pement et la promotion d (un nouveau produit.0)1 (aprшs son

pement et la promotion d (un nouveau produit.0)1 (aprшs son

)"
z
l
s
l
G
z
|
{
u
r
s
l
A

|
r
w
v
u
m
l
D
‚
w
v
|
m
Ž

C

u
m
4
l
A
‚
l
s
l
A

u
r
C

‹
m
Ž

,

A

”
r
w
ƒ
4
l
A
‚
s
}
?
—
s
l
w
ƒ
,


Žmyx'lsv†„…{Šls~GzG {6lslsz{_v†ƒ zGx”—?Alnrum|,{|vw„…mumy,x'{|zGvw,{ z‚ „Av†zƒ wl z ls,AAru—?Clˆm<x'Ž,AArur6M‚Dƒwl”Av†‚A{ˆ}s‡ —?lsƒw,x'AAŽru–nlsmo„…muls,zGz{ lqlspD{ Ž}sr|„vwlszv†ƒ tnwl”l€lslsA{•ruƒwClnm<m•Ž}s{|, A‚Ar<lnƒmox…‚AAl<A„4“Aƒ†x'vwtsruv†t {u} } Žlslsƒ†ƒ†wwll
Ž‚Al,Ar|ry„x6v†—?ƒ wlsl”z ‚DlsArul_ruClsm<zG—M‚ v†x'ruz ,m6z ƒ xAA“Aƒ†vwtsv†{u} T~G lsƒIlnm|A{6zAƒ v†{uv†}nzGmˆ—?‡ lnDm|{|x,vwt mu)mulsx'„…zG{*ls~GzG{€~Glsƒ†Awl_v „4lnm|x`{pDtnv†,„zGvw{|muryl x'v†ƒwzGln{um6l —?6lszGz {ul*ln)mŠx,‚AmIl v†zGƒ —?lslnzGm|{|{|ruv†lsrPAAr|ƒ†vw mulm
ƒw,rumu~G l ƒw,rumu~G l M,ƒ†A{|vw,z
‡
ls{
Ž,ArŠƒwlnm
tn,z mu}n~G lsz tnlnmo„…,z }s{yx'v†rulnm —?z }sr|x'v Œ?Tlsx'zGzG{‹{ x4Az l ,z ts{|vw,z ‚ A{|v†ƒ v†{u}…‚Al _lsr|z ,Aƒ† v
=>% !s. #&.X% 39BYU0#3D &# /@% !u*&% /B4%71U@% /
uP
Vi
f
!
d
p
n
N
f
ž
l
B(d,p) = d p
!
"
"
p
N
e
M
p = 6#
p = 3 #%$
(d,p) = (15,5)
(d,p) = (17,3)&
=>% !s. #&.X% 5 8' ,_!s'#31,F*3#5U@
K
(
u:X →R
*
)
x∈X
3/4
1/4
Š
s
}
u
{
s
l
|
r
„
†
v
z
,+…ƒ xxK ,z ts{|vw,z ‚ A{|v†ƒ v†{u}…‚Al-(_lsr|z ,Aƒ† v
l
?
—
s
}
|
r
*)Tx'zG{
v
s
l
{
G
~
A

