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ResearchNote
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eshtehardian@modares.ac.ir
abbasnia@iust.ac.ir
j.mohammadi.t@gmail.com
a.chalekaee@gmail.com
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CU= 2 w 1
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w|v=O}t |}xv=N@=Dm|]}LtQOw|:tm|}=QkDU=|OQm}wQ=@'u=oOvU}wvQw_vt
|OQ@Q=m |WywSB ?r=k QO OwHwt lQ=Ot w O=vU= R= |}=yxO=O |Qw;OQo j}Q] R=
R}v w OQ@Q=mQB |r[at lQO R= TB 'wQ u}= R= [35]Ov=xDN=OQB VywSB x@ |O}}-=D
|rL x=Q |=y|R=@ |x}Q_v R= xO=iDU= =@ '`H=Qt QO xOWs=Hv= |=yVywSB |xar=]t
CU= xOW pY=L |OQwt |xar=]t pL =@ |H}=Dv w KQ]
123

4. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
Q}N-=D =@ xH=wt |=yxSwQB |R=@ CNQO 4 pmW
f Pht+Lht; Cht CVht Lhtg=tQiQ=mwQ=mv=t}B|R=@u}iQ]|=Q@
Ow@ Oy=wN
OW=@ Q=mv=t}B |wU R= t Q}N-=D u=tR pm u=Q@H Q=DU=wN =tQiQ=m xm |DQwY QO ?
sOa =} VQ}PB Q@ |v@t |Oa@ s}tYD '4 pmW QO t u=tR |=Q@ xQm=Pt |xN=W
VQ}PB R= |W=v |=yOt=}B OwW PN= Q=mv=t}B |wU R= O}=@ xDU=wN u}= VQ}PB
4 pmW QO t u=tR |=Q@ xQm=Pt VQ}PB ?=NDv= Q=mv=t}B |=Q@ t Q}N-=D `iQ
%R= Ov=CQ=@a
'CVt |xv}Ry ptLD 1
( Ct) t `wtHt=DxSwQBR=xOv=t}k=@|=yC}r=aiCOtuOQmx=Dwm|xv}Ry 2
CW=O Oy=wN =tQiQ=m |=Q@ QiY pO=at |Ot=}B 'QwmPt s}tYD Qo}O |wU R=
|=Q@xQm=PtVQ}PB?=NDv=Q}N-=Dpm`iQVQ}PBs}tYDR=pY=LOt=}BTB
xOW ZQi Ow@ Oy=wN f0; Ct CVtg u}iQ] |=Q@ 4 pmW QO t u=tR
QO 'Q}N-=D |xt}QH R= =tQiQ=m 'Q}N-=D `iQ CyH u}iQ] ji=wD CQwY QO xm CU=
OQm Oy=wN |WwBsWJ 'ji=wD OQwt u=tR =D uOWjkLt CQwY
xQm=Pt VQ}PB sOa ?=NDv= Q=mv=t}B |wU R= t Q}N-=D pm `iQ VQ}PB sOa G
O=O Oy=wN Q=Qk |Q}os}tYD `[wt QO =Q =tQiQ=m R}v 4 pmW QO t u=tR |=Q@
%R= Ov=CQ=@a Ovm ?=NDv= =yv; u}@ R= O}=@ =tQiQ=m xm |}=yxv}Ro
VQ}PB sOa gt O=yvW}B ?=NDv= t Q}N-=D R= |WN@ u=Q@H |=Q@ ji=wD 1
'4 pmW QO t u=tR |=Q@ xQm=Pt
QO t u=tR |=Q@ xQm=Pt VQ}PB sOa u=t}B MUi ?=NDv= u=t}B MUi 2
'4 pmW
t u=tR |=Q@ xQm=Pt VQ}PB sOa u=t}B |xtD=N ?=NDv= u=t}B |xtD=N 3
4 pmW QO
xm |Q}N-=D u=R}t Qy =@ u=t}B =}; xm OQ}o|t s}tYD xrLQt u}= QO =tQiQ=m `k=w QO
|=Q@ ji=wD pwYL Qw_vt x@ O@=} xtD=N =} w MUi 'xt=O= 'OW Oy=wN XNWt
COt Q=mv=t}B xm Ovm|t O=yvW}B =tQiQ=m xrLQt u}= QO 'Q}N-=D R= |WN@ u=Q@H
xQm=Pt VQ}PB sOa gt O=yvW}B ?=NDv= Ovm u=Q@H =Q Q}N-=D R= g:t u=tR
0 g 1 xm |DQwY x@ '4 pmW QO t u=tR |=Q@
CU= xH=wt Q}N-=D =@ xm |}xSwQB QO u=tR =tQiQ=m O}rwD Q=Owtv 5 pmW
s=tD= M}Q=D x@ C@Uv t COt x@ Q}N-=D p}rO x@ O}=@ Q=mv=t}B xm |}xt}QH 2
s}t=v|t Ltr =Q u; xm OR=OQB@ =tQiQ=m x@ tp ?wYt
%CU= CQwY u}= x@ =tQiQ=m s}tYD u}= p}rO x@ Q=mv=t}B Ot=}B Qo}O |wU R=
(Ltr) xt}QH CN=OQB 1
CU= u}= |k]vt ZQi (CVtr) tr =D xSwQB s=tD= |=yxv}Ry V}=Ri= 2
j}kOQ}e |@=}RQ= =} w Q=mv=t}B pR=v |yOR=@ R= |W=v CV |xv}Ry xm
p=@vO x@ =tQiQ=m |=Q@ |Ot=}B CV |xv}Ry 'Qo}O |v=}@ x@ 'CU=yC}r=ai
|=yQ=my=Q R= |Q}oxQy@ =@ xm OQ}o|t s}tYD OwN Q=mv=t}B w CW=O Oy=wNv
QwmPt |xv}Ry Vy=m CyH QO |D}Q}Ot |=yOQm}wQ Q}}eD w Cw=iDt
u}iQ] |=Q@ xQm=Pt sOa CyH =tQiQ=m s}tYD R= pY=L Ot=}B TB O};Q@
Ow@ Oy=wN f Ptr + Ltr; CVtr Ltrg
|QUq=@ |=yxv}Ry Vy=m Qw_vt x@,=YNW Q=mv=t}B CU= umtt 'Qo}O |wU R=
4 pmW QO |R=Uxv}y@ |xN=W Ovm u=Q@H =Q Q}N-=D h:t COt x@ w OwN
wOv=t|tR=@Pht u=R}tx@OwNO}rwDR==tQiQ=mCQwYu}=QO(0 h 1)
Q=mv=t}B Ovm|t x@r=]t Q=mv=t}B R= =Q (Lht) Q}N-=D |xt}QH |w p}rO u}ty x@
V}=Ri=R}vwOwWptLDt=Q Cht |xv}Ry'QwmPtQ}N-=Du=Q@HQw_vtx@O}=@R}v
R=pY=LOt=}BTBOvmCN=OQBO}=@Q=mv=t}B=Q(CVht) xSwQBs=tD=|=yxv}Ry
