R}Qxt=vQ

Transcription

R}Qxt=vQ
OWQ= |U=vWQ |wHWv=O
Original Article
109101 "X '2 |xQ=tW '30 1 |xQwO
1393 u=DUtR 'h} QW C} Q}Ot w `}=vY |UOvyt
|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
|y=oQ=m u=} QH |xrUt |R}Qxt=vQ@
|iO=YD Cr=L QO |O=OUv=
=k;p; =[QOtLt
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|r}=[i OtLt
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Q=}Wv=O
|=iW pwUQ
|Uw] u}Or=Q}Yv xH=wN x=oWv=O '`}=vY |UOvyt |xOmWv=O
QO |O}rm pt=wa R= |m} O}rwD |R}Qxt=vQ@ p=Ut QO C=}rta |r=wD w |Ov@u=tR |xt=vQ@
'C=a}=[ p}rkD 'x}=tQU CW=@v= R= |Q}owrH Ea=@ xm CU= |O}rwD |=yu=tR=U C}kiwt
x@ `kwtx@ |} woMU=B w =yu; |xv}y@ OQ@Q=m w Cq;u}W=t |Q=m}@ hPL =} Vy=m
u; Q@ ZQi |Ov@u=tR w |R}Qxt=vQ@ OQ=Ov=DU= |=yVwQ QO "OwW|t u=} QDWt |=yVQ=iU
`wvD p}rOx@ ZQi u}= &ODi=|t j=iD= u}at w |a]k \}=QW l} QO xt=vQ@ |=QH= xm CU=
u}vJ QO "CU}v |rta w CUQO ZQi 'u; Q@ sm =L C}a]k sOa \}=QW w R=}v OQwt `@=vt
Q=OQwNQ@ |}q=@ C}ty= R= |R=Uxv}y@ |=Hx@ pL |=yVwQ |Q=wDU= |UQQ@ |]}=QW
CU= |Dr=L QO |O=OUv= |y=oQ=m |R}Qxt=vQ@ |xrUt pL j}kLD u}= |rY= hOy "CU=
pL |=Q@ |Q=mD@==Qi VwQ CWy j}kLD u}= QO "CU= Q}PB Q}}eD =yQ=m VR=OQB u=tR xm
OQmrta |@=}RQ= |=Q@ 1 =D@ |Q=wDU= Q=}at R= "CU= xDiQo Q=Qk xO=iDU= OQwt Qwm Pt |xrUt
|xOvyOu=Wv =y|UQQ@ |xH}Dv "CU= xOW xO=iDU= u}at=v \}=QW QO |O=yvW}B |=yVwQ
"CU=yVwQ Q}=U x@ C@Uv u=tRtyQ}e |wHwCUH =@ l}DvS VwQ QDq=@ |Q=wDU=
maleagha@ kntu.ac.ir
mohammad 1504@kntu.ac.ir
rbashirzadeh@kntu.ac.ir
shafaei@kntu.ac.ir
|=ysD}Qwor= 'Q=wDU= |R}Qxt=vQ@ '|O=OUv= |y=oQ=m |R}Qxt=vQ@ %|O}rm u=oS=w
"|iO=YD Cr=L QO |R}Qxt=vQ@ '|Q=mD@==Qi
t t "1
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&O}; p}=v |QDQ=wDU= MU=B x@ C}a]k sOa \}=QW QO Ov=wD@ xm CU= ?wr]t |WwQ p=Ut XwYNQO |O=}R C=k}kLD '|y=oQ=m O}rwD p=Ut OQ@Q=m |v=w=Qi x@ xHwD =@
|QDsm C}U=UL R= C}a]k sOa \}=QW x@ C@Uv VwQ |HwQN xm =vat u}O@ p}rOx@ |O}rwD C=Hv=NQ=m R= |Q=}U@ QO 'pta QO "CU= xOW s=Hv= |y=oQ=m O}rwD
p=Ft |=Q@ "CU= C}a]k sOa Vy=m Q@ RmQtD 'swO OQm}wQ QO [3] "OW=@ Q=OQwNQ@ |v=}t |xQ}NP C}OwOLt O}=@ C=a]k |}=}t}W w |m} R}i C}i}m Ci= R= |Q}owrH
u}W=t |@=QN R= |W=v C}a]k sOa Q}F-=D u=wD|t xv=Q}oW}B C=Q}taD QFw-t |=QH= =@
u}W=t wO u}@ C=a]k Q=_Dv= u=tR =} u}W=t wO u}@ xOW xQ}NP Q=m O=OaD pmWx@ =Q
xDiQo Q_v QO C}a]k sOa w CU= Q_v Ot pw= OQm}wQ xr=kt u}= QO "O=O Vy=m =Q
u=} QH p=Ut XwYNQO xDiQo CQwY |=yQ=m |UQQ@ seQ|ra [1] "CiQo Q_v QO
"CU=yQ=m s=Hv= u=tR x@ \w@ Qt xOW |a]k ,qt=m =Q \}=QW xOW s=Hv= C=ar=]t |t=tD QO u}kkLt [2] '|O=OUv= |y=oQ=m
"CU= 2 xv=Q}oW}B |=yxt=vQ@ uDN=U |=Q@ |WwQ |xaUwD 'j}kLD u}= hOy
hrDNt `@=vt OwHw p}rOx@ ZQi u}= s}v=O|t xm u=vJ "Ov=xOQm ZQi u}at w
* ]}Lt C=i=QLv= Q@ x@re |=Q@ |i=m h=]av= R= O}=@ xt=vQ@ u}= Q=DWwv u}= QO 'Qw_vt u}tyx@ [3] "CU}v jO=Y \}=QW |t=tD QO C}a]k sOa O=H}=
Vy=m w \NQ@ |
u}= QO xOW |UQQ@ pOt R= hOy 'XN= Qw]x@ "OW=@ Q=OQwNQ@ C=i=QLv= u}= Q}F-=D
C}a]k sOa \}=QW QO |O=OUv= QiY |v=}t |xQ}NP =@ |y=oQ=m O}rwD |xrUt
3
"CU= C@=F Q=Okt l} R= C=}rta |xvt=O Qw@a sOa p=tDL= |R=Uxv}W}@ j}kLD
"CU= xDiQo Q=Qk xar=]t OQwt
u=} QH |xrUt u}OvJ |=Q@ Q=wDU= |xt=vQ@ l} PN= Qw_vtx@ |D=W}=tR; TBU |x=Q= 'pw= OQm}wQ QO %OQ=O OwHw |rm OQm}wQ wO =yC}a]k sOa =@ xr@=kt |=Q@
QO "CU= xOW s=Hv= nQR@ w \UwDt 'lJwm |=yxR=Ov= QO 4 |O=OUv= |y=oQ=m
ut[ w '?=NDv= p=Ut pL |=Q@ hrDNt |Q=mD@==Qi VwQ CWy OQmrta 'xt=O=
pwUt xOvU} wv "1392 4 1 VQ}PB '1392 2 9 x}LqY= '1391 7 15 Ci=}QO %M}Q=D
