Exercices de diagramme PERT

Ybnhd`dcn|doh l'}h yuokm| Bn ybnhd`dcn|doh l'}h yuokm| lm sts|êfm l'dh`oufn|doh cohsds|m é yuäpodu b'oulohhnhcmfmh| lms oyäun|dohs s}u bm ybnh lms läbnds m| s}u bm ybnh lm b'}|dbdsn|doh lms umsso}ucms( Db cohpdmh| lnhs }h yumfdmu |mfys lm fms}umu bm %yodls% l'}h yuokm| mh |mufm lm cjnugms m| lohc lm l }uäm 1 lnhs }h smcohl |mfys" db s'ngd| l'oy|dfdsmu bn s}ccmssdoh lms |åcjms m| neo}|du ndhsd é }h cnbmhludmu lms oyäun|dohs( Mh`dh" lnhs bm läpmboyymfmh| l} yuokm|" db `n}| m``mc|}mu uäg}bdêumfmh| lms coh|uübms lm s}dpd m| äpmh|}mbbmfmh| nyyou|mu lms fold`dcn|dohs n} cnbmhludmu(

Fä|jolm YMU\  Bn fä|jolm YMU\ *Yuogunf Mpnb}n|doh nhl Umpdmw \mcjhd~}m$ }|dbdsm }hm umyuäsmh|n|doh mh gunyjm yo}u lä|mufdhmu bn l}uäm fdhdf}f l'}h yuokm| cohhndssnh| bn l}uäm lm cjn~}m |åcjm m| bms coh|undh|ms l'mhcjnèhmfmh|( Mbbm ms| cofybä|äm ynu b'ä|nebdssmfmh| l} ldngu nffm lm Gnh|| ~}m b'oh ä|}ldmun yb}s bodh( Bm gunyjm umyuäsmh|m bms |åcjms m| bms |unhsd|dohs mh|um bms |åcjms( Lm}z `oufnbdsfms soh| }|dbdsäs ; ‥

‥

bm gunyjm lms |åcjms ; cjn~}m |åcjm ms| umyuäsmh|äm ynu }h umc|nhgbm m| bms |unhsd|dohs ynu lms `bêcjms bm gunyjm lms äpähmfmh|s ; cjn~}m äpähmfmh| *`dh l'}hm |åcjm ynu mzmfybm$ ms| umyuäsmh|ä ynu }h opnbm m| bms |åcjms ynu lms `bêcjms(

Bms lm}z `oufnbdsfms soh| ä~}dpnbmh|s( Oh h'}|dbdsmun dcd ~}m bm gunyjm lms |åcjms( Bms bdmhs mh|um bms |åcjms ym}pmh| ë|um lm hn|}ums ldpmusms ld pmusms ; `dh &8 läe}| l äe}| *bn |åcjm s}dpnh|m hm ym}| coffmhcmu ~}m sd bn |åcjm yuäcälmh|m ms| `dhdm$" `dh &8 `dh *bn |åcjm s}dpnh|m sm |mufdhm ~}nhl bn |åcjm yuäcälmh|m sm |mufdhm$" läe}| &8 läe}| *bm läe}| lm bn |åcjm yuäcälmh|m läcbmhcjm bm

läe}| lm bn |åcjm s}dpnh|m$" läe}| &8 `dh *bm läe}| lm bn |åcjm yuäcälmh|m fnu~}m bn `dh lm b n |åcjm s}dpnh|m$( Bms bdmhs ym}pmh| ë|um pnb}äs ;

Bn coh`mc|doh lms km}z l'mssnd coffmhcm >9  ko}us npnh| bn yuogunffn|doh(

Ynufd |o}s bms cjmfdhs l'}h gunyjm db mh mzds|m }h nyymbä cjmfdh cud|d~}m ~}d u mbdm bms |åcjms %cud|d~}ms% ~}d soh| bms |åcjms loh| bm um|nul dfybd~}mun }h u m|nul m``mc|d` l} yuokm|1 oh lä|mufdhm cm cjmfdh cud|d~}m npmc bms ynunfê|ums s}dpnh|s ; ‥ ‥ ‥

ln|ms n} yb}s |ü| ; läe}| *L!|ü|$ m| `dh *@!|ü|$ ln|ms n} yb}s |nul ; läe}| *L!|nul$ m| `dh *@!|nul$ fnugm ; *L!|nul$ & *L!|ü|$ 6 *@!|nul$ & *@!|ü|$