=tQiQ=mCU=wNQOCU=wNuwO@wu;u=tRCOt|R=Uxv}y@CyHQ=mv=t}Bs}tYD
124

5. w=}vT=@a=[Q'u=}OQ=yDW=xr=u=UL=
1 pL 123
=Q gt O=yvW}B =tQiQ=m 'OQ}PB|tv =Q u=tR pm u=Q@H Q=mv=t}B Ovm|t xQm=Pt =tQiQ=m
OyO|t xtD=N u=t}B x@ =tQiQ=m 'Ovm|tv pw@k Q=mv=t}B 'OyO|t
QO w O=Di= Oy=wN j}waD x@ Q=}U@ xSwQB s=tD= 'u=tR MUi CQwY QO xm s}v=O|t
@=wQ `}}[D '|UQO=O p}@k R= |Oa@ |=yxv}Ry p}rO x@ u=}=tQiQ=m |w=Ut }=QW
Q=QkQ@ 4 @=wQ,qwtat TB 'OvDU}v u=t}B MUi x@ p}=t xQ}e w u=Q=mv=t}B Q}=U =@
%CU=
Rir; Pt00iiPt0
R Pt00 + Gh r Pt0 (4)
u=t}B|xtD=N|w'=tQiQ=mO=yvW}BOQCQwYQO Ov=O|tQ=mv=t}Bu;R=p@ks=oQO
ut[ Q=mv=t}B =D OW=@ Q=QkQ@ 5 |x]@=Q QW u}= O}=@ =Pr OQm Oy=wN ?=NDv= =Q
%Ovm ?=NDv= =Q VQ}PB sOa g Q=Okt R= |y=o;
CVt0 + mh Cgt + CVgt
mh Cgt + CVgt CVt0 (5)
QDtm Q=mv=t}B |=Q@ =tQiQ=m =@ @=wQ `}}[D |=yxv}Ry xm CU= u; 5 |x]@=Q swyit
x@ Q=mv=t}B 'Qo}O CQ=@a x@ =} CU=tQiQ=m |O=yvW}B u=tR u=Q@H |=yxv}Ry R=
R= QDxv}RyQB =tQiQ=m |v=tR O=yvW}B j@=]t xSwQB |xt=O= xm CU= xO}UQ xH}Dv u}=
CU= u; |xtD=N
%CU= Q=QkQ@ 6 |x]@=Q =tQiQ=m |=yOt=}B u}@ Qo}O hQ] R=
r Pt0i Pht + Lht
Pt0hPht r Lht
Pt0hhPht (6)
Cr=Lu}=QOxSwQBs=tD=|=Q@=tQiQ=mxmCU=|}xv}Ry|oQR@|xOvvmu=}@'6|x]@=Q
R= QD|vqw] w QDW}@ Q=}U@ 'u=tR w xv}Ry xm |wLv x@ 'OR=OQB|t Q=mv=t}B u}ty =@ w
MUi xm CU= sRq QmPD u}= xD@r= CU= O}OH Q=mv=t}B |v}Ro}=H w u=t}B |xtD=N
QO MUi |=Q@ xOWQmP }=QW R= |m} xmv; Q@ wQWt 'OW=@ pO=aD Ov=wD|t R}v u=t}B
%OW=@ Q=QkQ@ R}v 7 |x]@=Q w OyO MQ Q_vOQwt u=t}B |twta }=QW
R Pt00 + Gi r Pt0
riPt00 Pt0 G + R (7)
CQwY QO =tQiQ=m |D}F}L |=yxv}Ry Q=}U@ V}=Ri= |xOvvmh}YwD '7 |x]@=Q
|oQR@ |D}F}L |=yxv}Ry u}vJ CU= xOWQmP }=QW =@ |}xSwQB u=t}B |xtD=N
%OW=@ pt=wa u}= R= |W=v Ov=wD|t xSwQB l} u=t}B |xtD=N |=Q@
'u=Q=mv=t}B Q}=U p@=kt QO =tQiQ=m xyHw `}}[D 1
p}rO x@ |D; |Q=Oyov w Q}taD |=yxv}Ry R= |WN@ u=Q@H u=mt= uO=OCUO R= 2
Q=mv=t}B |=QH= pR=v C}i}m
u=mt= X=N }=QW QO =t= 'CU= QO=v Q=}U@ =yxSwQB QO |Dr=L u}vJ O=ONQ
SPNE VwQ x@ pw= Cr=L 1 pL |=Q@ |}=yv pL w pL pL=Qt OQ=O `wkw
CU= xOW x=Q= 7 w 6 |=ypmW QO
|=yOt=}B 'Ovvm ji=wD g:t u=R}t x@ Q}N-=D R= |WN@ `iQ =@ Q=mv=t}B xm |DQwY QO
%R= Ow@ Ovy=wN CQ=@a |w
CVgt |xv}Ry ptLD 1
( Cgt) g:t `wtHt =D xSwQB R= xOv=t}k=@ |=yC}r=ai uOQmx=Dwm |xv}Ry 2
=tQiQ=m uOv=tswQLt R= CU= CQ=@a R}v Q=mv=t}B s}tYD u}= =R= x@ =tQiQ=m Ot=}B
s}tYD u}= R= pY=L Ot=}B TB (Pgt) te =D tp R= O}rwD R= pY=L OwU R=
Ow@Oy=wNf Pgt; Cgt CVgtg=tQiQ=mwQ=mv=t}Bu}iQ]|=Q@=tQiQ=m
xQm=PtVQ}PBsOau=t}B|xtD=N?=NDv=u=t}B|xtD=NO=ONQCQwYQO O
|Q=OQ@xQy@ u=tR =D O}rwD R= pY=L OwU R= =tQiQ=m '4 pmW QO t u=tR |=Q@
x@C@UvO}=@=tQiQ=mxwqax@(Pt0) Ow@Oy=wNswQLtt0 COtx@xSwQBpt=m
R}vwOvms=Ok=xSwQBp}tmDCyH|Q=mv=t}B?=NDv=Qw_vtx@|}xYk=vt|Q=RoQ@
=tQiQ=m xyHw `}}[D uwJ |D}F}L |=yxv}Ry u=t}B |xtD=N Q@ |v@t |w s}tYD
h}a[D u}vJty w xSwQB `kwt x@ s=tD= w h=Oy= OQ@W}B QO |}=v=wD sOa p}rO x@
|Q=RoQ@ |=yxv}Ry `wtHt CW=O Oy=wN u=Q=mv=t}B Q}=U p=@k QO |w `[wt
'Q=mv=t}B O}O |x}w=R R= s}Q}o|t Q_v QO r =Q |D}F}L |=yxv}Ry w xYk=vt
=tQiQ=m Q_v R= Q=mv=t}B xyHw x@ uOW Q=OxWON x@ QHvt u=t}B |xtD=N O=ONQ
s}t=v|t m =Q OwW|t OQ=w Q=mv=t}B x@ p}rO u}= x@ xm |}xv}Ry 'OW Oy=wN
|xv}Ry |w 'Q=mv=t}B u}}=B |QwxQy@ w CUQO=v C}Q}Ot p}rO x@ xm OwW xHwD
|=Q@ u=t}B |xtD=N R= pY=L Ot=}B xH}Dv QO CU= xOW ptLDt R}v =Q CVt0
Ow@Oy=wNf r Pt0; CVt0 mg CQwYx@=tQiQ=mwQ=mv=t}Bu}iQ]
sOa u=t}B MUi ?=NDv= OQ}o@ u=t}B MUi x@ s}tYD =tQiQ=m xm |DQwY QO w
u=tR =D O}rwD R= pY=L OwU R= w= '4 pmW QO t u=tR |=Q@ xQm=Pt VQ}PB