v
Žlsr|„…ls{6‚Al€rulsAru}nmulszG{ulsr6ƒ x”„%.s„…l K ,z ts{|vw,z‚ A{|v†ƒ v†{u} lnm|Ž}sru}nl€‚Al0/ d21 ~G l ‡
=>% !s. #&.X% `354e!s%71')!s%a')% /x!$#&/@{>6% /6 z‹tn,z m|vw‚A–srulPƒ x_ƒw,{ulsr|vwl:~GAvCryx'AŽ,r|{ul7olsAruCmIxn—?lntPAz l:tf)x'z tnl
m|Ar6‚AlsDp !98lsAruCm6xn—?lnt€Az l tf)x'z tnl‹m|Ar•{|ru,vwm:! ls{•r|vwlszxn—?lnt€Az l tf)x'z tnl‹m|Ar<;D‡
= H?>A@ x'ryx,ts{u}sr|vwmu,l +”ls{•rulsAru}nmulszG{u,l +”ƒ x K ,z ts{|vw,z‚Al€ru}s)x'r|{|v†{|vw,z‚Al€tnls{|{ul€ƒw,{ulsr|vwlC‡
ƒw,{ulsr|= Pvwl >C# B  lsƒ)„…,zG{yx'zGD{ )ApAlo„4x`pDv†„‹A„ Az x'Œ?lszG{%z lsA{|rulŠx'4r|vwmu~G l6lnm|h{ iRv†ƒ)Ar .s{ l€)Fx E?lsr%Ž,A>r j|, lsr l tnls{|{ul
= cG> 1H.s„…l ~G lnm|{|vw,z"Ž,Ar<Az x'Œ?lszG{‹Fx EGx'zG{ ‚Al”"ƒ xn—?lsrum|vw,z Ž,Ar<ƒwl”r|vwmu~G l”ls{Šƒ Bx K ,z ts{|vw,z ‚ A{|v†ƒ v†{u} ‚Al
(_lsr|z ,Aƒ† v
#
#
= 7 > 1H.s„…lŠ~G lnm|{|vw,z Ž,Ar%Azx'Œ?lszG{6Fx EGx'zG{•Az l<AruŠ} K }srulsz tnlŠŽ,Ar%ƒwl<r|vwmu~G l<ls{_ƒ x K ,z ts{|vw,z‚ A{|v†ƒ v†{u}Š‚Al
(_lsr|z ,Aƒ† v
#
Ž ,=>g{ % f !s–n. muln#&.Xm6% ‚AKlk/ pId2g1z!s> my6>x'4{|vw% hm !uK ,')zG{ % /BY)!s AC !s%71.X% / k9lnm%AruŠ} K }srulsz tnlnm_‚ Azx'Œ?lszG{_ryx'{|vw,zAz lsƒ = —?}sr|*v )Tx'zG{•ƒwlnzm fJE i
u(x) = 32 ≤ u(x) ≤ u(x) = 212,
∀ x ∈ X.
v:X →R
u(x) =
v(x) = 0
u
v(x) = 100
√
x u(x) = ln (1 + x)
u(x) = x2
L ≺ D1 ≺ D2 ≺ W,
sl {
Aru}ŠK L9}sruruls,z Atn—?l‹l,+‚AlŠAzƒ" lxx'Œ?K ls,zGz {<ts{|m|vwA,r•z ƒwln‚m• Aƒw,{|v†{uƒ lsv†{ur|}vwlnm‚AlM/ sl d2{ 1 ~GtsAv i v%x'ruAlsruA–nrumˆ}n‡ mulszG{ultnlnm”Aru}ŠK }srulsz tnlnmˆ‡NPz A‚ }n‚DAv†rul ƒ" ,ru‚Drul ‚Al
L
0.6
D1 ∼
D2 ∼
0.4
W
M
0.2
L
0.8
W
N
L
0.25
M
0.25
0.25
0.25
0.20
D1
N
D2
W
a€‚ƒ@„Tg…T†@‡TaˆŠ‰‹‰TŒ
L
0.15
0.50
0.15
D1
D2
W
‚Ž0T‚‡0‘‚u’T@€u“Š”@•+–—T•TŠ‡0˜‹‘‹˜‚@€š™&›Fœž0Š@€‹€ŠŸŠŠ‡s =>% !s. #&.X% 5G r%H4\,_!s,_')7=>%('zy u*3*&,F#&/
= H?>
K
L
!
ƒwƒwlnl€mP„…AMƒ† ‚Am –sƒwlru}n‚ ~G Als{|zGv†ƒ {uv†m:{u} ‚AlnlnmPm|Žv†z}sru‚D}nv†l—Mvw‚D€ls{•x'm:Az muƒ†m ,ƒwzGmoln{ mIA‚Aru}nlstsDlsvwpmu{ }sA„…ru,ls‡zG“AN{Šƒw–spDxn„…A—?ƒ†lnlnvwmP~Gt€‚Aƒ"l,l*x`+•pDt fŽvw,,,„…v‘Ap”rul ~G‚A‚ l*, v†ƒwv)z,{utn‚Alsln}sr|mPŽvwl%tlsfz ts,‚v i v‘x'x'p…zAmutnru,lC–nzGmI‡ {Pƒwlnv†zmItnt,f „,v‘)p”x'ls{|„v†“AAƒwlnv†r|m_vw~Gxn—?lnlntm
L4
1
H
L1
c —Dmˆ‡
7J
0.8
L2
0.2
c 0.25
L3
0.75
=P >
ls{
—Dmˆ‡
7J
0.2
L4
0.8
‡ 1,zG{|rul,+”~G6 lŠz ƒ"tn x`,pDz vwm|,vw„…‚A–sl rul%‚ƒw v†lnz m ‚AA}sruŽ,ls“Az ƒw–s‚ „…x'z lntnmPl ‚Av†l%„t Af ƒ†,vwv‘~Gp  ‚Al l*ƒw,{ulsr|vwl%tsv i x'Aru–nm:!, ‡
D
—
ˆ
m
‡
#*
!"#$"#%&%&(')
0<X <Y
r ∈ (0,1)
p>q
L 1 L2 ⇔ L3 L4
p
X
L1
1−p
rp
X
L3
1 − rp
—Dmˆ‡
q
Y
L2
1−q
rq
Y
L4
1 − rq
€
'
x
z
Š
m
w
ƒ
n
l
Š
m
A

