Re: Transladate problem from Octave to R
"Atwood, Joseph" <[email protected]> Tue, 2 Aug 2022 20:14:34 +0000
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Sebastian
The matrix arguments you are passing to the Rglpk_solve_LP function are not=
of conformable dimensions. (In addition, I don't think the Rglpk functio=
n will replicate the elements of argument dir =3D c("<=3D", "<=3D", "<=3D")=
to be of the appropriate dimension either. With R the script dir=3Dc("<=
=3D", "<=3D", "<=3D") will generate a vector of length of dimension 3)
From the code (and your email) the object c is of length 30, the matrix A i=
s a 21 by 30 matrix,
b is of length 50, the 'dir' vector will be of length 3, vlb is of length =
30, vub is of length 30
In addition, if used, the types argument must be a character string vector=
.
> str(ctype)
chr [1:21] "S" "S" "S" "S" "S" "S" "S" "S" "S" "S" "S" "U" "U" "U" "U" "U" =
"U" "U" "U" "U" "U"
ctype is a vector
> str(vartype)
chr [1:3, 1:10] "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C"=
"C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C"
The matrix 3x10 vartype can be converted to a vector using the command as.v=
ector(vartype) but will read the matrix in column-major-order.
In any case in the command:
Rglpk_solve_LP(obj =3D c, mat =3D A, dir =3D c("<=3D", "<=3D", "<=3D"), rhs=
=3D b)
the length of the c vector (30) must match the number of columns in the A m=
atrix (30), the length of the b vector i.e. (50) must match the number of r=
ows in the A matrix (21), and the length of the dir vector (3) must match t=
he number of rows in the A matrix (21).
This is why the error message:
Error in Rglpk_call(obj =3D obj, mat =3D mat, dir =3D dir, rhs =3D rhs, bou=
nds =3D bounds, :
Arguments 'mat', 'dir', and/or 'rhs' not conformable.
Joseph Atwood
208 Linfield Hall
Montana State University
Bozeman, MT 59717
406-994-5614
________________________________
From: Help-glpk <[email protected]> on behalf=
of Sebasti=E1n Kruk Gencarelli <[email protected]>
Sent: Tuesday, August 2, 2022 9:18 AM
To: [email protected] <[email protected]>
Subject: Transladate problem from Octave to R
**External Sender**
Dear glpk-users,
In Octave:
[z_opt,f_min,errnum,extra]=3Dglpk(c,A,b,vlb,vub,ctype,vartype,sense)
How can be transformed to use it in R?
If I use it:
Rglpk_solve_LP(obj =3D c, mat =3D A, dir =3D c("<=3D", "<=3D", "<=3D"), rhs=
=3D b)
Give me an error:
Error in Rglpk_call(obj =3D obj, mat =3D mat, dir =3D dir, rhs =3D rhs, bou=
nds =3D bounds, :
Arguments 'mat', 'dir', and/or 'rhs' not conformable.
Where:
> str(c)
num [1:30, 1] 0 0 0 0 0 0 0 0 0 0 ...
> str(A)
num [1:21, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
> str(b)
num [1:50, 1] 22 37 37 37 37 37 37 37 37 37 ...
> str(vlb)
num [1:30, 1] 0 0 0 0 0 0 0 0 0 0 ...
> str(vub)
num [1:30, 1] 150 150 150 150 150 150 150 150 150 150 ...