|=yxt=vCv=t[ 'Pt00 Ow@ Oy=wN swQLt t00 COt x@ xSwQB pt=m |Q=OQ@xQy@
sOa CQwY QO w OW Oy=wN @[ =tQiQ=m `iv x@ G u=t}B =@ @DQt |mv=@
=Rxv}Ry u}iQ] |=Q@ xm 'xSwQB |=yC}r=ai C}a[w |UQO=O |xOvwQB 'xLr=Yt
|WN@ u=wvax@ |R=@ CNQO QO xm 'R dr@t O=Di= Oy=wN u=}QH x@ 'Ow@ Oy=wN
R= CU= CQ=@a 'CU= xOW xOQw; u=t}B MUi O=ONQ CQwY QO =tQiQ=m Ot=}B R=
|xwqax@xYk=vt|xQ=@wO|Q=RoQ@w=tQiQ=mx@OQ=w|UQO=O|=yxv}Ry`wtHt
@[ w CV w M |=yxv}Ry MUi CQwY QO R}v Q=mv=t}B |D}F}L |=yxv}Ry
|}=yxv}Ry `wtHt R= CQ=@a =H u}= QO M dr@t CU= xOW ptLDt =Q G dr@t
`}}[D w |UQO=O |xO=a= p}rO x@ w u=t}B MUi CQwY QO Q=mv=t}B x@ xm CU=
|=Q@ u=t}B MUi R= pY=L Ot=}B xH}Dv QO OW Oy=wN OQ=w =tQiQ=m =@ V]@=wQ
f R Pt00 + G; CVt0 M Gg =tQiQ=m w Q=mv=t}B |R=@ u}iQ]
u=t}B MUi =} w xtD=N |=Q@ =tQiQ=m s}tYD |=yOt=}B xm OwW xHwD Ow@ Oy=wN
u=Um}'OwW xDiQou;R= TB=}wg:t O=yvW}B|x=Q=R= V}Bxmv}=x@xHwDuwO@
Ow@ Oy=wN
OwW ZQi C@=F (g) Q}N-=D Vy=m OYQO u=R}t Qo= %pw= Cr=L 23
'OQ=OvOwHwg p@=kDtO=yvW}Bu=mt=|va}'OwW|tR=e;Cr=Lu}QDxO=UQOp}rLD
Qo= CU= swrat |OOa hQ] wO Qy |=Q@ w CU= C@=F xQm=Pt `wkw R= p@k g OOa
OW Oy=wN |UQQ@ xQm=Pt Cr=L QO R}v u; xm 'OW=@ Q}eDt Ov=wD|t g `k=w QO xJ
OwW|t pL sQi 4 u}= QO xrUt ?ka x@ CWoQ@ VwQ ltm x@
125

6. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
pw= Cr=L 1 pL |=Q@ SPNE Twmat G=DvDU= pL=Qt 6 pmW
126

7. w=}vT=@a=[Q'u=}OQ=yDW=xr=u=UL=
pw= Cr=L 1 pL |R=@ CNQO 7 pmW
pw= Cr=L 2 pL |R=@ CNQO 8 pmW
pL |=Q@ |}=yv pL CW=Ov gt u=tR QU Q@ ji=wD x@ |}xkqa =tQiQ=m 'Ow@ QDW}@
CU= xOW x=Q= 8 pmW QO SPNE VwQ x@ pw= Cr=L 2
3 pL 323
}=QW Ov=O|t Q=mv=t}B OQ}PB|t =Q u=tR pm u=Q@H Q=mv=t}B Ovm|t xQm=Pt =tQiQ=m
pm uwt=Q}B xQm=Pt QO ji=wD sOa CQwY QO xm CU= |}xvwo x@ pL u}= QO xSwQB
%OQm Oy=wN ?=NDv= =Q u=t}B |xtD=N =} w MUi Oa@ s=o QO =tQiQ=m 't u=tR
CVt0 mh Ct CVt
mi Ct + CVt CVt0 (10)
Q=}U@Q=mv=t}B|=Q@=tQiQ=m=@@=wQ`}}[D|=yxv}RyxmCU=u;10|x]@=Qswyit
=@ @=wQ `}}[D sOa Q]=N x@ CU= Q[=L Q=mv=t}B 'Qo}O CQ=@a x@ =} CU= h=Ro
xOt;OwHwx@Q}N-=Du=tRpmxm|OL=D'OyOV}=Ri=Q=}U@=QOwN|=yxv}Ry=tQiQ=m
=D OW=@ Q=QkQ@ R}v 11 |x]@=Q O}=@ 'Qo}O hQ] R= Ovm u=Q@H =Q umtt u=tR s=tD =}
%OQ}PBv =Q Q=mv=t}B |R=Uxv}y@ |xv}Ro =tQiQ=m
Pht + Lhth0
LhthPht (11)
2 pL 223
=Q gt O=yvW}B =tQiQ=m 'OQ}PB|tv =Q u=tR pm u=Q@H Q=mv=t}B Ovm|t xQm=Pt =tQiQ=m
Ovm|t pw@k Q=mv=t}B 'OyO|t
u=t}B |xtD=N |w '=tQiQ=m O=yvW}B OQ CQwY QO Ov=O|t Q=mv=t}B pL u}= QO
ut[ Q=mv=t}B =D OW=@ Q=QkQ@ 8 |x]@=Q QW u}= O}=@ =Pr OQm Oy=wN ?=NDv= =Q
%Ovm ?=NDv= =Q VQ}PB sOa g Q=Okt R= |y=o;
CVt0 mh Cgt CVgt
mi Cgt + CVgt CVt0 (8)
O=}R Q=mv=t}B |=Q@ =tQiQ=m =@ @=wQ `}}[D |=yxv}Ry xm CU= u; 8 |x]@=Q swyit
=tQiQ=m=@@=wQ`}}[DsOaQ]=Nx@CU=Q[=LQ=mv=t}B'Qo}OCQ=@ax@=}CU=
%9 |x]@=Q OyO V}=Ri= V}=Ri= =tQiQ=m Q_v u}t-=D OL =D =Q OwN |=yxv}Ry
Pgti Pht + Lht
LhthPht Pgt (9)
pwYw Ov=wD|t Q=mv=t}B R= =tQiQ=m xm |Q}N-=D |xt}QH OyO|t K}[wD '9 |x]@=Q
Q}N-=D|xt}QHu}=Qo=w CU=tQiQ=mQ_vOQwt|v=tR|xR=@Q_=vDtO}rwDR= QDtm'Ovm
127

8. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
'QwmPt }=QW R= |m} smCUO u}t-=D sOa CQwY QO Ovm|t sy=Qi =tQiQ=m
GwR 's=o x@ s=o |@=}RQ= QO u}=Q@=v@ CW=O Oy=wNv =Q u=t}B MUi jL =tQiQ=m
Q}e |=y?=wH |x=Q= p}rO x@ u=t}B MUi |=yOt=}B =@ u}iQ] |=yOt=}B ?DQt
OvwW xU}=kt O}=@v 'Q@Dat
|xtD=Nx@C@Uv|QDO@Ot=}BxW}tyQ=mv=t}B|=Q@u=t}BMUixmCU=K[=w 2
xm Ovm|t VqD ji=wD sOa CQwY QO Q=mv=t}B u}=Q@=v@ CW=O Oy=wN u;
=tQiQ=m '`wkw CQwY QO w OwWv EO=L Q_vOQwt u=t}B MUi }=QW R= l}I}y