"CU= xOW xU}=kt R}v =yu; uOw@ Q=wDU= 'Qo}Om} =@ u=WOQmrta |xU}=kt
|Ov@u=tR QO xO=iDU= OQwt |=yVwQ |xRwL QO xDiQoCQwY C=ar=]t u}kkLt
[5w4] "Ov=xO=O Q=Qk |UQQ@ OQwt =Q C}a]k sOa Cr=L QO =yQ=m
Q}eDt \}=QW p}rOx@
QO |iO=YD w =} wB \}Lt QO |Q}os}tYD |=Q@ |y=oQ=m K]U |=yxt=vQ@ '|]}Lt
KqY= x@ O}=@ |y=o OvJ R= Qy p}rO u}tyx@ "Ow@ Ovy=wNv wo?=wH |vqw] COt
|R}Qxt=vQ@ |t=ovy xJ "1 %OwW|t KQ]t p=w-U wO =Hv}= QO "CN=OQB =yxt=vQ@
#OQ}o CQwY |R}Qxt=vQ@ xvwoJ "2 #OQ}o CQwY
x@ =Q sDU}U MU=B '|R}Qxt=vQ@ |=QH= u=tR XwYNQO p=w-U x@ |} woMU=B
'O@=} V}=Ri= |R}Qxt=vQ@ pL=Qt O=OaD xJQy "Ovm|t XNWt |]}Lt hrDNt p=Ut
|Q}os}tYD |=Q@ "O@=}|t V}=Ri= R}v sDU}U |xv} Ry xH}DvQO w sDU}U |} woMU=B
|R}Qxt=vQ@ 'xDUw}B |R}Qxt=vQ@ %OQ=O OwHw |irDNt |=yVwQ |R}Qxt=vQ@ OQwtQO
"|@}mQD |R}Qxt=vQ@ |=yVwQ w '5 |k=@]v= |R}Qxt=vQ@ '|}xQwO
OwQw =} 'u}W=t l} |@=QN Ovv=t syt C=k=iD= R= TB xDUw}B |R}Qxt=vQ@ VwQ QO
[6]
C@=F |=yxQwO QO xt=vQ@ |}xQwO |R}Qxt=vQ@ QO "OwW|t RwQ x@ xt=vQ@ syt Q=m l}
|=yxQwO uDiQo Q_v QO =@ |}xQwO |R}Qxt=vQ@ R= |}xvwtv QO "OwW|t RwQx@ Q}eDt w
|R}Qxt=vQ@ "OwW|t RwQ x@ u; R= |YNWt w C@=F OYQO `wkw R= TB xt=vQ@ [7] Q}eDt
xm OQ}o|t CQwY |t=ovy OOHt |R}Qxt=vQ@ 'u; QO xm CU= |Qo}O VwQ |k=@]v=
XNWt RQt l} R= '|ak=w Cr=L w xt=vQ@ R= |YNWt pt=a |=yCw=iD `wtHt
|R}Qxt=vQ@ |=yVwQ |UQQ@ QO "OW=@ QDW}@ xOWu}}aD V}B R= |xv=DU; OL R= =}
xDUw}B |R}Qxt=vQ@ w |}xQwO |R}Qxt=vQ@ R= ?mQt |R}Qxt=vQ@ VwQ l} 'R}v |@}mQD
[8] "OW x=Q= 6 QwLtxFO=L VwQ s=v x@ =Q C}a]k sOa Cr=L QO |R}Qxt=vQ@ |=yVwQ 'swO p=w-U x@ |} woMU=B |=Q@
[9] %Ov=xOQm |Ov@s}UkD xDUO Q=yJ QO
&7 |r=aiv= =} |Wvm=w ,qt=m |R}Qxt=vQ@ "1
&8 |r=aiv= |xv=} woV}B |R}Qxt=vQ@ "2
&xv=Q}oW}B ,qt=m |R}Qxt=vQ@ "3
"9 |r=aiv= |xv=Q}oW}B |R}Qxt=vQ@ "4
OW=@ Q}osWJ |oDiW; u=R}t xm OwW|t xO=iDU= |t=ovy CUNv |R}Qxt=vQ@ R=
QO "OvR=U umtt Q}e =Q xv=Q}oW}B |R}Qxt=vQ@ w OvwW XNWt Q}O Q=}U@ C=aq]= =}
'OwW|t xO=iDU= sDU}U Cr=L uDiQoQ_v QO =@ xOW RwQx@ C=aq]= R= 'VwQ u}=
u}v=wk =@ OL=w u; QO =ys}tYD 'OwW|tv xO=O sDU}U x@ |}xv=Q}oW}B |xt=vQ@ I}y
u}tyx@ "OQ}o|t Q=Qk =t TQDUO QO s=o x@ s=o C=aq]= w 'OwW|t xDiQo XNWt
"Ovt=v|t \NQ@ =} u}qv; |R}Qxt=vQ@ =Q |R}Qxt=vQ@ `wv u}= p}rO
Q_vQO uwO@ xv=} woV}B |xt=vQ@ l} =OD@= '|r=aiv= |xv=} woV}B VwQ QO
^iL |=Q@ |r=aiv= |xt=vQ@ l} R= TBU "OwW|t |R}Q|B |r=tDL= C=i=QLv= uDiQo
|R}Qxt=vQ@ `wv u}= [10] "OwW|t xO=iDU= xt=vQ@ u}= OQmrta Ow@y@ w xt=vQ@ |Q}PBu=mt=
OyO MQ h=QLv= xm |t=ovy =yvD w Ovm|tv ^=Lr ,=t}kDUt =Q xt=vQ@ QO C}a]k sOa
R=Q@= |=Q@ x=Q u} QDy@ |r=aiv= |R}Qxt=vQ@ Qo}O CQ=@ax@ "Ovm|t K}LYD =Q xt=vQ@
"O@=}|t =Q xO=O MQ h=QLv= x@ Vvm=w
|OQmrta |=yQ=}at s=Om R= xm OQ}o@ s}tYD O}=@ R}Qxt=vQ@ 'Oa@ |xrLQt QO
10 u=} QH QO u=tR 'C=}rta |xvt=O uwJty |DvU |=yQ=}at R= pta QO "Ovm xO=iDU=
|=yQ=}at CU=} wB w Q}eDt \}Lt xm |]}=QW QO =t= 'OwW|t xO=iDU= OQmQ}O =}
Qw_vt u}= |=Q@ "OQ=O OQ@Q=m C}a]k sOa Q@ x@re |=Q@ 12 |Q=O}=B w 11 |Q=wDU=
xt=vQ@ u}= '\}Lt QO OwHwt C=i=QLv= QF=Q@ &OwW|t s=Hv= x}rw= |R}Qxt=vQ@ l} =OD@=
'|]}Lt C=i=QLv= u=R}t x@ xDU@ "OwW ^iL u; |Q}PBu=mt= =D OQ=O KqY= x@ R=}v
102
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
|Q=wDU= |=yQ=}at "OW=@ Cw=iDt x}rw= |xt=vQ@ =@ ,qt=m xt=vQ@ CU= umtt |DL
xv}tm xt=vQ@ QO =Q C=i=QLv= u}= Q}F-=D w OvQ=O Q=mwQU C=i=QLv= u}= =@ |Q=O}=B w
"Ovvm|t
w OW=@ xO=t; |r=tDL= \}=QW =@ xr@=kt QO Ov=wD@ xm CU= Q=wDU= |}xt=vQ@
|Q=wDU= xv=Q}oW}B |R}Qxt=vQ@ QO u}=Q@=v@ "OyOv CUO R= =Q OwN |OQmrta C}i}m
