hOy `@=D Q=Okt "5 pwOHPrsi Pri Xpi
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|rY= |xr�Ut QO xv}y@ ?=wH hqDN= Qo = =Q} R &CU= xDU@=w xr�Ut |=yQDt=Q=B x@Oy=wN O=} R R}v |OQw;Q@ |=]N u} QDW}@ Q=Okt 'OW=@ O=} R xDi=}VQDUo |xr�Ut w
"OW=@v O=} R |ak=w |=]N u=R}t xm OvJQy 'OW
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"s}vm|tV}=Ri= =@ wv CqwYLt O}rwD u=R}t 'OwW|t xOy=Wt 2 pmW QO xm u=vJC}iQ_ V}=Ri= =@ 'xOW O}rwDR=@ CqwYLt u=R}t xm |r=L QO xDi=} V}=Ri= 'C}iQ_|QDsm `@=vt x@ =yu; O}rwD x@ C@Uv CqwYLt O}rwDR=@ xm =QJ &O@=}|t Vy=m
'OW xO=O K}[wD |OOa p=FtCtUk QO xm|WwQ j@=]t 'u; R=TB "OW Oy=wN|]sD} Qwor= |=ys=o xQ=@ wO w xOW hPL |R=Uxv}y@ |=DU=Q QO =yC}OwOLt R= |m}xm u=vJ "OwW|t |] 'O}OH |xr�Ut |xv}y@ x@ l}ORv ?=wH uDi=} |=Q@ l}DvS|xr�Ut |=Q@ xv}y@ w |vOWv ?=wH l} xOt; CUO x@ ?=wH 'OW xO=O K}[wD ,q@ku}= "OQw;CUO x@ =Q pL |=]N OYQO u} QDW}@ u=wD|t u; ltmx@ w CU= |rY=�|}xQwO xOR=wO =D |}xQwOlD p�=Ut� |UQQ@ OQwt |=yxR=Ov= R= l} Qy |=Q@ pL=Qt6 pwOH QO "CU= xOW x�=Q= 7 w 6 pw=OH QO xrY=L G}=Dv "OwW|t Q=QmD Q=@ 30w 'xk}kO ?ULQ@ hrDNt O=a@= =@ p�=Ut pL |=Q@ R=}v OQwt u=tR COt u}ov=}thrDNt O=a@= QO pL |=]N OYQO u} QDW}@ Q=}at h=QLv= w u}ov=}t 7 pwOH QOwMatlab 2010 Q=Ri=sQv =@ C=@U=Lt |t=tD CU= QmP x@ sRq "CU= xOW VQ=Rou=vJ "CU= xOW s=Hv= RAM: 4GB 'CPU: corei7 1 7GHz Q=Ri=CNU =@O=a@= QO |rw CU= QDW}@ |tm u}}=B O=a@= QO sD} Qwor= CkO 'OwW|t x_Lqt xm
"CU= Q=OQwNQ@ |}q=@ CkO R= R}v q=@Q=}U@ 'OwW|t x@U=Lt xm |}=]N xv}W}@ u=R}t 'pL |=[i VQDUo VwQ QO
48
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"hrDNt |=yC}iQ_ QO ptaDUt CqwYLt CWoQ@ Ct}k |UQQ@ "3 pmW|xOvvmu}}aD Q=R=@ |=[=kD u=R}t xOwOLt u}= QO "CW=O Oy=wNv CWoQ@ Ct}k Q@
"CW=Po Oy=wNv u; Q@ |Q}F-=D C}iQ_ Q}}eD w Ow@ Oy=wN OwU u=R}t
|Q}oxH}Dv "7|xQ}HvR sDU}U l} QO |rwYLtOvJ O}rwD |R} Qxt=vQ@ |xr�Ut l} Q=DWwv u}= QOO}rwD u=R}t %R= Ov=CQ=@a pOt u}= s}tYD |=yQ}eDt "OW |iQat xDU@xkrL u}t-=D'Q=R=@ R= CqwYLt CWoQ@ Ct}k 'ptaDUt CqwYLt O}rwDR=@ u=R}t 'wv CqwYLtu=R}t w s=N O=wt x@ ptaDUt CqwYLt Ci=} R=@ u=R}t 'CqwYLt VwQi Ct}kxQ}HvR pm OwU |R=Uxv}W}@ 'R}v hOy `@=D "�|Qw;`tH w O}rwDR=@ 'O}rwD� |Q=BUuwQ@=@ QwmPt pOt w Ov=xOW ZQi |a]k Q}e pOt u}= QO CWoQ@ w =[=kD u=R}t "CU=
"CU= xOW pL l}DvS sD} Qwor= VwQ R= xO=iDU=w xOW pL OQm} wQ u}= =@ |iO=YD |xr�Ut 360 'pL VwQ |@=} RQ= |=Q@x@ \=kv |xrY=i u}ov=}t u}vJty "OW =O}B |@ wNx@ u; |xv}y@ l}ORv |x]kvxm OwW|t x@U=Lt �3 59 QFm =OL =yu; �|vOWv� |q=@ OL x@ C@Uv xOt; CUO
"CU= pL VwQ ?wN OQmrta Qou=WvCWoQ@ u=R}t QDj}kO |v}@V}B xrtHR= |OQ=wt u=wD|t |D; C=k}kLD u=wvax@u}vJty "OQ@ s=v =Q |v=tR |=y|QU |=yVwQ Q}=U =} |@Ya |xm@W R= xO=iDU= =@u=wD|t OUQ|t Q_v x@ "O=O Q=Qk |UQQ@ OQwt R}v xiOyOvJ CQwYx@ =Q pOt u=wD|txO=iDU= |R=Uxv}tm =} CU} R \}Lt Q@ xQ}HvR Q}F-=D |R=Uxv}tm TvH R= hOy `@=wD|rY= h=Oy= R= |m} xm =QJ 'O=O Q=Qk Q_v Ot ?wN |=yxv} Ro u=wvax@ =Q s=N O=wt R=
