Problème de flot

download Problème de flot

of 18

Transcript of Problème de flot

  • 7/25/2019 Problme de flot

    1/18

    !"#$%&'() +( ,#-

    !"#$%&%'(%")*

    !"#$ &'()*+, -. /01234 "0#4.$5 6 . 7"884$7 4$ 8 1097 -:* -;*

  • 7/25/2019 Problme de flot

    2/18

    "#$%$&$'% " #$ %&&'((' ')&%*' +') ,(-.) / (' )-0)1')&%*' +' !23 '$4'$+56 &%5 (')

    7'*.'05) 5'&56)'$.%.8,) +' *9*(') +' :;

    !"#$%&'"" #$%& ' () *$+,-) .) /$+'$01*&)0 /$**)2)0 .) 34 5* 1 1($-0 ".%+678 !+ 9 6*:'84

    !"#$%$&$'%! #$%& '!() #$%& *+$,- "./'0 /,1-2) "3/'00 +415-167+1 84*,9- 81 : *;*5& +16%&> %5%&%*+1 /,1-2)&1,6%5*+10 8*5- ' 1& +16%&> &1,6%5*+1 /,1-2) %5%&%*+10

    ?$,- 81 ') @1 9$9;9+1 ,1+*&%A B 'C 5$&> "/'0C 1-& >D*+ B "./'0#"3/'0) E "F "/'0C $5

    *--$9%1 8*5- $G6

    -$5 H19&1-15&*&%A %F /%%0%FICJCK68>A%5% 2*,

    .I -%

  • 7/25/2019 Problme de flot

    3/18

    !"#$%$&$'%" #$ %&&'((' ')&%*' +') ,(-.) / (' )-0)1')&%*' +' !23 '$4'$+56 &%5 (')

    7'*.'05) 5'&56)'$.%.8,) +' *9*(') +' :;

    ()*+,-.)"

  • 7/25/2019 Problme de flot

    4/18

    !"#$%$&$'%! #$ %&&'((' ')&%*' +') ,(-.) / (' )-0)1')&%*' +' !23 '$4'$+56 &%5 (')

    7'*.'05) 5'&56)'$.%.8,) +' *-*9*(') +' :;

    ()*+,-.)! & $* 789:+; < -=&3

    !"#$%$&$'% " #$%& '()*+,- ./ 012345 6 / 7$885&7 9:+ 9;+

  • 7/25/2019 Problme de flot

    5/18

    !"#$%&'"" #$%&'( )*+% ',-.%/- -0.$%'1+*2 )*( 3%$4)5&*( 6* 7)$- $,- +, ',-.%/-

    3%8-'1+* 98% ')( 7$+%,'((*,- +, 986%* *- +, &$65)* :.,.%8) 3$+% +, :%8,6 ,$&4%* 6*

    3%$4)5&*( 9$,9%*-(;

  • 7/25/2019 Problme de flot

    6/18

    !"#$%&'( *+ ,%#- './0'+'

    !" !"#$%$"& () *+",-./0$

    !" $%"&'()*+ ," *-&+., /0121$3 %4 $ +&5 ,"+ .667'$.5'%" (+ 2 (."& !89:,' .&&%$'+ ;

    ," .*$ , &. < $.6.$'5- =1 '>+ 7. 7'?'5+ &,6-*'+,*+ (+ 7. :,."5'5- (+ @7,A :,' 6+,5 6.&&+*

    &,* ,>

    B+ 6*%C7)?+ $%"&'&5+ .7%*& ; +"D%E+* 7. 67,& F*."(+ :,."5'5- (+ @7,A (G," &%??+5

    &%,*$+ & ; ," &%??+5 6,'5& 6 &.$H."5 :,+ $+ @7,A (%'5 I5*+ $%"&+*D.5'@ +" 5%,5 &%??+5

    '"5+*?-('.'*+ A1 '>+ 7. &%??+ (+& @7,A &,* 7+& .*$& +"5*."5 +" A +&5 -F.7+ ; 7. &%??+

    (+& @7,A &,* 7+& .*$& &%*5."5 (+ A>

    !"#$%$&$'% " #$%& '()*+,- ./ 012345 $1%5/&67 #$%& . 1()3+8- ./ 219 8369%2: ;%& < 219 ;5

