<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=us-ascii"><meta name=Generator content="Microsoft Word 12 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.E-MailFormatvorlage17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=DE link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>Hello everybody,<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>I have a problem with a piecewise linear function in Symphony (release 5.3.1). <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>In my C++-Code I'm using the following lines to build up a model of a piecewise linear function (only the part with the problem is shown here):<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //add the bounds of the variables<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[0]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[0]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[1]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[1]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[2]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[2]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[3]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[3]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[4]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[4]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable [0..1]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[5]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[5]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[6]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[7]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[8]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[8]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[9]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[9]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[10]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[10]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> // continuous variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_lb[11]=9.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> variable_ub[11]=9.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //add the bounds of the constraints<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[0]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[0]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[1]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[1]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[2]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[2]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[3]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[3]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[4]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[4]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[5]=-COIN_DBL_MAX;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[5]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_lb[8]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_ub[8]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //add the values of the constraints<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[0][0]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[6][0]=-1.0; //binary variable, the two dimensions describe the following: column 6; row 0<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[1][1]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[6][1]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[7][1]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[2][2]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[7][2]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[8][2]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[3][3]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[8][3]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[9][3]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[4][4]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[9][4]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[10][4]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[5][5]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[10][5]=-1.0; //binary variable<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[0][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[1][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[2][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[3][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[4][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[5][6]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> //only one binary variable can be chosen <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[6][7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[7][7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[8][7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[9][7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[10][7]=1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[11][8]=-1.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[0][8]=0.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[1][8]=10.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[2][8]=14.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[3][8]=18.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[4][8]=22.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> constraint_value[5][8]=50.0;<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>In this part a piecewise linear function is described and built.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>Normally, this code should work like this:<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>1.) Set the variable 11 to a value of [0..50]<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>2.) By using constraint 8 the variables 0 to 5 should describe the variable 11<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>The constraints 0-5 make sure that two neighbor continuous variables are selected because only one binary variable can have the value of 1.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>The building works very well except for some values. If I enter the value 9.4 for the variable 11, the optimization is infeasible. But, if you take other values like 9.9 or 9.0 that lie in the same interval everything works.<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>I really don't understand this failure. Can you please help me to find my mistake or to understand why Symphony has a problem with the value mentioned before?<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>This would be really great! Many thanks in advance!<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>Kind regards<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'>Aiko Vogelsang<o:p></o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p><p class=MsoNormal><span lang=EN-US style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></p></div></body></html>