|R}Qxt=vQ@ |SD=QDU= R= xm |t=ovy 'C}a]k sOa =@ xr@=kt C}r@=k R= CU= CQ=@a
x=Q= xt=vQ@ |Q=wDU= |UQQ@ |=Q@ |irDNt |=yQ=}at u}kkLt "OwWv xO=iDU= OOHt
Cw=iD u=R}t =Q |Q=wDU= u=v; "OR=U|t xv}tm =Q |}=Q=m Q=}at Tv=}Q=w xm [11] Ov=xO=O
'u=v; Q_v R= |DQ=@ax@ w Ov=xOQm |iQat |ak=w w xOW |R}Qxt=vQ@ hOy `@=wD Q=Okt
|v=OvJ Q}}eD '|]}Lt C=i=QLv= =@ xyH=wt QO u; OQmrta xm CU= Q=wDU= |}xt=vQ@
|=yu=tR Q}}eD uDiQov Q_vQO =@ [12] 'C=ar=]t u}= R= |}xvwtv QO "Ov=t@ xv}y@ w Ovmv
=yQ=m VR=OQB u=tR QO xv}W}@ Q}}eD TBU 'OwW|t O=H}= xv}y@ |xt=vQ@ VR=OQB
Q}}eD u}= Q=Okt Qwm Pt |xar=]t QO "Ov=t@ xv}y@ u=vJty xt=vQ@ u}= xm xOw@ |}xvwox@
C=Q}}eD s=tD |woMU=B |Q=O}=B `=aW Qo= &CU= xOW xO}t=v |Q=O}=B `=aW xv}W}@
|=Q@ O}=@ CQwY u}= Q}e QO &CU= Q=wDU= xt=vQ@ 'OW=@ VR=OQB |=yu=tR umtt
"OQm |Q}os}tYD |[Dkt s=Ok=
|=yQ=}at "1 [12] %OvOQm s}UkD xDUO wO x@ =Q |Q=wDU= |=yQ=}at u=QoVywSB
"2 &Ovvm|t xHwD xDUw}B `wkwx@ |xt=vQ@ OQmrta x@ \ki xm |ak=w OQmrta Q@ |vD@t
|xt=vQ@ w xDUw}B `wkw x@ |xt=vQ@ OQmrta Cw=iD x@ xm 13 QwLt|v=t}WB |=yQ=}at
Ciy |ak=w OQmrta Q@ |vD@t |=yQ=}at |va} pw= |xDUO |=Q@ "OvR=OQB|t xv}y@
xm CU= QmP x@ sRq "CU= xOW |iQat Q=}at Q=yJ swO |xDUO |=Q@ w 'Q=}at
CWPo =@ xm OvQ=O OQ@Q=m |t=ovy QwLt|v=t}WB |=yQ=}at |va} swO |xDUO
=Q |rai |xt=vQ@ s}y=wN@ w OwW XNWt =yC}a]k sOa xt=vQ@ CiQW}B w u=tR
xU}=kt 'Ow@ Oy=wN TQDUO p@=k C=aq]= OwHw CQwYQO xm xv}y@ |xt=vQ@ =@
xOW O=yvW}B Q=O}=B p=Ut |=Q@ Q=}at VW u}vJty xOWO=} |xar=]t QO "s}vm
"CU=
Q=}at Qw@a sOa ut[Dt =yQ=}at u}= xm Ov=xOQm xQ=W= |Qo}O u}kkLt
=Pr [13] "OvDU}v |r=tDL= hrDNt |=yCr=L QO hQ=aDt OL l} R= |}=Q=m
%R= Ow@ CQ=@a xm OvDiQo Q_v QO =D@ |Q=wDU= s=vx@ |Qo}O |}=Q=m Q=}at u=v;
p@=k Q}e XNWt OL R= xt=vQ@ l} |}=Q=m Q=}at Qw@a sOa p=tDL= |R=Uxv}W}@
"pw@k
=@ |y=oQ=m |Ov@u=tR |xrUt 'jwi |x} Q_v R= xO=iDU= =@ |Qo}O u=QoVywSB
u=tR uOw@ QDsm p=tDL= uOQm xv}W}@ hOy `@=D uDiQo Q_vQO =@ =Q u}W=t M w Q=m n
uOQw; CUO x@ |=Q@ =yu; [14] "OvOQm pL 'Q=_Dv= OQwt p}tmD u=tR R= =yQ=m p}tmD
=@ w xDiQo Q_v QO |Q=QmD O}rwD R= |a}Uw sHL (Cmax ) C=}rta |xvt=O `}RwD
'=Q C=}rta |xvt=O `}RwD |RmQt OL |x}[k R= xO=iDU= =@ =yQ=m O=}R O=OaD ZQi
u}= QO xm CU= |r=L QO u}= "OvOQm ZQi p=tQv '=yQ=m VR=OQB u=tR `}RwD R= =OH
"Q}N =} Ovm|t Q}}eD |v=QL@ Q}Ut '=yQ=m VR=OQB u=tR Q}}eD =@ CU}v XNWt xrUt
xO=iDU= |RmQt OL |x}[k R= u=wD|tv 'Ovm Q}}eD |v=QL@ Q}Ut xm |DQwY QO xm =QJ
OW Oy=wN Q}eDt `}RwD OvJ `wtHt C=}rta |xvt=O |v=QL@ Q}Ut Q}}eD =@ =Q}R OQm
ZQi =@ xrUt u}= QO hOy `@=D "CU}v jO=Y |RmQt OL |x}[k ZQi Qo}O w
ZQiV}B Q=Okt Cw=iD R= CU= CQ=@a 'xt=vQ@ C=}rta |xvt=O `}RwD uOw@ p=tQv
"xt=vQ@ C=}rta |xvt=O Tv=}Q=w Q@ s}UkD (Cmax ) xt=vQ@ C=}rta |xvt=O w (X )
C=ar=]t |xYqN "CU= xOW xO=iDU= l}DvS sD}Qwor= l} R= xrUt u}= pL |=Q@
|a]k xm CU= QmP x@ sRq "CU= xOW x=Q= 1 pwOH QO xv}tR u}= QO xOW s=Hv=
"""w |r}=[i OtLt '=k;p; =[QOtLt
"|a]k Q}e \}=QW QO |y=oQ=m |R}Qxt=vQ@ xRwL QO xOW s=Hv= |=yQ=m |r=tH= C=}@O= QwQt "1 pwOH
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=D@ |Q=wDU=
=yQ=m VR=OQB
u=tR Q}}eD |iO=YD
hOy `@=D Q}}eD |Q=wDU=
|Q=mD@= |=yVwQ
=yQ=m VR=OQB
|r@k xr=kt x@ C@Uv
VR=OQB u=tR Q}}eD |iO=YD |Q=mD@= sD}Qwor=
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p} wLD u=tR C}a]k sOa '=yQ=m
Qrwr
w u}W=t |@=QN |iO=YD
=yOQmQ}O |vRw `wtHt uOQm xv}tm l}DvS sD}Qwor=
x}rw= O=wt p} wLD OQmQ}O
C=}rta xvt=O uOQm xv}tm u=tR Q}}eD |iO=YD
l}DvS sD}Qwor=
|Q=wDU=
=yQ=m VR=OQB