Oh sm ybncmun lnhs b'jtyo|jêsm oô db h'mzds|m ~}m lms bdmhs `dh &8 läe}|( Bm cjmfdh cud|d~}m ms| nbous bm cjmfdh bm yb}s bohg( l äe}| lm yuokm|( >mu cns ; \d ms| }hm |åcjm lm l}uäm ld mh läe}|

L!|ü|*\d$ 6 |9 @!|ü|*\d$ 6 |9 ! ld

l m yuokm| 5êfm cns ; \d ms| }hm |åcjm lm l}uäm ld mh `dh lm

@!|nul*\d$ 6 |` L!|nul*\d$ 6 |` & ld

3êfm cns ; \d ms| }hm |åcjm lm l}uäm ld n} smdh l} yuokm|

L!|ü|*\d$ 6 S}yq@!|ü|*yuäläcmss m}us$v @!|ü|*\d$ 6 L!|ü|*\d$ ! ld @!|nul*\d$ 6 Dh`qL!|nul*s}ccmssm} us$v L!|nul*\d$ 6 @!|nul*\d$ & ld Npmc cms |uods säudms lm uêgbms" db ms| yossdebm lm lä|mufdhmu bm cjmfdh cud|d~}m( Oh yuocêlm lm bn fnhdêum s}dpnh|m( Mh coffmhçnh| ynu bms |åcjms lm läe}|" oh lä|mufdhm bms ln|ms n} yb}s |ü| 1 y}ds mh coffmhçnh| ynu bms |åcjms lm `dh" oh lä|mufdhm bms |åcjms n} yb}s |nul( Oh cnbc}bm mhs}d|m" yo}u cjn~}m |åcjm" bn fnugm( Bm cjmfdh cud|d~}m ms| bm cjmfdh couumsyohlnh| n}z fnugms h}bbms( mzmfybm ; sod| }h yuokm| cohs|d|}ä lms |åcjms | åcjms s}dpnh|ms ; |åcjm l}uäm yuäläcmssm}us s}ccmssm}us N

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3

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5

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Bm cjmfdh cud|d~}m ms| b'äydhm lousnbm lm b'äpob}|doh l} yuokm|( Bms fold`dcn|dohs you|mh| mhs}d|m s}u bms |åcjms ~}d hm soh| yns s}u bm cjmfdh cud|d~}m(

Ldngunffm lm Gnh|| N ynu|du l} gunyjm lm YMU\" oh ym}| lumssmu bm ldngunffm lm Gnh|| ~}d ä|nebd| bm ybnhhdhg lms oyäun|dohs( Yo}u mzybd~}mu soh ä|nebdssmfmh|" ä|nebdssmfmh|" ensohs ho}s s}u s}u b'mzmfybm yuäcälmh|( S}yyosohs ~}m b'oh ldsyosm lm lm}z umsso}ucms *ymusohhms$ dh|mucjnhgmnebms( Bn `dg}um cd& lmsso}s lohhm }hm yossdedbd|ä lm yuogunffn|doh ;

Oh ym}| n}ssd ybnhd`dmu %n} yb}s |ü|% ;

o} %n} yb}s |nul% ;

Sd b'oh hm ldsyosm ~}m l'}hm sm}bm umsso}ucms" edmh mh|mhl}" bn l}u äm l} yuokm| smun unbbohgäm 1 bm ldngunffm lm Gnh|| cd&lmsso}s lohhm }hm yossdedbd|ä ;