Ovm|t u=t}B |xtD=N x@ ?}eQD =Q
u}ty x@ CU= u=t}B |xtD=N R= QDO@ =tQiQ=m |=Q@ MUi Ot=}B =yxSwQB ?re= QO 3
,=twtau=t}BMUiu}=Q@=v@OvDU}vu=t}BMUix@Ovtkqa,qwtatu=}=tQiQ=mp}rO
Q=J=v x@ Q=mv=t}B ji=wD sOa CQwY QO =tQiQ=m xm CU= R}t;O}OyD |SD=QDU= l}
u=t}B |xtD=N w MUi |=yOt=}B |xU}=kt =@ =Hv}= QO Ovm|t ?=NDv= =Q u;
O}OyD Q=@Da= '=tQiQ=m |xrYwL w Q@Y w xSwQB |=y|oS}w |@=}RQ= u}vJty w
|xU}=kt 'O}OyD uOw@Q@Dat Q}e CQwY QO OwW|t XNWt MUi |=Q@ |w
OwW s=Hv= O}=@v MUi =@ ji=wD |=yOt=}B
xU}=kt Q=}at u}}aD w u=t}B MUi O}OyD Q=@Da= w u=mt= |@=}RQ= pw= s=o
Q@Dat|@=}RQ=wMUi}=QWu}t-=D|UQQ@=@'xDioV}B?r=]tx@xHwD=@s=ou}=QO
Oy=wN ji=wD R= pY=L Ot=}B =@ xU}=kt Q=}at xm |Ot=}B 'O}OyD uOw@Q@Dat Q}e =}
OwW|t XNWt 'Ow@
u=t}B |xtD=N =} MUi Q@ xQm=Pt |QDQ@ swO s=o
%OW=@v Q@Dat =} Q}PBu=mt= u=t}B MUi p@k s=o QO xm |DQwY QO 1
OwW|t ZQi u=t}B |xtD=N |=yOt=}B R= QDnQR@ gt QU Q@ xQm=Pt |=yOt=}B
%16 w 15 |=yx]@=Q
f r Pt0; CVt0 mghf Pgt;+ Cgt CVgtg
r + Pt0iPgt (15)
CVt0 + mi Cgt + CVgt (16)
=[Q= CyH g1 |=Q@ |@=wH xawtHt Qo= '16 w 15 |=yx]@=Q x@ xHwD =@
'CQwYu}=Q}eQOO};|tOwHwx@ji=wD'OW=@xDW=OOwHwxrO=atwOQy}=QW
Q=mv=t}B |R=Uxv}y@ =} u=t}B |xtD=N XwYN QO OwN Ot=}B |@=}RQ= =@ =tQiQ=m
%17 |x]@=Q OQm Oy=wN |Q}os}tYD
g1 = fx : r + Pt0iPxtCVt0 + mi Cxt + CVxtg (17)
xrO=at wO u}= ,qwtat xm CiQo xH}Dv u=wD|t QwmPt CqO=at QO CkO =@
OvW=@ |mJwm Q=}U@ O=Oa= m w r xmv}= Qot 'OvQ=O |mQDWt ?=wH |xawtHt
OW=@ O=}R |r}N uDUmW |=yxv}Ry xmv}= =}
Q=QkQ@ 19 w 18 @=wQ 'OW=@ Q@Dat w Q}PBu=mt= u=t}B MUi |SD=QDU= xJv=vJ 2
%CU=
f R Pt00 + G; CVt0 M Gghf Pgt;+ Cgt CVgtg
R + Pt00 GiPgt (18)
CVt0 + M + Gi Cgt + CVgt (19)
xm CU= |O}rwD R= QDtm Q=mv=t}B Q}N-=D |xt}QH xm CU= |vat u}= x@ 11 |x]@=Q
CUOu;x@Ov=wD|t(ht) Q=mv=t}BQ_vOQwtu=tRQOxSwQBp}wLDCQwYQO=tQiQ=m
xOW x=Q= 9 pmW QO SPNE VwQ x@ pw= Cr=L 3 pL |=Q@ |}=yv pL O@=}
CU=
4 pL 423
=Q u=tR ht u=R}t x@ OwN |=yxv}Ry uOQmsm |=Q@ Q=mv=t}B Ovm|tv xQm=Pt =tQiQ=m
Ovm|t u=Q@H
|xt}QH Q=mv=t}B 'gt u=tR |=Q@ xQm=Pt x@ OwQw CQwY QO Ov=O|t =tQiQ=m
%12 |x]@=Q OQm Oy=wNv CN=OQB gt u=tR u=Q@H CQwY QO =Q Q}N-=D
CVt0 + mi Cht + CVht + Lht
mi Cht + CVht CVt0 + Lht (12)
|x]@=Q CU= O=}R Q=}U@ =tQiQ=m =@ @=wQ `}}[D |xv}Ry R}v =Hv}= QO p@k x@=Wt
%13
Pht + Lhti Pgt
LhtiPht Pgt (13)
%CW=O s}y=wN =Q 14 |x]@=Q '13 w 12 |x]@=Q wO ?}mQD R=
Pht PgthLhthCVt0 + m + Cht CVht (14)
O}rwD x@ C@Uv Q}N-=D |xt}QH O=}R |r}N V}=Ri= |xOvvmh}YwD '14 |x]@=Q
R}v ht =D gt |v=tR |xR=@ QO |w Q_=vDt O}rwD R= |DL xm |Qw] x@ 'CU=tQiQ=m
Q}N-=D u=tR u=Q@H |=Q@ gt O=yvW}B x@ |}xkqa =tQiQ=m u}=Q@=v@ CU= xOW QDW}@
|xt=O=,=vt[ CU= xOw@ O=}R,=D@Uv R}v =tQiQ=m =@ @=wQ `}}[D |xv}Ry R}v w 'OQ=Ov
=@ xm pmW u}O@ OW=@ pO=aD l} X=N }=QW QO Ov=wD|t R}v xSwQB |r@k OvwQ
pL |=Q@ |}=yv pL OW=@ Q=QkQ@ R}v h = 0 '13 w 12 CqO=at=v }=QW C}=aQ
CU= xOW x=Q= 10 pmW QO SPNE VwQ x@ pw= Cr=L 4
OwWZQiQ}eDt(g) Q}N-=DVy=mOYQOu=R}tQo=%swOCr=L33
u=mt= s}vm|t ZQi 'ODi=|t j=iD= =yxSwQB QO ,=ak=w xJv; x@=Wt Cr=L u}= QO
Qy Ot=}B Qo= OQ=O OwHw g OOa u}}aD |=Q@ ji=wD w O=yvW}B pO@ w OQ w |vRxv=J
QO 'OwQ|t V}B ji=wD CtU x@ |R=@ 'OW=@ ji=wD sOa Cr=L R= QDW}@ um}R=@ wO
CtU x@ u=t}B xm CiQo xH}Dv u=wD|t w OQ=Ov OwHw ji=wD u=mt= CQwY u}= Q}e
SPNE VwQ x@ swO Cr=L |=Q@ |}=yv pL Ovm|t p}t MUi =} u=t}B |xtD=N
CU= xOW x=Q= 11 pmW QO
gt u=tR u}}aD |=Q@ ji=wD OvwQ 133
Qy R= QDW}@ ji=wD Cr=L QO u}iQ] |=yOt=}B O}=@ g OOa u}}aD CyH ji=wD |=Q@
'u=t}B |xtD=N 'u=t}B MUi =@ ji=wD Cr=L s=o x@ s=o |@=}RQ= =@ OW=@ |Qo}O Ot=}B