"CU= CU} R \}Lt R= C_=iL xDU@xkrL u}t-=D |xQ}HvR |Q}opmW
"hrDNt O=a@= QO xr�Ut pL u=tR u}ov=}t "6 pwOH�xk}kO� pL u=tR u}ov=}t �=yxQwO O=OaD� xr�Ut R}=U
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"hrDNt O=a@= QO =]N OYQO u} QDW}@ Q=}at h=QLv= w u}ov=}t "7 pwOHQFm =OL Q=}at h=QLv= QFm =OL u}ov=}t xr�Ut R}=U
=]N OYQO =]N OYQO �=yxQwO O=OaD�0 16219 0 60384 10 17696 0 65880 20 18501 0 69428 30 24223 0 90173 40 29493 1 10887 50 47323 1 78372 60 62637 2 68513 70 50504 2 04943 80 98164 3 58811 90 76549 1 25409 100 72717 1 87153 110 77485 2 22430 12
R= |t_a= VN@ 'OwW|t OwOLt Q=}U@ C}iQ_ xm |t=ovy wQ u}= R= "OQ=O R=}vC}iQ_ xm |t=ovy "OwW <=[Q= Q=R=@ |=[=kD =D O@=}|t X=YDN= O}rwDR=@ x@ `@=vtCU=wNQO |=H x@ wv CqwYLt O}rwD |=Q@ |QDW}@ `@=vt xOvvmO}rwD 'O@=}|t V}=Ri=
"CW=O Oy=wN QDq=@ CWoQ@ Ct}k =@ ptaDUt CqwYLtO}rwDR=@ w O}rwD CU=}U QO |Q}}eD 'OwW OL=w 24000 R= QDW}@ C}iQ_ |DkwuDW=O =@ |DL CU}v QO=k Qo}O xOvvmO}rwD xm OyO|t u=Wv Qt= u}= "O=O Oy=wNv MQ|xOvvmOwOLt pt=a =[=kD Cr=L u}= QO w "Ovm ?Um |QDW}@ OwU 'QDW}@ C}iQ_
"CU= OwUu=vJ "CU= xOW xO=O u=Wv 3 pmW QO CWoQ@ Ct}k Q@ C}iQ_ u=R}t Q}F-=DVy=m ptaDUt CqwYLt CWoQ@ Ct}k 'C}iQ_ V}=Ri= =@ 'OwW|t x_Lqt xm|Q}F-=D u; Vy=m =} V}=Ri= 'OwQ QD=Qi OL=w 24000 R= C}iQ_ xm |t=ovy "O@=}|t
49
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x�=Q==yCWwv=B1. original equipment manufacturer2. Kodak3. closed-loop supply chain (CLSC)4. solution representation5. cross-over6. mutaton
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tics of the research on reverse logistics (1995-2005)", In-ternational Journal of Production Research, 46(4), pp.1099-1120 (2008).
2. Guide Jr, V.D.R., Jayaraman, V., Srivastava, R. andBenton, W.C. \Supply chain management for recover-able manufacturing systems", Interfaces, 30, pp. 125-142(2000).
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4. Aras, N., Verter, V. and Boyaci, T. \Coordina-tion and priority decisions in hybrid manufactur-ing/remanufacturing systems", Production and Opera-tions Management, 15(4), pp. 528-543 (2006).
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7. Van Der Laan, E., Salomon, M., Dekker, R. and VanWassenhove, L. \Inventory control in hybrid systemswith remanufacturing",Management Science, 45(5), pp.733-747 (1999).
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9. Zhou, L, Naim, M.M., Tang, Q. and Towill, Q.R. \Dy-namic performance of a hybrid inventory system with aKanban policy in remanufacturing process", Omega, 34,pp. 585-598 (2006).
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