Lm}z oyäun|dohs ym}pmh| ë|um nyybd~}äms s}u bm ldngunffm lm Gnh|| ; bm hdpmbbmfmh| m| bm bdssngm( Bm hdpmbbmfmh| cohsds|m é bdfd|mu bm hofeum lm umsso}ucms" cm ~}d" mh gähäunb nbbohgm bn l}uäm l} yuokm|( bm ynssngm lm lm}z umsso}ucms é }hm sm}bm *podu `dg}um yuäcälmh|m$ mh ms| }h mzmfybm(

Bm bdssngm cohsds|m mh }h nk}s|mfmh| lm uäynu|d|doh lm bn cjnugm lm |unpndb lm cjn~}m umsso}ucm( Sd" ynu mzmfybm" bn umsso}ucm U> |unpndbbm é fd&|mfys m| bn umsso}ucm U5 é |mfys cofybm|" oh yo}uun npodu" npmc b'mzmfybm ä|}ldä ;

YMU\ yuoenedbds|m Db mzds|m }hm pmusdoh l} YMU\ ~}d yumhl mh cofy|m bms nbäns s}u bms ln|ms m| bms l}u äms( Soh nyybdcn|doh s'm``mc|}m mh yb}sdm}us ä|nyms ; >êum ä|nym ; mbbm cohcmuhm bn umcjmucjm lm bn bod lm yuoenedbd|ä lm bn l}uäm lm cjn~}m |åcjm \d( Lnhs bn yun|d~}m oh nloy|m }hm bod }hdpmusmbbm ; bn bod Eë|n ensäm s}u |uods ynunfê|ums ; ‥ ‥ ‥

bn l}uäm oy|dfds|m lm bn |åcjm \d ; |oy|*\d$ bn l}uäm ymssdfds|m lm bn |åcjm \d ; |yms*\d$ bn l}uäm pundsmfebnebm lm bn |åcjm \d ; |pun*\d$

Oh lä`dhd| ~}mb~}m`ods bm uds~}m ynu bn ~}nh|d|ä U*\d$ 6 Q|yms*\d$&|oy|*\d$V/|yms*\d$( Q|yms*\d$&|oy|*\d$V/|yms*\d$( Bm uds~}m fotmh ms| cofyuds mh|um U 6 9"5= m| U 6 9"=( 5êfm ä|nym ; N ynu|du lms ynunfê|ums yuäcälmh|s" oh cnbc}bm lm ho}pmn}z ynunfê|ums *yo}u bn bod Eë|n$ ; ‥ ‥ ‥

bn l}uäm yuoenebm lm bn |åcjm \d ; |yuo*\d$ 6 Q|oy|*\d$ ! <|pun*\d$ ! |yms*\d$V/0 b'äcun|&|tym m*\d$ 6 Q|yms*\d$ & |oy|*\d$V/0 bn pnudnhcm p*\d$ 6 m*\d$ 5

3êfm ä|nym ; Yo}u cjn~}m cjmfdh" oh ym}| nbous cnbc}bmu

‥

‥ ‥

bn l}uäm ms|dfäm

yo}u |o}|ms bms |åcjms \d l} cjmfdh

bn pnudnhcm ms|dfäm b'äcnu|&|tym ms|dfä ; Mms| 6 Pms| >/5

yo}u |o}|ms bms |åcjms \d l} cjmfdh

Oh s}yyosm }s}mbbmfmh| ~}m bn l}uäm lms cjmfdhs oeäd| é bn bod houfnbm *lm Gn}ss$ lm ynunfê|ums Lms| m| Mms|( Mh }|dbdsnh| }hm |nebm lm Gn}ss oh ym}| nbous mh läl}dum sod| }hm l}uäm é }hm yuoenedbd|ä `dzäm" sod| }hm yuoenedbd|ä l'ncjêpmfmh| l} yuokm| lnhs }h läbnd lohhä(

mzmfybm ; Yumhohs bm cjmfdh cud|d~}m lm b'mzmfybm yuäcälmh| *l}uäm |o|nbm 57 ko}us$( S}yyosohs ~}m bms |åcjms E" L" @" G couumsyohlmh| n}z ynunfê|ums coff}hs s}dpnh|s ;

|oy|*\d$ 6 9"7+ld

|yms*\d$ 6 >"5+ld

|pun*\d$ 6 ld

Oh mh läl}d|

|yuo*\E$ 6 0":: |yuo*\L$ 6 >>": |yuo*\@$ 6 ="4 |yuo*\G$ 6 >"40 m*\E$ 6 9"=: m*\L$ 6 > m*\@$ 6 9"= m*\G$ 6 9">0 Lms| 6 50"=< Pms| 6 >"0> Mms| 6 >"57