Kasperski 3
|O=OUv= Ovv=t@ Q=_Dv= QO u}W=t wO u}@ Ovv=wD|tv =yQ=m w CU}v u=tRty Q=m OvJ
VR=OQB u=tR Qou=Wv tij Qo= "OwW|t ZQi u=Um} =yQ=m |t=tD p} wLD u=tR w
Q=m `wQW u=tR Sij 'i u}W=t |wQ j Q=m p}tmD u=tR Cij 'i u}W=t |wQ j Q=m
u=}@ u}vJ xrUt pOt 'OW=@ =yQ=m C=}rta |xvt=O Cmax w i u}W=t |wQ j
%OwW|t
Objective = max[Probability(Cmax < X )]
( 1)
Cmax = CnM
( 2)
Carillo 2
v=
B
v=
B
v=
B
x Q}oW}
x Q}oW}
x Q}oW}
v= B
|r=aiv= x Q}oW}
v=
B
x Q}oW}
Daniels 1
m u=vJty &CU= u; |=yQDt=Q=B w =yQ=m |t=tD uOw@ XNWt |=vatx@ xt=vQ@ uOw@
|=OD@= QO =yQ=m |t=tD uOw@ TQDUO QO w uOw@ XNWt |=vatx@ xt=vQ@ |}=DU}=
"CU= |R}Qxt=vQ@
QDsm Cq=kt QO =D@ |Q=wDU= Q=}at 'CU= XNWt R}v 1 pwOH QO xm u=vJ
|Q=wDU= Q=}at =@ |O=OUv= |y=oQ=m O}rwD |xrUt x@ uwvm =D w xDiQo Q=Qk |UQQ@ OQwt
|y=oQ=m O}rwD |xrUt pL j}kLD u}= R= hOy u}=Q@=v@ "CU= xOWv xDN=OQB =D@
OwHwt |Q=mD@==Qi |=yVwQ u} QDy@ R= xO=iDU= =@ =D@ |Q=wDU= Q=}at =@ |O=OUv=
X=N Qw]x@ w |ak=w |=}vO QO "CU= |y=oQ=m p=Ut |=Q@ C=}@O= QO xOW x=Q=
xm OyO|t u=v}t]= =t x@ =D@ |Q=wDU= Q=}at R= xO=iDU= '|y=oQ=m u=} QH p=Ut QO
C11 = t11
( 3)
Oy=wNv QDW}@ |YNWt OL R= xOW u}}aD p=tDL= K]U QO xrUt C=}rta xvt=O
Sij = maxfCi(j 1) ; C(i 1)j g 1 j n; 1 i M (4) =@ =t '100 ?wr]t C=}rta |xvt=O w 0 9 p=tDL= K]U ZQi =@ p=Ft |=Q@ "Ow@
Cij = maxfSij + tij ; C(i+1)(j 1) g 1 j n;
C=}rta |xvt=O OQ=wt 90 QO xm s}DUy |}xt=vQ@ p=@vO x@ R} QolU}Q |OQm}wQ
"OW=@ xDW=O 100 R= QDsm
1i<M
( 5)
|UQQ@ OQwt |xrUt 2 VN@ QO %CU= CQwY u}O@ xr=kt xt=O= Q=DN=U
CMj = SMj + tMj 1 j n
( 6)
|Q=mD@= pL ?NDvt |=yVwQ 3 VN@ QO "OwW|t x=Q= xrUt pOt w xOW h} QaD
Ci1 = S(i 1)1 + ti1 1 < i M
( 7)
4 VN@ QO "OwW|t |iQat Qwm Pt |xrUt pL |=Q@ xO=iDU= OQwt |Q=mD@==Qi w
|xvt=O QO |}=yh=QLv= O=H}= Ea=@ xrUt VR=OQB |=yu=tR QO uOw@ |iO=YD x@ 5 VN@ QO C}=yv QO "CU= xOW x=Q= hrDNt p=Ut pL R= pY=L G}=Dv
u=tR R= xrUt C=}rta |xvt=O CU= umtt xQ=wty p}rO u}tyx@ "OwW|t C=}rta
"s}R=OQB|t |D; C=k}kLD |=Q@ C=O=yvW}B w j}kLD |Q}oxH}Dv
xQy@ u; R= xrUt u}= QO xm |iOy `@=D u}=Q@=v@ "OwW QDW}@ =yQ=m p}tmD ?wr]t
R= w XNWt Q=Okt R= =yQ=m p}tmD u=tR xm CU= p=tDL= u}= |R=Uxv}tm 's}=xOQ@
"1|x]@=Q OwW QDsm X |xOW u}}aD V}B
xrUt h} QaD "2
Qou=Wv 3 |x]@=Q 'C=}rta |xvt=O =} =yQ=m p}tmD u=tR Qou=Wv 2 |x]@=Q
u=tR Qou=Wv 5 |x]@=Q w '=yQ=m `wQW u=tR Qou=Wv 4 |x]@=Q 'pw= Q=m p}tmD u=tR Q=m n u=Um} |r=wD u}}aD p=@vO x@ =t 'Q_v Ot |y=oQ=m u=} QH O}rwD |xrUt QO
Ov=wD|t |v=tR i u}W=t |wQ j Q=m xm OvQ=O|t u=}@ \@=wQ u}= "CU=yQ=m p}tmD
=yQ=m |t=tD xm OwW|t ZQi "s}DUy OwHwt u}W=t M |wQ Q@ fj = 1; :::; ng
i 1 u}W=t |wQ j Q=m VR=OQB w p}tmD i u}W=t |wQ j 1 Q=m xm OwW `wQW Q@ =yQ=m |R=UxO=t; u=tR u}vJty w Ov=TQDUO QO (t = 0) |}=OD@= |x_Lr R=
u}rw= w u}W=t u} QN; x@ \w@ Qt ?}DQDx@ R}v 7 w 6 |x]@=Q "OW=@ xO}UQ u=}=B x@
|}=Hx@=H u=tR R= "CU= xOW xDiQo Q_v QO =yQ=m VR=OQB u=tR =@ =yu}W=t |wQ
"CU= Q=m s=Hv= x@ QO=k u}W=t Qy u=tR Qy QO "CU= xOW Q_v hQY R}v =yu}W=t u}@ =yQ=m
103
x
P (E; T ) =
T
(T 2 + E 2 )
t }= WQO 14 |DWo}=H |y=oQ=mu=} QH|xrUt pL|=Q@|OOaDt|=yVwQ
?=NDv= VwQ OvJ 'C=}@O= QwQt QO OwHwt pL |=yVwQ u}@ R= "CU= xOW x=Q=
l} Qy QYDNt K}[wD R= p@k "CU= xOW |R=U|tw@ q=@ |xrUt =@ ?U=vDt w xOW
"s}vm xQ=W= =ysD}Qwor= |t=tD QO x@=Wt C=}[Qi x@ CU= sRq =ysD}Qwor= u}= R=
w u}ov=}t ?=UDL= =@ xrUt QO =yC}r=ai u=tR |Q}PB Q}}eD uDiQoQ_v QO |=Q@ u=tR R= Cr=L 80 'p=tQv `}RwD R= xO=iDU= =@ w =yQ=m VR=OQB u=tR Tv=}Q=w
"OwW|t xQ}NP w O}rwD |iO=YD CQwYx@ =yQ=m VR=OQB