Oy=wN CUO x@ |@=wH |xawtHt Q=mv=t}B |wU R= |R=Uxv}y@ w t u=tR pm VQ}PB
hrDNt Cq=L Ot=}B |xU}=kt =@ 'OWv pY=L |@=wH |xawtHt xJv=vJ Ot;
C=mv u}= x@ O}=@ Cr=L u}= QO pOt p}rLD QO OwW|t u}}aD |R=@ pO=aD |x]kv
%CW=O xHwD
xawtHtR=QWl}smCUOu}t-=DsRrDUt=tQiQ=m|wUR=u=t}BMUiu=mt= 1
|=Q@ =Q u=t}B MUi Q=}DN= xm 'CU= xSwQB Q@ sm=L u=t}B QO xOW^=Lr }=QW
128

9. w=}vT=@a=[Q'u=}OQ=yDW=xr=u=UL=
pw= Cr=L 3 pL |R=@ CNQO 9 pmW
pw= Cr=L 4 pL |R=@ CNQO 10 pmW
swO Cr=L pL |R=@ CNQO 11 pmW
g2 =fx : R + Pt00 G Pxt w CVt0 + M + G Cxt
+ CVxtg (20)
t u=tR pm u=Q@H =@ gt QU Q@ ji=wD |xU}=kt swU s=o
|xtD=N w MUi 'OW=@ xDW=O OwHw g |=Q@ |@=wH |xawtHt swO s=o QO xJv=vJ
Oy=wNvp=@vOx@|QDy@Ot=}Bgt u=R}tx@C=Q}N-=Du=Q@Hx@C@Uv=tQiQ=m|=Q@u=t}B
=[Q= CyH g2 |=Q@ |@=wH xawtHt Qo= '19 w 18 |=yx]@=Q x@ xHwD =@
CQwYu}= Q}e QO O};|t OwHwx@ ji=wD 'OW=@ xDW=O OwHw xrO=at wO Qy }=QW
|Q}os}tYD Q=mv=t}B |R=Uxv}y@ w u=t}B MUi u}@ OwN Ot=}B |@=}RQ= =@ =tQiQ=m
|=yOt=}B =@ xU}=kt R= pY=L ?=wH xawtHt OwW|t x_Lqt OQm Oy=wN
=Q |QDnQR@ |=yg CU= Q[=L R}v Q=mv=t}B w CU= QDxOQDUo w QDnQR@ MUi
%20 |x]@=Q Ovm ?=NDv=
129

10. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
u=Q@H p@=k u=tR COt OYQO ?UL Q@ =yC}r=ai uDUmW |xv}Ry 1 pwOH
uDUmW |xv}Ry u=tR COt
u=twD OQ=}r}t
0 0
0 3 10
0 7 20
1 2 30
1 7 40
2 7 50
3 5 60
4 9 70
6 0 80
7 2 90
8 5 100
|wUR=CU=umttQ}e'OvDUyu=t}BMUiCQwYQOQ=mv=t}Bx@|r}tLD|xv}Ry
CQwYx@ |w TB CU= u=twD OQ=}r}t 5 95 Q@=Q@ Q=mv=t}B |xv}Ry |xv}tm 'Qo}O
p=L OQm Oy=wN s=Ok= Q}N-=D u=tR 10 =D u=Q@H w |R=Uxv}y@ x@ C@Uv xv=@r]w=O
|UQQ@ w xrUt p}rLD x@ |mUv}OQwtU= |}q=m w |v=RQ=y Vv pL x=Q ltm x@
u=tR|xv}W}@R=OYQO60=D10|xR=@QO=yC}r=aiuDUmWCyHu}iQ]ji=wD
CU= xOW xDN=OQB u=Q@H p@=k
|v=RQ=y Vv pL x=Q 24
XNWt xDUw}B ,=D@Uv OQ@y=Q l} QO Q=mv=t}B w =tQiQ=m Ot=}B '3 pwOH s}_vD =@
|x]@=Qltmx@xm'CU=VvhOy`@=DQ=Okt3pwOHR=sQ=yJuwDUOWOy=wN
%CU= xOt; CUOx@ 24
= maxf;d
(f1 d1)w1:(f2 d2)w2 (24)
CU=xOWxDiQoQ_vQO(w1 = w2 = 0 5) |w=Utu}iQ]p}RvDpt=au;QOxm
u}=Q@=v@ CU= xO=O MQ u=tR 20 QO hOy `@=D |xv}W}@ '3 pwOH |xOy=Wt =@
OW Oy=wN pY=L x=t 4 O}OtD =@ Q=mv=t}B w =tQiQ=m ji=wD
pL x=Q ltm x@ Q=mv=t}B w =tQiQ=m |vRxv=J CQOk uOQmOQ=w 34
|v=RQ=y Vv
0 3 w 0 7 ?}DQD x@ xrUt u}= QO Q=mv=t}B w =tQiQ=m |vRxv=J CQOk xm |DQwY QO
,=D@Uv|SD=QDU=l}QOQ=mv=t}Bw=tQiQ=mOt=}B'4pwOHs}_vD=@'OwWxDiQoQ_vQO
35 QO hOy `@=D |xv}W}@ pwOH u}= |xOy=Wt =@ OW Oy=wN XNWt xDUw}B
Oy=wNpY=LRwQ98O}OtD=@Q=mv=t}Bw=tQiQ=mji=wDu}=Q@=v@CU=xO=OMQu=tR
OW
=@ Q=mv=t}B u}=Q@=v@ Ow@ Oy=wN Q@DatQ}e =yO}OyD 'u=t}B |xtD=N w MUi w CW=O
|r= 21 |=yx]@=Q Ovm|t xQm=Pt x@ Q=O=w =Q =tQiQ=m t u=tR pm u=Q@H VQ}PB sOa
%23
f Pht + Lht;+ Cht CVht Lhtghf Pgt;+ Cgt CVgtg
Pht + Lhth Pgt
LhthPht Pgt (21)
+ Cht CVht Lhth+ Cgt CVgt
Lhti Cgt + CVgt + Cht CVht (22)
Cgt + CVgt + Cht CVhthLhthPht Pgt (23)
Q=mv=t}Bxm|wLvx@'CU=Q}N-=D|xt}QHQF-wt|xOwOLt|xOvvmu=}@'23|xrO=at
O}=@ |}xvwo x@ Q}N-=D |xt}QH Q=Okt xm =vat u}= x@ OvwW ji=wD x@ Ovtkqa =tQiQ=m w
ht Q=mv=t}B Q_vOQwt |=yC}r=ai uDUmW |xv}Ry hqDN= R= xmv}= ut[ xm OW=@
|xR=@ u=ty QO =tQiQ=m O}rwD hqDN= R= u=tRsy 'OW=@ QDW}@ gt ji=wD |xOwOLt =D
OW=@ QDtm |v=tR
CQwYQO23|x]@=Q?=wH|xawtHt=@swOs=o?=wH|xawtHtl=QDW=
=@ CQwYu}= Q}e QO Ow@ Oy=wN Q}eDt g Cr=L QO |}=yv ?=wH |xawtHt 'OwHw
Q=mv=t}B|R=Uxv}y@=}xtD=N CtU x@u=t}BLht 'OL R= V}@ uOw@ lJwm =} nQR@
p}rO x@ Q=mv=t}B 'OW=@ O=}R OL R= V}@ Q}N-=D |xt}QH Qo= CiQ Oy=wN V}B