u
r
,

A
“
w
ƒ
s
–
…
„
n
l
‹
m
A
‚
l
f ,v‘p ‚Al ƒw,{ulsr|vwl…tsv i x'Aru–nm = Aru,Žsi
t
tn‚mu}nln v†mm…z )‚Atfx'}sŽr,v‘lsp0o6z ƒ†‚ mux'x',zvwzGm tn{…lC= v†‡H z 8ntnO ,cG„>> )!9x'ƒw{|lnv†m”“Aƒwtlnf m ,xnv‘p —?lnlst„ƒwAl v†r|„…vw~GM ‚Aln–sm‹ƒwlƒwln‚m AA{|ƒ†v†ƒ mv†{u}K ru}nln~Gm|Žls}szGru}n{ulm”!Pmuls,{…zG{ Aƒ† mlsA{ ru}ntsvwmu‡ }s„…NpDlsAzGƒ†{ vw~Gxn —?l,ln+4tŽƒ", x`ApDruvw~G,„…,l v
= cG>
+ ,-$"#'./01'23$"#%&%&(')
L1
L1
‡
H 0.11
L3
0.89
a€‚ƒ@„Tg…T†@‡TaˆŠ‰‹‰TŒ
H 14
H 14
—Dmˆ‡
—Dmˆ‡
L2
O-14
0.10
0.89
H 14
0.01
0.10
O-14
L4
0.90
L4
‚Ž0T‚‡0‘‚u’T@€u“Š”@•+–—T•TŠ‡0˜‹‘‹˜‚@€š™&›Fœž0Š@€‹€ŠŸŠŠ‡s !
‰
tn,,r|z „…‚Dl€v†z{|vw‚Al%,lŠzAŒCzryŽx'lslsz„…{|‚Av†{ulsl_mzG“A{AryŽx,{ummu,muA”lsr”r|ƒ vwx”myl x 'Az „4ru,ln{umux'}nm|rulvw~G, z l4A'ls‚A‚A{•l…,v†ƒ {Px”“AvwA“A–sruruvwls–sl…zrulŠA‚Dr|ruAv†l•zruln‚Atsmuv†ln)m|mPvwx',‚AƒwzlC}n‡ts,vw“Am|vw{uls,lsƒ†z wzGl mP .tstnl v%,‚Az mulstnls—Mlsryryx'r|x'z)v†{‹v†x'{ zG—?s{*ls{|z ƒwrul%‚DlŠƒ „…x'l z ,tnx'v†lszD„…mop ls,)zGz x'{*}sr|ru‚ {|lsvwtsAAmuz l€ƒ†vwz ls„4ru,mAx'—?vwmum•lˆ,x'‚A  lm
~Gx'ƒ†)w,x'ƒ†v }{u}Š_}nƒ ~Gx•Aruv†ln—Ct x'ƒwlslszGrut {ul l%‹ls{Itnls‚Aƒ†w}sl<—?ls{|ƒwru,,AAŽ—?ls}n„…lŠ‚lszGx'{ˆz ‡ m%
ƒwlnƒ m_x_tˆAx ruls}n„mˆ‡Mvw–sk rux‹l%“A}s{yryx'x,Žmumul*lsr|lsvwƒ†l<wl:‚A‚A,}nv†ts{_vw‚A{u,l%A‚A{•l ‚ Rx'x'v†“Žrul*,rumu‚,v†{9‚AA}ntsz‹vw‚Av†zGls—?r_lnƒwm|l6{|vw„…mumu,lszG„…{yx'lszGzG{{
ls‚Az }ntsvwm|vw,z }sƒwls—?} ‚ ‚AA}nztsvw„…m|vw,,z zG{yx'zG{<‚A‚ l Az„…,”zG{ylsx'AzGru{<Cmˆ‚A‡ l ls{_v†zG—?lnm|{|lsvwAmurumuCls„…m lsmuzG,{6v†{•lnAm|{_zAv†zzG—?m|ln m|tn{|tnvwmu–nmum ls„…t lslnzGm|{<{ lsz .‚Dv†rul€tn,Rz x'‚Dv†“AAƒwv†l{