> str(ctype)
chr [1:21] "S" "S" "S" "S" "S" "S" "S" "S" "S" "S" "S" "U" "U" "U" "U" "U" =
"U" "U" "U" "U" "U"
> str(vartype)
chr [1:3, 1:10] "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C"=
"C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C" "C" "I" "C"
- attr(*, "dimnames")=3DList of 2
..$ : chr [1:3] "varcont" "varint" "varcont"
..$ : NULL
> str(sense)
num 1
My script in R is:
#1) Datos
#Per=EDodo de estudio (d=EDas)
T =3D 10
#Demanda diaria
dda =3D 37*matrix(1,T,1)
#Capacidad de cami=F3n (m3)
K=3D30
#Capacidad de tanque (m3)
cap_tqe=3D40
#Stock inicial (m3)
s0=3D15
#Max cantidad diaria de camiones
y_max=3D5
#Max volumen entrega diaria
x_max=3DK*y_max
#2) Modelo sin entrega los domingos
#Variables: z=3D[x; y; s], entega x(t), cant camiones y(t), stock final s(t=
)
c =3D matrix(rep(c(0,1,0),each =3D T)) #solo cuestan los viajes
vlb =3D matrix(rep(0,3*T))
vub =3D matrix(c(x_max*rep(1,T),y_max*rep(1,T), cap_tqe*rep(1,T)))
#
#Restricciones grupo1: balanceen cada t, s(t)=3Ds(t-1)+x(t)-dda(t)
A1=3Dmatrix(0,nrow=3DT,ncol=3D3*T)
A1[,1:T]=3Ddiag(1,dim(A1[,1:T]))
library(pracma)
A1[,(2*T+1):(3*T)]=3D-diag(1,T,T)+Diag(rep(1,T-1),-1)
b1 =3D dda
b1[1] =3D b1[1]-s0
#Restricciones grupo2: balanceen cada t, s(t)=3Ds(t-1)+x(t)-dda(t)
n7=3Dfloor(T/7)
A2=3Dmatrix(0,ncol=3D3*T,nrow=3Dn7)
b2=3Dmatrix(0,nrow=3D3*T,ncol=3D1)
ifelse(rem(col(A2),7)=3D=3D0,1,0)
#Restricciones grupo3: vol entregado menor y cant camiones, x(t)<K*y(t)
A3=3Dmatrix(0,nrow=3DT,ncol=3D3*T)
A3[,1:T]=3Ddiag(1,T)
A3[,(T+1):(2*T)]=3Ddiag(-K,T)
b3=3Dmatrix(0,nrow=3DT,ncol=3D1)
#
A =3D rbind(A1,A2,A3)
b =3D rbind(b1,b2,b3)
#Tipo de variables y restricciones
varint=3Drep("I",T)
varcont=3Drep("C",T)
ctype=3Drep("S",T)
vartype=3Drbind(varcont, varint, varcont)
ctype=3Dc(ctype, rep("S",n7))
ctype=3Dc(ctype, rep("U",T))
#
sense=3D1;
Thanks in advance!
See you!
Sebasti=E1n.
--_000_CY4PR0201MB3394CB4882758DE4D5F172FEBA9D9CY4PR0201MB3394_
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
<html>
<head>
<meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Diso-8859-=
1">
<style type=3D"text/css" style=3D"display:none;"> P {margin-top:0;margin-bo=
ttom:0;} </style>
</head>
<body dir=3D"ltr">
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
Sebastian</div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
The matrix arguments you are passing to the Rglpk_solve_LP function are not=
of conformable dimensions. (In addition, I don't think the Rgl=
pk function will replicate the elements of argument <span style=3D"col=
or:rgb(32,31,30); font-family:Calibri,sans-serif; font-size:14.6667px; back=
ground-color:rgb(255,255,255); display:inline!important">dir
=3D c("<=3D", "<=3D", "<=3D") to be=
of the appropriate dimension either. With R the script dir=3D<span s=
tyle=3D"background-color:rgb(255,255,255); display:inline!important">c(&quo=
t;<=3D", "<=3D", "<=3D") will generate a =
vector of length of dimension 3)</span></span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
>From the code (and your email) the
object c is of length 30, the matrix A is a 21 by 30 matrix, </span><=
/span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
b is of length 50, the 'dir' vector will be of length 3, vlb is of le=
ngth 30, vub is of length 30 </p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
<br>
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
In addition,<b> if used</b>, the types argument must be a character string&=
nbsp; vector. </p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
> str(ctype)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
chr [1:21] "S" "S" "S" "S" "S&=
quot; "S" "S" "S" "S" "S"=
"S" "U" "U" "U" "U" &quo=
t;U" "U" "U" "U" "U" "U&q=
uot;</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
ctype is a vector</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
<br>
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
> str(vartype)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;margin:0cm; font-=
size:11pt; background-color:rgb(255,255,255)">
chr [1:3, 1:10] "C" "I" "C" "C" &qu=
ot;I" "C" "C" "I" "C" "C&=
quot; "I" "C" "C" "I" "C"=
"C" "I" "C" "C" "I" &quo=
t;C" "C" "I" "C" "C" "I&q=
uot; "C" "C" "I" "C"</p>
<br>
</span></span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
>The matrix 3x10 vartype can be converted
to a vector using the command as.vector(vartype) but will read the matrix =
in column-major-order.</span></span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
><br>
</span></span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
>In any case in the command:</span></span></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<span style=3D"color:rgb(32,31,30); font-family:Calibri,sans-serif; font-si=
ze:14.6667px; background-color:rgb(255,255,255); display:inline!important">=
<span style=3D"background-color:rgb(255,255,255); display:inline!important"=
><span style=3D"color:rgb(0, 0, 0);background-color:rgb(255, 255, 255);disp=
lay:inline !important">Rglpk_solve_LP(obj
=3D c, mat =3D A, dir =3D c("<=3D", "<=3D", &quo=
t;<=3D"), rhs =3D b)</span><br>
</span></span></div>
<div class=3D"elementToProof" style=3D"color: rgb(0, 0, 0);"><font face=3D"=