VQ}PB R= 'ji=wD x@ |UQDUO sOa R= |y=o; x@ xHwD =@ w jwi |xt}QH R= |Q}oW}B
MUi =} xtD=N ?=NDv= x@ Q=O=w =tQiQ=m w O}Wm Oy=wN CUO =tQiQ=m O=yvW}B xvwoQy
Q=mv=t}B 'OW=@ sm OL R= V}@ Q}N-=D |xt}QH Qo= 'Qo}O |wU R= Ow@ Oy=wN u=t}B
Q}N-=D R= |WN@ u=Q@H w xSwQB |R=Uxv}y@ d=QU x@ ji=wD u=mt= sOa p}rO x@ sy R=@
=tQiQ=m CQwYu}= QO CiQ Oy=wN 'Ovm |w xHwDt =Q xv}Ry u}QDtm xm |v=R}t x@
OQm Oy=wN ?=NDv= =Q |m} Q=mv=t}B s}tYD pw@k =} u=t}B |xtD=N u}@
|OQwt |xar=]t 4
QO CU= xOw@ Q=Qk xm u=tQm x@ s@ ?; p=kDv= N w x}iYD |xSwQB |=tQiQ=m
|xt=vQ@ pQDvm =@ xSwQB `wQW R= TB x=t 6 'OUQ@ |Q=OQ@xQy@ x@ x=t 24 u=tR COt
Oy=wN |Q=OQ@xQy@ x@ Q}N-=D x=t 6 =@ xSwQB xm CU= xO}UQ xH}Dv u}= x@ |Ov@u=tR
|=Q@xSwQBCU=xOW|v}@V}BwxOw@u=twDOQ=}r}t100O=OQ=Qk|x}rw=dr@tO}UQ
|v}@V}B '|UQQ@ R= TB OQ=O R=}v |i=[= |xv}Ry u=twD OQ=}r}t 3 x@ uOWp}tmD
uDUmW |xv}Ry CU= u=Q@H p@=k Q}N-=D u=tR R= x=t 5 |xv}W}@ xm CU= xOW
CU= xOW x=Q= 1 pwOH QO u=Q@H p@=k u=tR |xv}W}@ OYQO ?UL Q@ =yC}r=ai
OQ=}r}t 1 5 =tQiQ=m x=t Qy O}rwD OwU w u=twD uw}r}t 600 xv=y=t Q}N-=D |xt}QH
?}DQD x@ u=t}B MUi CQwY QO Q=mv=t}B w =tQiQ=m x@ |r}tLD |xv}Ry CU= u=twD
u=twD OQ=}r}t 7 5 Q=mv=t}B |ivt Ot=}B |xv}W}@ CU= u=twD OQ=}r}t 7 5 w 12
CU= xOw@
p=Ft p}rLD 14
u=Q@H p@=k hrDNt |=yu=tR =R= x@ u}iQ] Ot=}B u; QO xm '2 pwOH |x_Lqt =@
R= QDW}@ uwJ '60 |q=@ |v=Q@H |=yu=tR xm CU= XNWt 'CU= xOW x@U=Lt
130

11. w=}vT=@a=[Q'u=}OQ=yDW=xr=u=UL=
u=Q@H p@=k u=tR OYQO =R= x@ =tQiQ=m w Q=mv=t}B |rm Ot=}B 2 pwOH
|=yxv}Ry pm `tH |=yxv}Ry pm `tH Q=mv=t}B |xv}Ry `tH CV
|xt}QH R= pY=L OwU uDUmW |xv}Ry p@=k u=tR
=tQiQ=m Q=mv=t}B xt}QH uwO@ Q}N-=D =tQiQ=m O}rwD u=twD OQ=}r}t u=Q@H
4 50 6 00 3 00 3 00 3 7 5 0 0
4 05 5 95 3 25 2 95 2 7 6 75 0 3 10
3 60 6 00 3 60 2 90 2 4 6 0 7 20
3 15 6 15 4 05 2 85 2 1 5 25 1 2 30
2 70 6 30 4 50 2 80 1 8 4 5 1 7 40
2 25 6 95 5 45 2 75 1 5 3 75 2 7 50
1 80 7 40 6 20 2 70 1 2 3 3 5 60
1 35 8 45 7 55 2 65 0 9 2 25 4 9 70
0 90 9 20 8 60 2 60 0 6 1 5 6 0 80
0 45 10 05 9 75 2 55 0 3 0 75 7 2 90
0 11 00 11 00 2 50 0 0 8 5 100
u=Q@Hp@=ku=tR|xv}W}@?ULQ@25|x]@=QF(u) hOy`@=DQ=Okt5pwOH
hOy `@=D Q=Okt |=yxv}Ry `tH |=yxv}Ry `tH p@=k u=tR
|mUv}OQwtU= |}q=m =tQiQ=m Q=mv=t}B u=Q@H
3 9525 4 05 5 95 10
2 73 3 60 6 00 20
0 4575 3 15 6 15 30
1 815 2 70 6 30 40
9 3375 2 25 6 95 50
14 76 1 80 7 40 60
|Q}os}tYD OvwQ 5
C=}[Qi 15
OvDUy swrat u}iQ] |=Q@ w |ivt Q}e O=Oa= :::;G;M;m;CV |=yQDt=Q=B 1
Ovvm|tv R}t;xQ]=Nt ?=NDv= w OvQ=O |vqka Q=DiQ u=vm}R=@ 2
CU= Q=QkQ@ 0 h g 1 |x]@=Q h w g O=Oa= u}@ 3
}=QWw|r=t|=yQ_vhqDN=w`@=vtw|ov}Okv'Q=@Da=Ow@tm|r=tCqmWt 4
OvDU}v Q}N-=D p}rO |}=wy w ?;
s}tYD Ov};Qi 25
CQwY x@ xQm=Pt |xR=@ 'OW=@ xO=O MQ MUi }=QW R= |m} smCUO xJv=vJ 1
%CU= u=}@ p@=k 26 |x]@=Q
g1 =fx : Pxt max(r + Pt0;R + Pt00 G;Pht Lht); Cxt
+ CVxt max(CVt0 + M + G; Cht + CVht + Lht)g
(26)
Q}e QO Ovm|t XNWt =Q xQm=Pt |xR=@ 'OW=@ |yDQ}e g1 |xawtHt Qo=
xm =Q |t}tYD '|R=Uxv}y@ w 'u=t}B |xtD=N 'MUi u}@ =tQiQ=m CQwYu}=
OQm Oy=wN ?=NDv= 'Ovm |w xHwDt =Q Ot=}B u}QDW}@
|w=Ut p}RvD pt=a =@ Vv hOy `@=D Q=Okt 3 pwOH
`@=D Q=Okt |=yxv}Ry pm `tH |=yxv}Ry pm `tH p@=k u=tR
Vv hOy =tQiQ=m Q=mv=t}B u=Q@H
12 32 4 05 5 95 10
12 60 3 60 6 00 20
11 95 3 15 6 15 30
11 16 2 70 6 30 40
5 36 2 25 6 95 50
1 02 1 80 7 40 60
u}iQ] Cw=iDt |vRxv=J CQOk =@ Vv hOy `@=D Q=Okt 4 pwOH
hOy `@=D Q=Okt |=yxv}Ry `tH |=yxv}Ry `tH p@=k u=tR
|v=RQ=y Vv =tQiQ=m Q=mv=t}B u=Q@H
4 87 4 05 5 95 10
5 01 3 60 6 00 20
5 03 3 15 6 15 30
5 03 2 70 6 30 40