VR=OQB u=tR 1/9 w 1 u}@ |iO=YD Qw]x@ =yQ=m VR=OQB u=tR Tv=}Q=w Q=Okt "Ovm|t Q}}eD =yQ=m
u}}aD u}W=t Qy Q@ Q=m Qy u=tR u}ov=}t w =yQ=m |r=wD x@ xHwD =@ X Q=Okt "OwW|t
'Cw=iDt u=tR 40 |=R=x@ C=}rta |xvt=O Q=Okt Q=@ 40 '|vOW ?=wH Qy |=Q@ x@U=Lt =yC}r=ai |=Q@ 'xOW ?=NDv= jwi u=tR 80 u}@ R= |iO=YD Qw]x@ xm
"OwW|t x@U=Lt |Q=wDU= u=R}t xOW x@U=Lt Q}O=kt x@ xHwD =@ w OwW|t
VwQ Ciy xOW s=Hv= |=y|UQQ@ =@ jwi |xOW KQ]t |xrUt pL |=Q@
u}= j}@]D =@ C}=yvQO "OW ?=NDv= C=}@O= QO OwHwt jiwt |Q=mD@==Qi hrDNt
"s}OQm xrUt pL x@ s=Ok= Q_v OQwt |xrUt =@ |Q=mD@==Qi |=yVwQ
hrDN \ Q
@ D Q=Okt u} QDy@ w |rai hOy `@=D Q=Okt Cw=iD E &Q[=L p=L |=tO T
27 uOWOQU |Ov@u=tR O@ ?=wH l} VQ}PB p=tDL= P (E; T ) &hOy
=@ |}=tv
"CU= Ti = Ti 1 pwtQi |Q}oQ=mx@
`=
28 C}atH |xQ=@wO O}rwD "1"1"4
r D iO=YD ?=wH l} OvW=@ xDW=O OwHw |rai C}atH QO xOW O}rwD u=OvRQi Qo=
sD}Qwor= |xr}Uwx@ |iO=YD ?=wH u}= "OwW|t |Q=QmD ?=wH u} Ro}=H w xOW
"OwW|t C}atH QO OwHwt ?=wH u} QDO@ u} Ro}=H w xDi=} Ow@y@ O} Q@D |R=Ux}@W
=@ VyH s=Hv= R= TB w xOW ?=NDv= CrwQ |xNQJ =@ Or=w l} VyH s=Hv= |=Q@
OwN Or=w u} Ro}=H xOW O=H}= OvRQi "OwW|t xO=O Ow@y@ O} Q@D |R=Ux}@W sD}Qwor=
"OwW xOy=Wt xtD=N \}=QW =D OwW|t Q=QmD QOkv; Ov}=Qi u}= w OwW|t
O} w |
29 O} Q@D |R=Ux}@W w xawvtt |wHwCUH |@}mQD sD}Qwor= "2"4
|O=yvW}B
|=Q@ 'u}r \UwD Q=@ u}rw= O} Q@D |R=Ux}@W w xawvtt |wHwCUH |@}mQD sD}Qwor=
[17] "OW x=Q= |DWo}=HQ}e |y=oQ=m u=} QH |xrUt
u}= OQmrta xm O=O u=Wv w=
sD}Qwor= u}= "CU= |}=yvDx@ =ysD}Qwor= u}= R= l} Qy OQmrta R= QDy@ |@}mQD sD}Qwor=
T=U=Q@ C=Q}taD w |Q=Oxov C}OwOLt =@ |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@
[18] "OW x=Q= C=}rta |xvt=O \UwDt Vy=m w \}=QW
|iO=YD CQwYx@ x}rw= ?=wH
'Z} waD |=yQ=DN=U R= |m} ?=NDv= =@ |o}=Uty ?=wH O=H}= "OwW|t ?=NDv=
30 |O=OUv= |Q=Po}=H '|Q=Po}=H
=@ sD}Qwor= u}= QO "CU= |iO=YD CQwYx@
31 xawvtt CU}r R= CmQL l} uOQm GQ=N u=mt= [19] xOW |iQat \}=QW |Q}oQ=mx@
Q}O=kt x@ C@Uv u; hOy `@=D uOw@ QDy@ \QWx@ u; R= |o}=Uty ?=wH O=H}= w
|O}OH |xawvtt CU}r =tO Vy=m Q=@ Qy =@ "OQ=O OwHw uwvm =D xOW xOy=Wt
Qy =@ "CU= 100 =D 7 u}@ |DN=wvm} |iO=YD Q}eDt u; |xR=Ov= xm OwW|t O=H}=
u; uOW s=tD =@ w xOW =QH= xawvtt |wHwCUH sD}Qwor= xawvtt CU}r O=H}= Q=@
?=wH u=wvax@ xOt; CUO x@ ?=wH O=tHv= |=tO x@ uO}UQ =@ "O@=}|t Vy=m =tO
Q=QmD u}= "OwW|t =QH= =OD@= R= xQ=@wO sD}Qwor= w xOW xDiQo Q_v QO sD}Qwor= |x}rw=
|}=tv `@=D =@ uOW OQU |Ov@u=tR "OwW s}_vD QDt=Q=B u}= =D OwW|t s=Hv= Q=@ N
"CU= 32 utRDrB O@ |=y?=wH |@=}RQ= Q=}at
P (E; T ) = e
|O=yvW}B pL VwQ "3
|O=yvW}B l}DvS sD}Qwor= "1"3
QO xm xJv; j@=]t xm U= 2011 p=U x@ \w@ Qt xOW x=Q= Q=m VwQ u}rw=
|xrUt |=Q@ l}DvS sD}Qwor= VwQ l} u; |] 'OW u=}@ C=}@O= QwQt CtUk
sD}Qwor= u}= QO "CU= xOW xO=O xaUwD |}xrLQt M |y=oQ=m u=} QH |R}Qxt=vQ@
15 |D@=kQ ?=NDv= l} R= u}Or=w ?=NDv= |=Q@
xm =vat u}O@ &CU= xOW xO=iDU=
?=NDv= R= TB "CU= QDW}@ OvQ=O |QDq=@ VR=Q@ `@=D xm |v}Or=w ?=NDv= p=tDL=
17 VyH w 16 `]=kD Qorta wO u}Or=w
`]=kD Qorta "OQ}PB|t CQwY u}Or=w |wQ
19
18 xOvQ=Oy=ov `]=kD '|@=NDv=
u}vJty "CU=
|v} Ro}=H VyH 'VyH Qorta w
`@=D O}OH pUv xm OvwW|t u=Wu}Or=w u} Ro}=H xOW O}rwD O}OH pUv |DQwYQO
"OW=@ xDW=O |QD?U=vt VR=Q@
[14] C
E
T
|O=yvW}B 33u=tRty Q}e |rLt |wHwCUH =@ l}DvS sD}Qwor= "3"4 |O=yvW}B |O} Q@D |R=Ux}@W w l}DvS |@}mQD VwQ "4
` t |R U m Q t @ } H y oQ m u } H | t |= @ }Q r= }=
|O=yvW}B 20O} Q@D |R=Ux}@W w l}DvS |@}mQD sD}Qwor= "1"4
wtH
= xv}t
=}a = |DWo =