Calibri, sans-serif"><span style=3D"font-size: 14.6667px;">the length of th=
e c vector (30) must match the number of columns in the A matrix (30), the =
length of the b vector i.e. (50) must match
the number of rows in the A matrix (21), and the length of the dir vector =
(3) must match the number of rows in the A matrix (21).</span></font></div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
This is why the error message:</div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<p class=3D"x_MsoNormal" style=3D"background-color:rgb(255, 255, 255);margi=
n:0cm;font-size:11pt;font-family:Calibri, sans-serif">
<span lang=3D"ES" style=3D"margin:0px"><br>
</span></p>
<p class=3D"x_MsoNormal" style=3D"background-color:rgb(255, 255, 255);margi=
n:0cm;font-size:11pt;font-family:Calibri, sans-serif">
<span lang=3D"ES" style=3D"margin:0px">Error in Rglpk_call(obj =3D obj, mat=
=3D mat, dir =3D dir, rhs =3D rhs, bounds =3D bounds, :</span></p>
<p class=3D"x_MsoNormal" style=3D"background-color:rgb(255, 255, 255);margi=
n:0cm;font-size:11pt;font-family:Calibri, sans-serif">
<span lang=3D"ES" style=3D"margin:0px"> Arguments 'mat', 'dir', =
and/or 'rhs' not conformable.</span></p>
<br>
</div>
<div class=3D"elementToProof" style=3D"font-family:Calibri,Arial,Helvetica,=
sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div>
<div id=3D"Signature">
<div>
<div style=3D"font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12p=
t; color:rgb(0,0,0)">
Joseph Atwood</div>
<div style=3D"font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12p=
t; color:rgb(0,0,0)">
208 Linfield Hall</div>
<div style=3D"font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12p=
t; color:rgb(0,0,0)">
Montana State University</div>
<div style=3D"font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12p=
t; color:rgb(0,0,0)">
Bozeman, MT 59717</div>
<div style=3D"font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12p=
t; color:rgb(0,0,0)">
406-994-5614</div>
</div>
</div>
</div>
<div id=3D"appendonsend"></div>
<hr tabindex=3D"-1" style=3D"display:inline-block; width:98%">
<div id=3D"divRplyFwdMsg" dir=3D"ltr"><font face=3D"Calibri, sans-serif" co=
lor=3D"#000000" style=3D"font-size:11pt"><b>From:</b> Help-glpk <help-gl=
[email protected]> on behalf of Sebasti=E1n Kruk =
Gencarelli <[email protected]><br>
<b>Sent:</b> Tuesday, August 2, 2022 9:18 AM<br>
<b>To:</b> [email protected] <[email protected]><br>
<b>Subject:</b> Transladate problem from Octave to R</font>
<div> </div>
</div>
<div lang=3D"ES-UY" style=3D"word-wrap:break-word">
<p style=3D"margin-top: 0px; margin-bottom: 0px;line-height:12pt; backgroun=
d-color:rgb(255,204,102); padding-top:1px; padding-bottom:1px">
<span style=3D"font-size:12pt; color:black"><strong>**External Sender**</st=
rong> </span>
</p>
<div>
<div class=3D"x_WordSection1">
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">Dear glpk-users,</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">In Octave:</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">[z_opt,f_min,errnum,extra]=3Dglpk(c,A,b,vlb,vub,ctype,var=
type,sense)</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">How can be transformed to use it in R?</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">If I use it:</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">Rglpk_solve_LP(obj =3D c, mat =3D A, dir =3D c("<=
=3D", "<=3D", "<=3D"), rhs =3D b)</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">Give me an error:</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">Error in Rglpk_call(obj =3D obj, mat =3D mat, dir =3D dir=
, rhs =3D rhs, bounds =3D bounds, :
</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> Arguments 'mat', 'dir', and/or 'rhs' not conf=
ormable.</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">Where:</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">> str(c)</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">num [1:30, 1] 0 0 0 0 0 0 0 0 0 0 ...</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">> str(A)</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES">num [1:21, 1:30] 1 0 0 0 0 0 0 0 0 0 ...</span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<span lang=3D"ES"> </span></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(b)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
num [1:50, 1] 22 37 37 37 37 37 37 37 37 37 ...</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(vlb)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
num [1:30, 1] 0 0 0 0 0 0 0 0 0 0 ...</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(vub)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
num [1:30, 1] 150 150 150 150 150 150 150 150 150 150 ...</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(ctype)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
chr [1:21] "S" "S" "S" "S" "S&=
quot; "S" "S" "S" "S" "S"=
"S" "U" "U" "U" "U" &quo=
t;U" "U" "U" "U" "U" "U&q=
uot;</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(vartype)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
chr [1:3, 1:10] "C" "I" "C" "C" &qu=
ot;I" "C" "C" "I" "C" "C&=
quot; "I" "C" "C" "I" "C"=
"C" "I" "C" "C" "I" &quo=
t;C" "C" "I" "C" "C" "I&q=