…Am|v:z lsl‹ƒ†wv†l4zAz x ˆ—CAx'r|vw{|m€vw,ƒ z"x{u‚Aln}nt tsAvwzm|vw,,ƒwz ,ŒCvw~G 9l xn—?xnln—?t lnt”Aru,“)‡ x'P“Av†z ƒ v†{utˆ} x,m‹‚ m|vI}nlst ƒ†wllntxƒwAlr|Avwm6ruMƒ x4‚DA‚Av†}n{ tszvwm|l vw,Žz lsA{ )lsx,{Šm xns—?{|lnrut”lA‚Aru}s,—?“)lsx'ƒw,“AAv†ƒŽv†{u}C} ‡
P)x'z2r tˆlqx,pAm”ls„‚Al4Aƒwm|l tnlstnz –nm‹Rx'ƒ vwx myx'zGr|{4„…Al4z Žlls}sA{|{” ls‚Az lm|A)v†x'{ur|l „‚Av<}ntsAvwzg‚Als}nr t )‚Ax'l…zG{u{|lnv†ƒm|w{u,lszer ‚A‚Al}ntstnvw,m|z vw,muz,„„4x'mu{u,lsz AruAm ruMŽ‚D,A{ulsv†{zG{|m|vwAlsƒwr‹m %ƒwl…,g„4x'‚Arult z } l
)‚A}sx,Žm<ls{uz lnmum|ls{ur%lsrŠAmuz ,z„…,AzGru{yMx'‚DzGA{•v†{Šm|Am|AAr6Aƒwƒw}sl‹„…„4lszGx'{yrux't v†ru} l€‚A‚Al }ntsvwm|vw,z lsA‡ruCGmˆvI‡ lsPƒ†wƒ†l”wl6{urulnl m|n{u,l‹v†{•mu,x'zƒw,Arum%ruMmu‚D,Av†{%v†{ŠAm|z4Arur<}nƒwm|l‹Aƒ†„4{yx'x'{%ruŽt C} m|v†{|lsvƒ†wl”z ‚A,,{uv†}{
tŒCˆx,ryx'm z ‚A{u,lnl” m|}n{€tA,z lsƒ†ruwz }nl ,m|Az ‚Aƒ†T{y}nŽx'ts{”vwCm|m|vwz v†,{|}sz v ŒG%x',{|v z Žz}s,ŒG,Ax'{uro}{|v Azls„…ƒ†wl ,ŽzG‚A,{y,x'Av†zGr‹{ {€ƒ m|z)}nAt x'A)ƒwAlsx'„…ƒwzG}s{|„…lsv†zGƒ wls{,zGz0‚A{yx'}n‚Av†tsrul4vwl ‚Atnls‚A,r€l z ‚Amul”,„„…„4ls{|x'{|…{urulsl lsAAlsrurum”zCm{u—?ln)lsm|,zG{u"{u}Cl‡ x'€mu“),x'x'zzz ‚Am‹A,ru{uzAM,z‚D Alsm‹rŠv†{ ƒwmylnxm
tnz,„,{u„…} lsrutsv x'ƒ†,vwmyx'{|Avwz,z }nt ‚A}nlntst‹vwm|tnvw,,„z „…lsru‡'tsk9v x'l*ƒ ƒ x'zz tn,ls{u„…} lszG{P‚A‡ l%Pmuz,z”tˆAx,rumoM‚A‚Dl Av†m|{ m|tnAtnr–nm6ƒwl*tn„4,„x'ru„…t lsru}_tslnv x'm|{Iƒ TAmuz”lnm•m| rulntntntnls–n{|m{utnln,m6„m „…}sƒwls–sru—?tslsv zGx'{ ƒ