4 12 2 25 6 95 50
2 55 1 80 7 40 60
|mUv}OQwtU= |}q=m pL x=Q 44
|w=UD hQ] wO p[=iD '|mUv}OQwtU= |}q=m pL x=Q x@ w@Qt hOy `@=D |=Q@
QiY Q@=Q@ O}=@ pL x=Q u}= QO |vRxv=J MU=B w CU= xOW xDiQo Q_v QO 25 |x]@=Q
%25 |x]@=Q OwW
F(u) = (f1 d1):(t2 d2) (f2 d2):(t1 d1) (25)
XNWt xDUw}B ,=D@Uv OQ@y=Q l} QO Q=mv=t}B w =tQiQ=m Ot=}B '5 pwOH s}_vD =@
'CU= |mUv}OQwtU= |}q=m hOy `@=D Q=Okt pwOH u}= sQ=yJ uwDU OW Oy=wN
'|@=}u=}t=@wpwOHu}=|xOy=Wt=@CU=xOt;CUOx@25|x]@=Q|ltmx@xm
OW Oy=wN pY=L RwQ 103 O}OtD =@ w u=tR 32 QO Q=mv=t}B w =tQiQ=m ji=wD
131

12. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
Q}N-=D =@ xH=wt |xSwQB l} |=Q@ |Q}os}tYD u=}QH Q=Owtv 12 pmW
=tQiQ=m |=yOQ@y=Q 16
QO =tQiQ=m |=Q@ QF-wt |=yQDt=Q=B 'CU= XNWt pOt R}r=v; R= uwvm=D xJv; j@=]t
%Ow@ Oy=wN CQwY u}= x@ Q=mv=t}B x@ VQ_v p=ta=
=tQiQ=m p}RvD pt=a
@=wQ `}}[D |xv}Ry
Q}N-=D |xt}QH
xYk=vt |xQ=@wO |Q=RoQ@ |xv}Ry
|UQO=O |=yxv}Ry
t0 |Ov@u=tR |xt=vQ@ R= h=QLv= hWm u=tR
|QDq=@|vRxv=J|}=v=wD'OyOu=WvQDtm=QOwNp}RvDpt=aOv=wD@=tQiQ=mxJQy 1
CW=O Oy=wN
CtU x@ QDW}@ =Q Q=mv=t}B 'OyO xwrH QDW}@ =Q OwN O}rwD OwU QOkJ Qy =tQiQ=m 2
Ovm|t p}=tDt QDW}@ u=tR u=Q@H w nQR@ |=yg
u}=Q@=v@ CW=O Oy=wN |QDq=@ CUO =tQiQ=m '@=wQ `}}[D |xv}Ry V}=Ri= =@ 3
CU=tQiQ=m `[wt C}wkD Ea=@ QDq=@ |ov}Okv u=}QH w uOw@ s=vVwN
O@=}|t Vy=m xQm=Pt QO =tQiQ=m |}=v=wD 'OW=@ xOWv EO=L MUi }=QW Qo= 2
%OwW|tu}}aD27|x]@=QCQwYx@g2 ?=wH|xawtHt'xQm=Pt|xR=@u}=Q@=v@
g2 =fx : Pxt max(r + Pt0;Pht Lht); Cxt + CVxt
max(CVt0 + m; Cht + CVht + Lht)g (27)
Q}e QO Ovm|t XNWt =Q xQm=Pt |xR=@ 'OW=@ |yDQ}e g2 |xawtHt Qo=
u}QDW}@ xm =Q |t}tYD '|R=Uxv}y@ w u=t}B |xtD=N u}@ =tQiQ=m CQwYu}=
OQm Oy=wN ?=NDv= 'Ovm |w xHwDt =Q Ot=}B
u=Wv =Q Q}N-=D =@ xH=wt |xSwQB l} |=Q@ |Q}os}tYD u=}QH Q=Owtv '12 pmW
QO xDioV}B |=yVwQ ltm x@ xQm=Pt |xR=@ u}}aD R= TB p=L Qy x@ OyO|t
w p}RvD pt=a u}}aD w |mUv}OQwtU= |}q=m '|v=RQ=y Vv C=}@O= Q@ QwQt
OQw; CUOx@ =Q ji=wD j}kO |x]kv u=wD|t 'u=vm}R=@ |xrYwL w Q@Y u=R}t
Q=mv=t}B w =tQiQ=m |=y|SD=QDU= 6
x@ Q=mv=t}B w =tQiQ=m |=Q@ =Q |}=yOQ@y=Q u=wD|t u; p}rLD w xOWx=Q= pOt T=U=Q@
O=O x=Q= CQwY wO
132

13. w=}vT=@a=[Q'u=}OQ=yDW=xr=u=UL=
}=QW CyH |oO=t; w xQ@N |qmw |Q}oQ=m x@ 'O=OQ=Qk O=it QO s=y@= sOa 5
OwW|t u=}R p=tDL= Vy=m Ea=@ 'xOWv|v}@V}B
'xSwQB |=Q@ |ak=w w K}LY |Ov@u=tR |xt=vQ@ |x=Q= w Ot;Q=m |vi QDiO OwHw 6
|Ov@u=tR|xt=vQ@R=h=QLv=QD`}QUxJQyhWmEa=@'|Ov@u=tR|xt=vQ@pQDvm
OwW|t
w |oO=t; '|v=Uv= |wQ}v w `@=vt |Q}oQ=mx@ QO q=@ |QwxQy@ w K}LY C}Q}Ot 7
'O}OH |=y|SwrwvmD |Q}oQ=m x@ swRr CQwY QO w xSwQB }=QW =@ j}@]D |}=v=wD
Ea=@ hrDNt }=QW =@ xyH=wt QO |Q}PBh=]av= w |D}Q}Ot |=yOQm}wQ Q}}eD
OwW|t Q=mv=t}B |r=tDL= u=}R w Q}N-=D p=tDL= Vy=m
w Ovm |Q}oW}B MUi }=QW EwOL R= |Q}@=OD |Q}oQ=mx@ =@ Ov=wD|t Q=mv=t}B 8
OwW|t =tQiQ=m |vRxv=J CQOk h}a[D Ea=@ u}=
|Q}oxH}Dv 7
pt=wa |}=U=vW w OyO |wQ |OOaDt p}qO x@ Ov=wD|t |v=Qta |=yxSwQB QO Q}N-=D
pOt l} |x=Q= ut[ Q=DWwv u}= CU= xDiQo Q=Qk xar=]t OQwt =yQ=@ u; QO QF-wt
|xrUt =@ Q}oQO u}iQ] OQ@y=Q w Q=DiQ p}rLD x@ s=o x@ s=o |OQm}wQ =@ |[=}Q
|rL x=Q |x=Q= w CN=U C=aR=vt `wv u}= pYi w pL xD@r= CU= xDN=OQB Q}N-=D
'xSwQB Qy |=Q@ Q}N-=D =@ xH=wt |=yxSwQB |R=@ CNQO |x=Q= j}Q] R= XNWt
x@ pOt u}= CU= xOW s=Hv= VywSB u}= QO Q=@ u}rw= |=Q@ xm CU= xOw@ |t=Ok=
'Q}N-=D|xrUtR=QDj}ta|mQO?Umut[=DOvm|tltmu=Q=mv=t}Bwu=}=tQiQ=m
u}vJ =@ xyH=wt QO umtt |=yOQ@y=Q w OwN C}akwt R= j}kO ,=D@Uv |r}rLD x@
OvUQ@ |]}=QW