| = =
= Q
xrU
Q sD wo
u
N=wvm} ?=NDv= CQwYx@ `]=kD |=Q@ u}Or=w ?=NDv= [20] "OW x=Q= u=} QH QO u=tR
Ow@y@ u=tRty Q}e |rLt |wHwCUH =@ Or=w wO ?=NDv= R= TB "OQ}o|t s=Hv=
34
O}rwD u=OvRQi ' p@wO |}x]kvwO `]=kD Qorta =@ `]=kD Ow@y@ R= TB w xOW xO=O
|xU}=kt =@ C}=yv QO "OwW|t xO=O Ow@y@ u=tRty Q}e |rLt |wHwCUH =@ xOW
"OQ}o|t CQwY O}OH C}atH O}rwD |=Q@ |v} Ro}=H 'xDi=} Ow@y@ u=OvRQi w u}Or=w
Ow@y@ |Q=Po}=H Qorta =@ ?=wH =OD@= u=tRtyQ}e |rLt |wHwCUH sD}Qwor= QO
Qorta u}= =@ |Ow@y@ Qo= w OwW|t C@F C=Q}}eD OW O=H}= Ow@y@ Qo= "OwW|t xO=O
C
w |Q=Oxov C}OwOLt =@ |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@ sD}Qwor= u}=
|xvt=O \UwDt |R=Uxv}tm Q=}at w Cq;u}W=t |@=QN w 21 \}=QW T=U=Q@ C=Q}taD
22 CrwQ |xNQJ Q=mwR=U wO =@ `]=kD |=Q@ u}Or=w ?=NDv= [15] "OW x=Q= C=}rta
w `]=kD |=Q@ xO=iDU= OQwt |=yQorta "OQ}o|t CQwY 23 CN=wvm} ?=NDv= w
?=wH O=H}= hrDNt |=yQ=DN=U "CU= 25 |Q=Po}=H w 24 |}x]kvwO `]=kD 'VyH
?=wH O=H}= |=Q@ Z} waD Q=DN=U C}=yv QO w xDiQo Q=Qk |UQQ@ OQwt |o}=Uty
'O@ |=y?=wH VQ}PB sOa =} VQ}PB |@=}RQ= Q=}at "CU= xOW ?=NDv= |o}=Uty
104
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
" U= 26 |Jw=m \UwD xOW x=Q= Q=}at u=ty
[16] C
"""w |r}=[i OtLt '=k;p; =[QOtLt
"OwW|t KqY= =yuwtwQi u; R= TB w xDiQo pmW xJQwt l} =yvD Q=QmD Qy QO
=Q =yuwtwQi w OvQ}o|t NEH VwQ R= =Q OwN |x}rw= ?=wH VwQ wO u}=
xv}tm w xv}W}@ uwtwQi =OD@= M-MMAS pw= VwQ QO "Ovvm|t |v=UQRwQx@
'=yuwtwQi T} QD=t u=ty =} T T} QD=t R= xO=iDU= =@ u; R= TB w OwW|t x@U=Lt
sD}Qwor= ZQat QO Q=@ 3 x}rw= ?=wH u}= "OwW|t =yQ=m Vv}J x@ `wQW =OD@= R=
QO "OwW pY=L |QDy@ ?=wH =D OwW|t xDW=Po 38 QwLtQ=m |rLt |wHwCUH
Q_v QO Q}N@D MQv T=U=Q@ '=yuwtwQi |v=UQRwQx@ 'swRwtwQm p}tmD R= TB C}=yv
s=Hv= 'xJQwt u}= pt=m CWo l} QF= QO xOv=t |=Hx@ uwtwQi u=R}t w xOW xDiQo
"OwW|t
|x}rw= Q=Okt QO M-MMAS pw= VwQ =@ PACO swO VwQ Cw=iD
|v=UQRwQx@ |xwLv w '=yuwtwQi |=Q@ xv}W}@ w xv}tm Q}O=kt OwHw sOa '=yuwtwQi
xDW=O pw= VwQ x@ C@Uv |Dw=iDt OQmrta swO VwQ =D xOW Ea=@ xm CU=yuwtwQi
"OW=@
QD
t=Q=B s}_vD "5
Y=L Ow@y@ u}rw= =@ "OwW|t xO=iDU= Ow@y@ |=Q@ Z} waD Qorta R= OWv pY=L
U D o= "OwW|t =QH= Ow@y@ |=Q@ |Q=Po}=H Qorta xQ=@wO w 'C@F C=Q}}eD xOW
xtD=N |rLt |wHwCUH Q=QmD 'OWv pY=L |Ow@y@ Qorta wO u}= R= s=OmI}y
|iO=YD |OOa `]=kD R= p@k wHwCUH Qorta u}= |=yQ=QmD O=OaD "CU= xDi=}
umtt |=yQ=QmD O=OaD xv}W}@ `]=kD R= Oa@ w umtt |=yQ=QmD O=OaD xv}W}@ w xv}tm
"CU=
p
\ w Q
|O=yvW}B 35QwLtC}atH O} Q@D |R=Ux}@W sD}Qwor= "4"4
|xvt=O |R=Uxv}tm Q=}at =@ |y=oQ=m u=} QH |Ov@u=tR |xrUt |=Q@ sD}Qwor= u}=
|=ysD}Qwor= Q}=U =@ xU}=kt QO sD}Qwor= u}= |rY= Cw=iD [21] "OW x=Q= C=}rta
|=Hx@ u=tRty w |R=wt CQwYx@ x]kv OvJ |wHwCUH QO O} Q@D |R=Ux}@W
`wQW |iO=YD |x}rw= C}atH l} =@ sD}Qwor= u}= "CU= x]kv l} QO wHwCUH
Q=}at "O};|t CUO x@ Z} waD Qorta =@ |o}=Uty ?=wH "Ovm|t wHwCUH x@
x=Q= `@=D R= =tO Vy=m |=Q@ "CU= utRDrB |=y?=wH VQ}PB sOa =} VQ}PB |@=}RQ=
QO |rw '`} QU q=@ |=tO QO `@=D u}= [22] "CU= xOW xO=iDU= |Ovwr \UwD xOW
"OwW|t OQU xDUy; u}}=B |=tO
u; |=yQDt=Q=B R= QF-=Dt |O=}R OL =D |Q=mD@==Qi w |Q=mD@= |=ysD}Qwor= OQmrta Ti = Ti 1
1 + Ti 1
|=yQDt=Q=B "CU}v u=Um} Cw=iDt |=ysD}Qwor= QO =yQDt=Q=B u}= w CU= sD}Qwor=
|=Q@ xOW |UQQ@ Kw]U w xr=kt u}= QO xOW xO=iDU= |=ysD}Qwor= OQmrta QO QFw-t Ow@y@ |rLt[23|]wHwCUH Q=DN=U l} =@ C}atH R= |QUm =tO Vy=m Q=@ Qy R= TB
QO NEH Q=DN=U =@ j@=]t =Q swO w pw= Q=m =OD@= Q=DN=U u}= "OwW|t xO=O