m|xn—Cx'tntnzG–n{<m_ƒ tnx ,„„vw„…mu‚ l lsrulstsAz)v rux'x'Cƒ7ƒwml‹lnAm|m|ls{%A{ ro}sŒGƒwx'l€ƒwl„4m|v†x'z ru,t z9‡ }”mu,v†{oŽCm|‡Av†{|€m|v v9:x'x'zln m|m%{6ts{uA}s,zŒGAx'{u{uƒwlnlnl m%m|{oƒwln‚Am%lŠtn„4,z x'ruŒCt A}€ryx'z {|vw,lnm|z {om Ml 7ƒ x lnm|v9tsA{|ƒrux,} “)tnDx',ƒ “A„x”v†ƒ „…Av†{uruls}Š,ru“)~Gtsx'v x'“Aloƒ†v†vwƒƒwmyv†l6x'{u}{|{uvwln,‚Am|z l{
mulsryx Azm| tntn–nm ls{
m|v7ƒ x tn,„„…lsrutsv x'ƒ†vwmyx'{|vw,z"mulsryx”Az}nt lntC‡
m|m| tntntntn–n–nmm tntnP,,zg„„„…„…A{|lslsv†ruruƒ tsvwtsmyvv x'x'x'zGƒ%ƒŠ{m|m|vv6ƒ xƒwƒwl lru{u–s{ulnŒClnm|ƒwm|{ l"{ m ‚Am lnl lnm|{‹m|•{ xnx —?xn?—?}slnru}sm }ru_}z ‚AŽ}s}sŒG{uCx'lsm|r|{|v†{|„v |v ‡ v†*z Šlls}s{ r|v )l 4~G Az {ulnm|{€*:Žƒƒ xx Cm|AAv†{|ruruv ,,_“)“)lnx'x'm|“A“A{€v†v†ƒƒ“Av†v†{u{uvwls}} z Rxn—?,ryx'“Aƒwl A‚A‚Az ll
ƒ“Am|x  vwlstnAz2tnru–n,‚Am‹“)} tnx'R,xn“A„—?v†ƒ,v†„…{ury}”x'ls“Arux ƒwtsl vAx'r|ƒ vw,Atr|z
v ln‚Am|m|{l  tnm|tn. ‚D–ntnm”v†tnru–nl…tnm ,~G„ „…v†ƒ%lsrux'tsAv ŒCx'„…ƒ lst zGln{ul…m|{ ƒ x .‚DAv†ruru,l “)x'~G“A v†‡ ƒv†v†Šƒ%{u} l€‚Dv†x„„sŽv†zG„…C m|l l {uAlsƒ—?r|xvw}s,r|Ar|v v:)ru,l‚A“)”l…x'~G“Am| v†ƒ tnv†A{utnz}–nm€{uxln)m|Žx'{orCzm|ry{u}sx'lsŒGAr|x'vwŽ,{|v,r|:v%r|{ln‚Am|l{
m| tntn–nmo)x'r•ryx'AŽ,r|\{ l ƒ x”Aru,“)x'“Av†ƒ v†{u}”x”Ar|vw,r|vI‚Al€m| tntn–n>m M
‡
= P > 6lsAru}nmulszG{u,l +€ƒwl<Aru,“Aƒw–s„…l ‚AlŠ‚A}ntsvwm|vw,zmu}n~G lszG{|vwlsƒ†wl ‚Al<ƒ x‹“Aryx,mumulsr|vwl€mu, m%ƒ ex K ,r|„…l€‚ Azx'r|“ArulŠ‚Al
‚A}ntsvwm|vw,z9‡
ls{
‡
€x'z m•ƒ x m|Av†{ul ‚AlŠ"ƒ lqpAlsrutsvwtnl‹,zŽCmul
