p SAC - creden - Université Montpellier I

!"#$%&'()'*+",%$#&'-)'''''''''''''''''''''''''''''''''''''''''.&/$%01'2'3'45&6,7&8'9&'609:7&8'9&'/"7/;7'
4&!4)3(9)>7()*+;!7()*+A!17)3!&+37)(&!67!+):&67!47!0*4&!4&!'*22&'(&;!
!
\;!F):&67!47!>79&67!4)3(9)>7(&79;!
X+! )+(9*47)(! 06)+(&+6+(! 7+&! 4)0&+3)*+! ?B*?961C)=7&! :)6! 7+&!
4)DDB9&+')6()*+!&+(9&!>79&67/!4)3(9)>7(&793!'*8(&7/!`169(!4&!4)3(9)>7()*+!V!1)&43!
V!:B2*!)01*9(6+(&a!&(!>79&67/!4)3(9)>7(&793!1&7!'*8(&7/!`169(!1&7!)01*9(6+(&a;!
@&3! '*8(3! '*007+3! 4&3! >79&67/! 4&! 4)3(9)>7()*+! 633*')B! V! 7+! (E1&!
169()'72)&9!4&!>79&67!`! Fl
a!3*+(!6733)!19)3!&+!'*01(&!46+3!2K6+62E3&;!
⎡
⎤
@&!'*8(!)+'9B0&+(62!4K7+!0*4&!4&!4)3(9)>7()*+! j !&3(! ⎢∑∑
Cijk + Dj
⎥;!X+!
⎣ i k ⎦
+*(&! s
jl
!26!169(!4&!>79&67/!4)3(9)>7(&793!4&!(E1&!46+3!2&!+*0>9&!(*(62!4&!D27/!
4&33&9:)3!V!1)&4A!4&!D27/!4&33&9:)3!&+!:BC)'72&!0*(*9)3BA!4&!D27/!4&33&9:)3!169!
>*i(&3!1*3(62&3!&(';j!@&!'*8(!)+'9B0&+(62!4&3!D27/!16336+(!169!7+!(E1&!4&!
>79&67!4&!4)3(9)>7()*+!l !&3(!62*93!4*++B!169!2K&/19&33)*+!37):6+(&!-!
!
⎡
⎤
∑∑∑ ⎢ Cijk + Dj ⎥sjl + F ! ! ! ! ! ! ! `H]a!
l
j i k
!
!
37):6+(&!-!
⎣
⎦
*d! ijk ! 3*+(! 2&3! D27/! =7)! 36()3D*+(! 2&3! '*+4)()*+3! `NaA! `$a! &(! 2K&/19&33)*+!
∑∑C + E ≤∑∑ R ! ! ! ! ! ! ! `HHa!
!
ijk k ijk
i k i k
^+!(E1&!4&!>79&67!4)3(9)>7(&79!l !>B+BD)')&!62*93!4K7+&!37>:&+()*+!3)!-!
⎡ ⎤ ⎡ ⎤
⎢ Cijk + Dj ⎥sjl + Fl > ⎢ Rijk ⎥sjl
j ⎣ i k ⎦ j ⎣ i k ⎦
*d!ijk !3*+(!2&3!D27/!36()3D6)36+(!2&3!'*+4)()*+3!`NaA!`$a!&(!`HHa;!
∑∑∑ ∑∑∑ ! ! ! ! `H"a!
@&3!37>:&+()*+3!'9*)3B&3!3*+(!6((9)>7B&3!67!379'*8(!47!3&9:)'&!7+):&93&2!
&(! 2&3! >79&67/! 4)3(9)>7(&793! 37>:&+()*++B3! 3*+(! 37119)0B3;! M&((&! 37119&33)*+!
! "\h!