K]U x@ uO}UQ |=Q@ xm CU= QmP x@ sRq "CU= xOW QmP 2 pwOH QO =yu; R= l} Qy
w xOW ?=NDv= |iO=YD CQwYx@ Q=m wO 'xOv=t|k=@ |=yQ=m u}@ "OyO|t Q=Qk |r=wD
u}tyx@ "OwW u}}aD O}=@ =yQDt=Q=B Kw]U ?}mQD u} QDy@ '=ysD}Qwor= OQmrta |xv}y@
u}= "OwW|t C@F C=Q}}eD OW O=H}= |Ow@y@ xJv=vJ &OwW|t Z} waD =yv; C}akwt
|=yV}=tR; KQ] R= '=yQDt=Q=B hrDNt Kw]U ?}mQD OQmrta |UQQ@ |=Q@ p}rO
s}_vD sD}Qwor= u}= |=yQDt=Q=B Q}=U Q=vm QO O}=@ w P "OwW|t Q=QmD Q=@ P Ov}=Qi
sD}Qwor= |=QH= u=tR =Hv}= QO |OQmrta |=yXN=W "CU= xOW xO=iDU= |Jwo =D
"OwW
CQwYx@ |OQmrta |=yXN=W R= s=OmQy XN=W xm CU= C=}rta |xvt=O w
xv}y@ K]U w x@U=Lt =yXN=W |vRw \UwDt C}=yv QO w xOW x@U=Lt xv=o=OH
|O=yvW}B QQmt |xv=Y} QL |wHwCUH sD}Qwor= "5"4
"CU= xOW ?=NDv=
[24] "OW x=Q= |DWo}=H |y=oQ=m u=} QH |xrUt |=Q@ sD}Qwor= u}=
u}= Q=m T=U=
|rY= |xO}= "CU= QDy@ ?=wH x@ uO}UQ |=Q@ =yQ=m |r=wD |R=UR=@ w ?} QND VwQ
|OOa G}=Dv "6 xOt; CUO x@ |r=wD "CU= xOW xDiQo NEH VwQ R= =yQ=m |r=wD |R=UR=@ |=Q@
QO OwHwt ?NDvt VwQ CWy |Q=wDU= u=R}t |xU}=kt |=Q@ VN@ u}= QO Oa@ |xrLQt QO "OwW|t xDiQo Q_v QO sD}Qwor= |OwQw u=wvax@ NEH VwQ R=
,=D}=yv w 'VwQ CWy u}= =@ p=Ft u}= pL w |OOa p=Ft l} u=}@ x@ 'C=}@O= |x_i=L l} QO w xOW hPL ?=NDv= ?=wH R= |iO=YD CQwYx@ =yQ=m R= |[a@
|Ov@u=tR xQ=@wO w hPL |r=wD R= O}=@ xm |}=yQ=m O=OaD "OwW|t xQ}NP Ckwt
|HwQN |xt=vQ@ C=}rta |xvt=O u}ov=}t u=R}t w |Q=wDU= G}=Dv |xU}=kt
"s}R=OQB|t QO xOv=t|k=@ |=yQ=m "OwW s}_vD O}=@ xm CU= xrUt u}= |=yQDt=Q=B <RH OvwW
"OvQ}o@ Q=Qk Qo}Om} Q=vm QO '=yQ=m hPL R= p@k |r=wD j@=]t O}=@ |rY= |r=wD
?=wH R= CU= |Q=wDU= u=R}t u}}aD |=Q@ xU}=kt |=v@t xm X Q=Okt u}}aD |=Q@
u=wvax@ '=yC}r=ai u=tR u}ov=}t uDiQo Q_v QO =@ xv=Y} QL |wHwCUH sD}Qwor= ?=NDv= |iO=YD CQwYx@ Ckwt |x_i=L QO |=yQ=m R= |m} Oa@ |xrLQt QO
u=tR NEH sD}Qwor= |Q}oQ=m@ =@ xOW ?=NDv= Q=m "OwW|t hPL x_i=L R= w
u}= ?=wH "CU= xOW xO=iDU= hrDNt |=yxR=Ov= =@ p=Ut QO =yQ=m s=Hv= u=tR
u=} QH |xrUt |=Q@ w}r nvw}m xm NEH VwQ x@ C@Uv =Q |QDl}Q=@ OwOL VwQ O=OaD &OwW |r=N Ckwt |x_i=L =D OwW|t Q=QmD QOku; Q=m u}= "OwW|t |Ov@
x=Q= pwtQi R= |rLt |xv}y@ s=O R= Q=Qi |=Q@ "OwW s}_vD O}=@ Ov}=Qi u}= |=yQ=QmD
x@ p=Ut 'xvwtv |xrUt O}rwD |=Q@ "Ovm|t O=H}= CiQo Q=m x@ |DWo}=H |y=oQ=m
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y W vB
= C w=
1. -robust
2. proactive
3. makespan
4. blocking
5. adaptive scheduling
6. event driven
7. reactive
8. predictive-reactive
9. proactive-reactive
10. owtime
11. robustness
12. stability
13. regret based
14. permutation ow shop
15. tournament selection
16. crossover
17. mutation
18. precedence preservative crossover (PPX)
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
swap crossover
hybrid genetic and simulated annealing algorithm
condition-based maintenance
Roulette wheel
uniform selection
two point cross over
insertion
Cauchy
cooling schedule
population reproduction
hybrid tabu search and simulated annealing algorithm
block insertion
tabu list
Poltzman
asynchronous genetic local search algorithm
twice two point cross over
population based simulated anealing
M-MMAS
PACO
job-index-based local search
108
"""|=Q@ |Q=mD@==Qi |=yVwQ |Q=wDU= |UQQ@
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"""w |r}=[i OtLt '=k;p; =[QOtLt
References `@=vt
1. Grabowski, J. and Pempera, J. \The permutation ow
shop problem with blocking. A tabu search approach",
International Journal of Management Science Omega,
35, pp. 302-311 (2007).