uot; "C" "C" "I" "C"</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
- attr(*, "dimnames")=3DList of 2</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
..$ : chr [1:3] "varcont" "varint" "varcont=
"</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
..$ : NULL</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
> str(sense)</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
num 1</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
My script in R is:</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#1) Datos</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Per=EDodo de estudio (d=EDas)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">T =3D 10</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Demanda diaria</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">dda =3D 37*matrix(1,T,1)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Capacidad de cami=F3n (m3)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">K=3D30</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Capacidad de tanque (m3)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">cap_tqe=3D40</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Stock inicial (m3)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">s0=3D15</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Max cantidad diaria de camiones</span></b></p=
>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">y_max=3D5</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Max volumen entrega diaria</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">x_max=3DK*y_max</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#2) Modelo sin entrega los domingos</span></b>=
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Variables: z=3D[x; y; s], entega x(t), cant c=
amiones y(t), stock final s(t)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">c =3D matrix(rep(c(0,1,0),each =3D T)) #solo c=
uestan los viajes</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">vlb =3D matrix(rep(0,3*T))</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">vub =3D matrix(c(x_max*rep(1,T),y_max*rep(1,T)=
, cap_tqe*rep(1,T)))</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Restricciones grupo1: balanceen cada t, =
s(t)=3Ds(t-1)+x(t)-dda(t)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A1=3Dmatrix(0,nrow=3DT,ncol=3D3*T)</span></b><=
/p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A1[,1:T]=3Ddiag(1,dim(A1[,1:T]))</span></b></p=
>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">library(pracma)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A1[,(2*T+1):(3*T)]=3D-diag(1,T,T)+Diag(rep(1,T=
-1),-1)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">b1 =3D dda</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">b1[1] =3D b1[1]-s0</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Restricciones grupo2: balanceen cada t, =
s(t)=3Ds(t-1)+x(t)-dda(t)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">n7=3Dfloor(T/7)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A2=3Dmatrix(0,ncol=3D3*T,nrow=3Dn7)</span></b>=
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">b2=3Dmatrix(0,nrow=3D3*T,ncol=3D1)</span></b><=
/p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">ifelse(rem(col(A2),7)=3D=3D0,1,0)</span></b></=
p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Restricciones grupo3: vol entregado menor y c=
ant camiones, x(t)<K*y(t)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A3=3Dmatrix(0,nrow=3DT,ncol=3D3*T)</span></b><=
/p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A3[,1:T]=3Ddiag(1,T)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A3[,(T+1):(2*T)]=3Ddiag(-K,T)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">b3=3Dmatrix(0,nrow=3DT,ncol=3D1)</span></b></p=
>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">A =3D rbind(A1,A2,A3)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">b =3D rbind(b1,b2,b3)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#Tipo de variables y restricciones</span></b><=
/p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">varint=3Drep("I",T)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">varcont=3Drep("C",T)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">ctype=3Drep("S",T)</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">vartype=3Drbind(varcont, varint, varcont)</spa=
n></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">ctype=3Dc(ctype, rep("S",n7))</span>=
</b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">ctype=3Dc(ctype, rep("U",T))</span><=
/b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red"> </span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">#</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
<b><span style=3D"color:red">sense=3D1;</span></b></p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
Thanks in advance!</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
See you!</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
Sebasti=E1n.</p>
<p class=3D"x_MsoNormal" style=3D"margin-top: 0px; margin-bottom: 0px;margi=
n: 0cm; font-size: 11pt; font-family: Calibri, sans-serif;">
</p>
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