    15&$.1 =7 #$%& 9 " ,!!>?"{+#}7

    @5 31$A:BC5 ;. D:$& C2E%C.C ;5 8 F 3 ;2/8 >()*+,+9- 9$/8%8&5 F 94519451 D $!>!,!&5:

    G.5 "

    HI D 8$%& ./ D:$& 8.1 )*+,-+

    JI K%D).-%9).- &.$, L %9%+ D).- 58& :2 9$C3$82/&5 ;5 D 9$11583$/;2/& F .M

    NI D).1- 8$%& C2E%C.C 8$.8 :58 9$/;%&%$/8 HI 5& JI7

  • 7/25/2019 Problme de flot

    7/18

    51

    1

    s

    2

    p24

    3

    #

    Exercice 4 :

    Des pices circulent dans un atelier sur le graphe orientdes AGV (Automated Guided Vehicles) entre lentre Eet la sortie S reprsent ci-dessous. Dterminer un

    nombre minimum de tronons o des contrles de

    qualit seront effectus de manire quaucun itinraire

    nchappe au contrle.

  • 7/25/2019 Problme de flot

    8/18

    !"#$%&'"" #$ %&'()*+$ %$,- .$ /'&+,)$& #'++$ ,0 %&'1&2++$ )30423&$ 5$ )2

    +203*&$ .,3620-$ "

    7/ 8 9

    / !# :#$--$ 0'-2-3'0 .3103/3$ " /:,;!#:,; ",#;

    !"#$% (# $)(*&+,-.+)/ 0)$$# 1/ %2)3&4$# (# 5&). $-"+$1$6

    !""#$%&%'() +# , %-$.#/ 0 1 2&$.')#/ 3

    4) $())&5% ,(67 $.&16# 2&$.')# 8#/ %-$.#/ 169#88# ,#6% 7:&8'/#7; #$%'" #/% +#

    +:%#72')#7 8# )(2=7# 2&?'262 +# %-$.#/ ,(6@&)% A%7# #?:$6%:#/ /'268%&):2#)%;

    ti mj

    Tches Machines

    s

    Tous ces arcs existent Tous ces arcs existentCet arc existe seulement si

    mjpeut raliser tj

  • 7/25/2019 Problme de flot

    9/18

    !"#$%&'()* ,* -$%, *' -."/*%0$1 2$.% ,3'*%)&1*% .1 4"$' )56&).)7

    !"#$%#&' )' *+,*-."#/01'" #$%&'()*+,-. /)(012. /%) %-3&*()%+*(45 5600.55*7.5 " /%)+%4+

    2$64 8&(+ 5%+*58%*5%4+ &.5 0(42*+*(45 9: .+ ;: 6.-.4+ 46&?@ *&

    0,.)0,. A %6'-.4+.) 8%-3 #@ ,-) A*B&CD7B&C$&%!EF #

    (03 03$-*3(,()3 2%0-3-78

    7G#"(03 ()*%$( &) 7?%3 $64?-04=?( :&- 2($,(3 /54,6?-%$($ 7B&$C8

  • 7/25/2019 Problme de flot

    10/18

    !"#$%&'" %)*""#$% &' ()%* &'+,-.& ,) /0&1%20&3&* #$% /&$* 4& (-01$,&0 5-11& 4$%* 6

    70-$8&0 $'& 59):'& ;,;1&'*)%0& < =-%+')'* 4 &* / *&,,& #$& ,-04#$>-' /0&'? ,& 4&'4 ?&

    $05-11& 4&'4 ?& /)05-$04 4$0 !=

  • 7/25/2019 Problme de flot

    11/18

    !"#$%&'()* ,* -$%, *' -."/*%0$1

    !"##$%&' )*+,-.-/0 1# 2$&%314 / ' .!!)5"{+#}4 12*+6-&0 1# 32/ 2%7"128

    9"737:"#& ' ;% ?%2#:%2 32/ ?% >3 /@3A#% B":C#3#7 & D = %7 $+=0

    2%62$&%#7% >3 E3>%12 /"123#7% ?% %31 #:E%31 ?% = ;8

    +F0G":7 H 1# H>"7 2$3>:&3I>% &12 ) +"# 6%17 62%#?2% H :?%#7:J1%K%#7 #1>0

    +L0

    M '*N&O4 $+&0 '*/+120PH+120 4$+&0*F 3>"2& 2345&:#"# "2& H3:2%

    M '*M"NTO 4 >%2 %# +Q0

    &:#"# S IV62"/%&&1& :#E%2&% ;