Cnbc}bohs bn yuoenedbd|ä yo}u ~}m bn l}uäm l} cjmfdh sod| dh`äudm}um é bn pnbm}u 57( Bn pnudnebm lm Gn}ss uäl}d|m ms| *57 & 50"=<$/>"57 6 9"30055( Bms |nebms yo}u | 2 9"30055 lohhmh| bn pnbm}u nyyuozdfn|dpm 9"0<( Db t n lohc 0<- lm cjnhcms yo}u ~}m bn l}uäm l} cjmfdh sod| dh`äudm}um é 57( Sd fndh|mhnh| oh cjodsd| 5= n} bdm} lm 57" oh |uo}pm |u o}pm }hm yuoenedbd|ä lm >>-( Dhpmusmfmh| sd oh sm `dzm }hm yuoenedbd|ä lm :9- ~}m ym}|&oh msyäumu coffm fmdbbm}um pnbm}u lm bn l}uäm l} cjmfdh( Bms |nebms lohhmh| 57"0( Sd bn yuoenedbd|ä ms| lm =9-" oh oe|dmh| nbous äpdlmffmh| 50"=<(

Mzmucdcm > Bn cohs|u}c|doh l'}h mh|umyü| ms| läco}yäm mh ldz |åcjms loh| bms cnunc|äuds|d~}ms soh| lohhäms lnhs bm |nebmn} s}dpnh| ;

|åcjms hn|}um

l}uäm yuäläcmssm}us mh  ko}us

N

nccmy|n|doh lms ybnhs ynu bm yuoyudä|ndum

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yuäynun|doh l} |muundh

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coffnhlm lms fn|äudn}z N

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cum}sngm lms `ohln|dohs

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coffnhlm lms you|ms m| `mhë|ums

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bdpundsoh lms fn|äudn}z

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co}bngm lms `ohln|dohs

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bdpundsoh lms you|ms m| `mhë|ums

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yosm lms f}us" lm bn cjnuymh|m m| l} |od|

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fdsm mh ybncm lms you|ms m| `mhë|ums

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\uncmu bm ldngunffm Ymu| m| mh läl}dum bm cjmfdh cud|d~}m(

Mzmucdcm 5 B'mh|umyudsm SLE&Yb}s `neud~}m m| coffmucdnbdsm" n}yuês lms ynu|dc}bdmus" l} foedbdmu lm snbbm lm endhs( Bms smupdcms lm `neudcn|doh lm bn SLE&Yb}s oh| ä|}ldä b'oulohhnhcmfmh| lms |åcjms é ynu|du lm bn coffnhlm l'}h cbdmh| lnhs }h fngnsdh k}s~}'é k}s~}' é bn bdpundsoh( Bm |nebmn} s}dpnh| uäymu|oudm bms |åcjms m| bms coh|undh|ms l'mhcjnèhmfmh|( l}uäm |åcjms mh yuäläcmssm}us s}ccmssm}us  ko}us N

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Lä|mufdhmu bm cjmfdh cud|d~}m(

Mzmucdcm 3 Bn cohs|u}c|doh l'}h mh|umyü| ym}| sm l äcofyosmu mh ldz |åcjms" umbdäms mh|um mbbms ynu lms cohld|dohs l'nh|äudoud|ä mzyudfäms lnhs bm |nebmn} cd&lmsso}s ;

B'mh|umyumhm}u cjnugä lm bn cohs|u}c|doh lod| ybnhd`dmu bms |unpn}z( >$ Db lod| |uncmu bm gunyjm Ymu| m| lä|mufdhmu bm cjmfdh cud|d~}m 5$ Bms umsso}ucms j}fndhms é }|dbdsmu soh| ; ‥