l„…szlszm|=AtncGA,l > +oŽ6C)}nmyx'x'mur*,zGtˆ {6x'‚D~Gƒwruts l6A ƒwls)lsƒ†x'r:wl€r%"ƒ lnv†lnz m|m|{•‚DŽ z}stsryls{|x'Avwz ,{|tnruaz l€l•l€„4—Mvwrux'hm lsig{ “Žl0f ,iR}s—MA„4vwrum•m_x'‚D{|lsvw{_~G lsr|xzvwlomu~G‚AK , lnz m:l tsm|={|v‘lsvwp ,ƒ†wzƒwlŠ,{u‚A„4lsl r|x`vwpDlnv†m:ƒw„l6‚AvwAl_mul€ruƒ ,<x mu“Aln) ƒwm•–sz…„…AArulŠA )vw‚Am:{ul<mo‚A‚A}sln}n{um|tslsŽvwr|m|}s„vwru,}nv†zz m >,l ‚A‡+ol6$ ƒwo6lnƒ x€m:vw‚A‚A“Al }nryMtsx,vw@mum|muvw,ls,„r|z vwlmi
ru,}nAm|{|Av†„4ƒ†{yx'x'{uƒwlnm6m€‚Alslnzm•{urulnlsm|„…{u:m ,! zG{yx'zG{€Aru,lsŒC{ rulnmum|v†—?ls„…lszG‡ & {Š‡ ƒ" x'r|“Arul ‚Al”‚A}ntsvwm|vw,z9‡ @ x'ƒwtsAƒwl,+ ƒwlnm6Aru,“)x'“Av†ƒ v†{u}nm ‚Alnm
6)x'lsr|A{|=ruvw7 ts}n>MAmulsƒ†BvwzGls{urul,mˆls+…‡ ƒŠlslnz+m|{ K ,ƒwzlts„…{|vw,,z zG{y‚Ax'lzG{„4ƒ x4x`pDAv†ru„4,“)x'x'ƒ€“A~Gv†ƒ v†{ul}ƒ ‚Ax l”“A{|ryrux,,muAmu—?lsr|lsvwr l‚Alnl”m|{ ƒ x4A“Ar .svw–s{urul l l Aru)lnFx muE?m|vwls,r z Žls,z"ArŽlsl {|7v†{ulnmmts{|K Als{urmŠŽƒwl,A{urŠlnm|ƒw{ ln#m
=>% !s. #&.X% 3 !s|)!s%(')%a') . #&/0#&1 r#31'6.nU0#&1 -!s% |r6!s/B%XUx!sZ }*&%(')%(],X^% /
!
!
B
@ Ši
K
K žl
!
<.
el
0K
l f f
K
=
K
:!
K K
> H I+
=
=
P
h
i
0
l
i
>
@
I−
l
f
>
p
I+
!
N
f
.
q
=
f !
N
) I− p > q
>T
WK
f
:!
f =
f
>T <N
N
K=
H K = TN>
" f
>
TP =
!
K
K>
2)
el
f =
P
:!
>
= M A>
f
= EC > 9N
= SC >
f
"!
:
l H :! ml-
!
f !
l Pr(SC) = s J
)
:!
K)
f
K
l Pr(T P | SC) = π
:! Pr(T P | EC) = π < π
f
= H?> N
H( FE :!
,+ Pr(SC | T P ) !
!
:
K! Pr(SC
:
K / *) ,+ | T N )
K
K
l
"! hi l0i
l
>M Pr(SC | T P ) > Pr(SC) %. ! *) ,+ K
ŠK
l
"! hi l0i
2 "#
0
" . "#
3" . "#
Pr(SC | T N ) < Pr(SC)
q = s = 1/2
π = 1 − π 0 = 0.85
p
2 "#
Pr(T P )
Pr(T N )
p
a€‚ƒ@„Tg…T†@‡TaˆŠ‰‹‰TŒ
‚Ž0T‚‡0‘‚u’T@€u“Š”@•+–—T•TŠ‡0˜‹‘‹˜‚@€š™&›Fœž0Š@€‹€ŠŸŠŠ‡s