    &: (1*+=-T0*127%> J1% T'M- =)M %7 H+10XF 3>"2& H3:2%

    M '*M"N=O 4 >%2 %# +Q0

    &:#"# 2345' S "# %&7 D >U"67:K1K ;

    H:#&:

    H:#&:

    +R0Y"&%2 =*6 4 +5 '*N12O 4 +P '*&

    +:0 &: =*& 3>"2& 3>>%2 %# +Z0

    &:#"# &":7 1*"2&

    +5 '* +5"N1O 4 , '*\+10 4 3>>%2 %# +:0

    &:#"# +P '* +P"N1O 4 , '*[+10 4 3>>%2 %# +:0

    +Z0 Y"&%2 $*$+608 Y"&%2 H+10 '*H+105%&: 1'++

    H+10P%&: 1 '+,

    H+10 &: 1 )+5"+P

    3>>%2 %# +L0

  • 7/25/2019 Problme de flot

    12/18

    "#$%$&$'%! #$%& !"' ( ! )*& +,) -$+.) */.010,& * 2) . *3%4 )5%*&) 6#7 &)4 8+) *$6 9

    .%6 )& !:!; ?0 -0.0-%&/ 2) !)*& ,$&/) -

    uc )(

    !"#$%&'"" #$%&'( ) *' )+$( ,-.+%/.0+& &( !*'& 1$*2& /-2.,.'( / 3& 24 5' . "

    )6*,7"16!7 687

    "#$%&%'($%)* ,- .( /(.%,%$0 ,- .1(.2)3%$45- ,- 6)3, -$ 6".7-3#)*

    !" $% &'() (*)%+, %-) ./0'1-0*'% 20. 3(+-).,3)1(+4

    5" $% 2.%61%. 3.1)7.% 890..:) %-) /;18%+)4

  • 7/25/2019 Problme de flot

    13/18

    (%)*+,#" .' /)0 1$2$+345 #$63#'#!"#$%& ()*+,-,.,/0 1% 234$51 $& 12)*6,40 1% 52/ 463/#57 8$ 2$&"12 "9

    . : -!!("{;#}?$ 81 @7"& /5%57#43 ?5A#?1? 8$ 4 B 6 85%4 /"%4#4&$ B 83&$2?#%$2 @ &!(!-!

    &$7 C1$ :

    DE @ 4"#& 1% @7"& 412 *+,-0,FE .*10$@*10$/*10 %1&-

    GE @*120 4"#& ?5A#?1? 4"14 7$4 /"%8#"%4 DE $& FE?

    - !" $%&'()*+"*,'( $- ." /'($,*,'( )011,)"(*- -)* ".2'+,*3&,40-5 !6".2'+,*3&-

    7-+&-* $- /'()*+0,+- )',* 0( 1.'* /"(".,)% )',* 0( -()-&8.- 9 40, :,'.- ."

    /'($,*,'( $;

  • 7/25/2019 Problme de flot

    16/18

    !"#$%&'()*"

    #$%&'() *+ ,-') .*/-0'+.*/ #'+ 1/*) 12/+32/ , (3/+)(.*/4/+) +*-% 5 6( , /6)

    278-(689-/ 8-'26 &:;

  • 7/25/2019 Problme de flot

    17/18

    !"#$ &'()*+,- $./ 0&. 1)&'-23)&'-4 56"&$.7 &8 973 &7(),+*- 9:.3 ;

    3=)&7-( 1)&'-?3)&'-

    1)&7-(>

    9@@/#0&.7 /=9/A"7#$BC. D. E"7D .$ E&/F.7G"8 C"D#1#H @"&7 C9*#C#G.7 /.

    1/"$ G&7 /=973 &7D98G I=9&AC.8$H D. &74 !"#$ 1= /. 1/"$ "

  • 7/25/2019 Problme de flot

    18/18

    !"#"$%$& ( $%)*" "+",-." -*",/"*

    !"#$#%'("' %*+, -./0

    123+#$43%$#("

    5 ' 1 6

    ! " 7 7

    8 9 :';1< :1;6+ #$43%$#("

    5 ' = 6

    ! " = =

    8 9 :';=< :=;6+ #$43%$#("

    5 '

    ! "

    8 9

    ,?:#:5