‥

sod| ; }h nucjd|mc|m n``mc|ä é bn |åcjm N" }h |muunssdmu> n``mc|ä n}z |åcjms E" L" G" } h |muunssdmu 5 n``mc|ä n}z |åcjms E" L" G" }h |muunssdmu 3 n``mc|ä n}z |åcjms L m| G" }h ymusohhmb smupdcm ncjn| > n``mc|ä n}z |åcjms C m| J" }h ymusohhmb smupdcm ncjn| 5 n``mc|ä é bn |åcjm M" }h ymusohhmb smupdcm ncjn| 3 n``mc|ä é bn |åcjm @" lm}z cjnuymh|dmus > m| 5 n``mc|äs n}z |åcjms D m| K( sod| ; }h nucjd|mc|m n``mc|ä é bn |åcjm N" }h |muunssdmu n``mc|ä n}z |åcjms E" L" G" } h ymusohhmb smupdcm ncjn| n``mc|ä n}z |åcjms C" M" @" J" }h cjnuymh|dmu n``mc|ä n}z |åcjms D m| K(

Bms lm}z cns soh| é ä|}ldmu(

Mzmucdcm < Oh mhpdsngm lm uänbdsmu }hm ybn|m&`oufm lm `oufn|doh é lds|nhcm cofyou|nh| 3 cofyosnh|ms ; ‥ ‥ ‥

Cofyosnh|m > ; Bn gms|doh lms coh|mh}s mh bdghm Cofyosnh|m 5 ; Bn gms|doh lms dhscud|s Cofyosnh|m 3 ; Bms o}|dbs l'nccofynghmfmh| yälngogd~}m *`ou}f" cjn|" @N^$

Bms |uods cofyosnh|ms h'ä|nh| yns cofybê|mfmh| dhläymhlnh|ms" }hm dh|ägun|doh" dhcb}nh| lms läpmboyymfmh|s cofybäfmh|ndums" ms| é yuäpodu Oh s}yyosm ~}m bms ld``äumh|ms |åcjms soh| coh|undh|ms ynu bm}u cjnugm m| bm}us läymhlnhcm coffm dhld~}ä lnhs bm |nebmn} cd&lmsso}s ; |åcjms

Cjnugm *mh fodszjoffms$ \åcjms yuänbnebms

N ; Nhnbtsm gboenbm

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E ; Nhnbtsm lä|ndbbäm

0

N

C ; Yuogunffn|doh cofyosnh|m >

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M ; Yuogunffn|doh cofyosnh|m 3

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@ ; Dh|ägun|doh

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G ; Mzyäudfmh|n|doh/äpnb}n|doh

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J ; \unpn}z lm fdsm n} yodh|

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D ; Umcm||m

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>$ \uncmu bm ldngunffm YMU\ l} yuokm|( Lä|mufdhmu bm cjmfdh cud|d~}m 5$ Oh s}yyosm ~}m b'oh n``mc|m n} yuokm| lm}z nhnbts|ms&yuogunffm}us" Ko m| [m||m" é ybmdh |mfys( Yuoyosmu }h ldngunffm lm Gnh||(

Sob}|doh lm b'mzmucdcm > Mh }|dbdsnh| FSY" oh oe|dmh| *bm cjmfdh cud|d~}m ms| mh uo}gm$;

Sob}|doh lm b'mzmucdcm 5 Mh }|dbdsnh| FSY" oh oe|dmh| *bm cjmfdh cud|d~}m ms| mh uo}gm$ ;

Sob}|doh lm b'mzmucdcm 3 Bm ldngunffm lm Ymu| ms| *cjmfdh cud|d~}m mh uo}gm$ ;

B'n``mc|n|doh lms umsso}ucms ms| ;

Mbbm couumsyohl n} ldngunffm lm Gnh|| s}dpnh| ;

Lnhs bm smcohl cns" db t n fodhs lm umsso}ucms ;

Bm ldngunffm lm Gnh|| ms| lohc fold`dä mh cohsä~}mhcm ;