QO Ovv=wD|t xrUt QO p}NO |=yQDt=Q=B xm Ci=}QO u=wD|t pOt p}rLD =@
xQm=PtxR=@'OW=@QDW}@=tQiQ=m|vRxv=Ju=wDxJQyOvW=@QF-wtxQm=Pt|xR=@CaUw
|v=Q@H |=yu=tR u; Vy=m =@ w O@=}|t VQDUo QDW}@ |v=Q@H |=yu=tR CtU x@
OvwW|t Q@DatQ}e nQR@
QO Ov=wD|t 'OW=@ xSwQB |=yQDt=Q=B Q}=U =@ ?U=vDt=v Q}N-=D |xt}QH xJv=vJ
Q}N-=D |xt}QH OL R= V}@ |oQR@ =@ xm =vat u}= x@ OW=@ QF= |@ xQm=Pt |xH}Dv
=@ w CU= Q=}at =yvD u=t}B |xtD=N =} MUi =@ ji=wD Ot=}B |xU}=kt '=tQiQ=m |=Q@
Q}N-=D |xt}QH 'u}=Q@=v@ OQ=Ov Q}N-=D CyH R= |v=Qov Q=mv=t}B 'R}v u; uOw@lJwm
xR=@ QO Ov=wD|t Q}N-=D |xt}QH CUQO ?=NDv= =t= OwW|t QF=|@ xQm=Pt xR=@ QO
xv=@r]w=O CQwYx@ Q=mv=t}B w O}OyD uwO@ =tQiQ=m xm |wLv x@ 'OW=@ Q=PoQF= xQm=Pt
CUO Q}N-=D R= |k]vt |v=tR u=Q@H |=Q@ |ki=wD x@ |tm |xv}Ry w u=tR hQY =@
Ov@=}
CQOk V}=Ri= =@ xm OwW|t x_Lqt xOWx=Q= |OQwt |xar=]t QO CkO =@
w Ovm|t p}t QDx=Dwm |=yO}OtD u=tR CtU x@ ji=wD |x]kv '=tQiQ=m |vRxv=J
Tmar=@
=Q xQm=Pt Ov=wD|t |}=y|oS}w xJ xm CU= xO=O u=Wv pOt s=o x@ s=o R}r=v;
pOtCU=xOWx=Q=hQ]wO|=yOQ@y=Q|=Q@|}=yO=yvW}Bu;|x}=BQ@wOvmO}OyD
'O=}R Ckw hQY |=H x@ 'xSwQB XwYN QO =D Ovm ltm u}iQ] x@ Ov=wD|t QwmPt
xOW^=Lr|D=}[QipOtQOu}vJtyOvUQ@xv=}=Qo`k=ww|k]vt|}xH}Dvx@QDOwR
OR=U|t QwOkt =Q u=Qo}O |=Q@ u; |xaUwD u=mt= xm CU=
sOa CQwY QO OW=@ Q=PoQ}F-=D =D OwW ?=NDv= CkO x@ O}=@ Q}N-=D |xt}QH 4
'OW=@ QDW}@ xJ Qy xQm=Pt |xOwOLt QO |rw OQ=Ov OwHw ji=wD u=mt= '?U=vD
Ovm|t QDQw@Y =Q =tQiQ=m
Q=mv=t}B`}QU|v}Ro}=Hu=mt='xYk=vt|xQ=@wO|Q=RoQ@|xv}RyuO=OxwrHsm 5
|=Q@ =tQiQ=m =@ |Q=mty uOw@?=PH w u=t}B |xtD=N =} MUi CQwY QO O}OH
OW=@ QF-wt CyH u}= QO Ov=wD|t u=Q=mv=t}B Q}=U
QO 'OvQ=O |r@k |Q=mty |xk@=U xm s=vVwN w |tw@ u=Q=mv=t}B R= xO=iDU= 6
p=tDL=Vy=mut[wOvm|t=O}B|O=}RC}ty=C@=Fs=tD=M}Q=D=@|}=yxSwQB
OW Oy=wN =tQiQ=m |vRxv=J CQOk C}wkD Ea=@ Q}N-=D RwQ@
|qmw R= xO=iDU= 'O=OQ=Qk |twta w |YwYN }=QW h=iW w K}LY u}wOD 7
|kwkL p=Ut w xOWv|v}@V}B }=QW CyH uDW=O |oO=t; w xQ@N w Qy=t
Ovm |Q}owrH |r=tDL= |=yu=}R R= Ov=wD|t
'Qy=twxO}RQw|xSwQBpQDvm|=ys}DR=xO=iDU=wOt;Q=m|viQDiO=}Qw=WtOwHw 8
'=yC}r=ai u=tR w sHL C=@U=Lt pL=Qt R= l} Qy QO xDUw}B w j}kO CQ=_v
C=]=@DQ= '|Ov@u=tR |xt=vQ@ pQDvm 'xSwQB |Ov@u=tR |xt=vQ@ ?}wYD w u}wOD
u}= QD`}QU xJ Qy hWm Ea=@ |r=tDL= h=QLv= u}}aD w Q=mv=t}B =@ l}ORv
QDtm uO}O u=}R w h=QLv= V}=Ri= R= |Q}oW}B u; |xH}Dv w OwW|t h=QLv=
Ow@ Oy=wN u}iQ]
C}wkD Ea=@ s}tYD QO C}a]=k uO=Ou=Wv w MUi O}OyD x@ uO}WN@Q=@Da= 9
CU=tQiQ=m `[wt
Q=mv=t}B |=yOQ@y=Q 26
%CU=u}vJQ=mv=t}B|=Q@VN@QF=|=yQDt=Q=B|xDioV}B?r=]twpOtx@xHwD=@
Q=mv=t}B p}RvD pt=a
=tQiQ=m =@ @=wQ `}}[D |xv}Ry
Q}N-=D |xt}QH
CV
|UQO=O |=yxv}Ry
MUi p}rO u}t-=D R= |Q}oW}B
t0 |Ov@u=tR |xt=vQ@ R= h=QLv= hWm u=tR
Q=mv=t}B |vRxv=J u=wD V}=Ri= Ea=@ QDtm p}RvD pt=a w OwN uO=OxwrH Qw@Y 1
OwW|t
u=Q@H x@ =tQiQ=m 'OyO xwrH QDW}@ =Q OwN uDUmW |=yxv}Ry Q=mv=t}B xJ Qy 2
OQm Oy=wN Ca=vk |QDtm u=tR
Q}=UQOpvUQBw`@=vt|Q}oQ=mx@u=mt='Q=mv=t}B|q=@|Ovtv=wD'CQyWuUL 3
C}wkD Ea=@ w OyO|t xwrH sm =Q =tQiQ=m =@ @=wQ `}}[D |xv}Ry '=yxSwQB
CU= Q=mv=t}B `[wt
p}RvD pt=a 'OwW ?=NDv= xQm=Pt |xOwOLt QO |QDtm Q}N-=D |xt}QH xJ Qy 4
OwW|t QDW}@ Q=mv=t}B
133

14. |xSwQBQOQ=mv=t}Bw=tQiQ=m|xv}y@OQ@y=Q
=yCWwv=B
1. public- private partnership
2. action
3. payo functions
4. rationality
5. extensive form
6. perfect knowledge game
7. non-cooperative
8. Nash equilibrium
9. backward induction
10. the sub game- perfect Nash equilibrium (SPNE)
11. non-credible
12. discount factor
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