2. Hall, N.G. and Sriskandarajah, C. \A survey of machine
scheduling problems with blocking and no-wait in process", Operations Research, 44, pp. 510-25 (1996).
3. Shafaei, R. and Brunn, P. \A framework to integrate
job releasing, routing and scheduling functions to create a robust predictive schedule", European Journal of
Production Research, 38(1), pp. 85-99 (2000).
4. Herroelen, W. and Leus, R. \Project scheduling under
uncertainty: Survey and research potentials", European
Journal of Operational Research, 165(2), pp. 289-306
(2005).
5. Davenport, A.J. and Beck, J.C. \A survey of techniques for scheduling with uncertainty", Unpublished
manuscript (2000), Available from http://www.eil.
utoronto.ca/proles/chris/chris.papers.html.
6. Raman, N., Rachamadugu, R.V. and Talbot, B. \Realtime scheduling of an automated manufacturing center",
European Journal of Operations Research, 40, pp. 222242 (1989).
7. Sabuncuoglu, I. and Karabuk, S. \Rescheduling frequency in an FMS with uncertain processing times and
unreliable machines", Journal of Manufacturing Systems, 18(4) pp. 1-16 (1999).
8. Yamamoto, M. and Nof, S.Y. \Scheduling/rescheduling
in a manufacturing operating system environment", International Journal of Production Research, 23(4), pp.
705-72 (1985).
9. Aloulou, M.A. and Portmann, M.-C. \An ecient proactive reactive scheduling approach to hedge against
shop oor disturbances", In Multidisciplinary Scheduling: Theory and Applications 1st International Conference, MISTA '03, Nottingham, UK, (13-15 August 2003).
10. Vieira, G.E., Herrmann, J.W. and Lin, E. \Rescheduling
manufacturing systems: A framework of strategies, policies and methods", Journal of Scheduling, 6, pp. 39-62
(2003).
11. Sabuncuoglu, I. and Goren, S. \Hedging production
schedules against uncertainty in manufacturing environment with a review of robustness and stability research", Int. J. Computer Integr Manuf, 22(2), pp. 138157 (2009).
12. Sotskov, Y., Sotskova, N.Y. and Werner, F. \Stability
of an optimal schedule in a job shop", Omega: the In-
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25.
ternational Journal of Management Science, 25(4), pp.
397-414 (1997).
Wu, C.W., Brown, K.N. and Beck, J.C. \Scheduling
with uncertain durations: Modeling ^a-robust scheduling
with constraints", Comput Oper Res, 36, pp. 2348-2356
(2009).
Liu, Q., Ullah, S. and Zhang, C. \An improved genetic
algorithm for robust permutation owshop scheduling",
Int J Adv Manuf Technol, 56, pp. 345-354 (2011).
Safari, E. and Sadjadi, S.J. \A hybrid method for owshops scheduling with condition-based maintenance constraint and machines breakdown", Expert Systems with
Applications, 38, pp. 2020-2029 (2011).
Ogbu, F.A. and Smith, D.K. \The application of the
simulated annealing algorithm to the solution of the
n = m = Cmax ow shop problem", Computers and
Operations Research, 17, pp. 243-253 (1989).
Lin, S.W. and Ying, K.C. \Applying a hybrid simulated
annealingand tabu search approach to non-permutation
ow shop scheduling problems", Int J Prod Res, 47, pp.
1411-1424 (2008).
Safari, E., Sadjadi, S.J. and Shahanaghi, K. \Scheduling
owshops with condition-based maintenance constraint
to minimize expected makespan", Int J Adv Manuf Technol, 46, pp. 757-767 (2010).
Glover, F. \A user's guide tabu search", Ann Oper Res,
41, pp. 3-28 (1993).
Xu, X., Xu, Z. and Gu, X. \An asynchronous genetic
local search algorithm for the permutation owshop
scheduling problem with total owtime minimization",
Expect Systems with Appl., 38, pp. 7970-7979 (2011).
Nearchou, A.C. \A novel metaheuristic approach for the
ow shop scheduling problem", Engineering Applications
of Articial Intelligence, 17, pp. 289-300 (2004).
Lundy, M. and Mees, A. \Convergence of an annealing
algorithm", Mathematical Programming, 34, pp. 111-124
(1986).
Nawaz, M., Enscore Jr., E.E. and Ham, I. \A heuristic
algorithm for the m-machine, n-job owshop sequencing
problem", OMEGA, 11, pp. 91-95 (1983).
Ruiz, R. and Stutzle, T. \A simple and eective iterated greedy algorithm for the permutation owshop
scheduling problem", European Journal of Operational
Research, 177, pp. 2033-2049 (2007).
Rajendran, C. and Ziegler, H. \Ant-colony algorithms
for permutation ow shop scheduling to minimize
makespan/total owtime of jobs", Discrete Optimization, 155, pp. 426-438 (2004).

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