<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:st1="urn:schemas-microsoft-com:office:smarttags" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<!--[if !mso]>
<style>
v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style>
<![endif]--><o:SmartTagType
namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="PersonName"/>
<!--[if !mso]>
<style>
st1\:*{behavior:url(#default#ieooui) }
</style>
<![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:Wingdings;
panose-1:5 0 0 0 0 0 0 0 0 0;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Verdana;
panose-1:2 11 6 4 3 5 4 4 2 4;}
@font-face
{font-family:Webdings;
panose-1:5 3 1 2 1 5 9 6 7 3;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
span.EstiloCorreo17
{mso-style-type:personal-compose;
font-family:Arial;
color:windowtext;}
@page Section1
{size:595.3pt 841.9pt;
margin:70.85pt 3.0cm 70.85pt 3.0cm;}
div.Section1
{page:Section1;}
/* List Definitions */
@list l0
{mso-list-id:1179613502;
mso-list-type:hybrid;
mso-list-template-ids:474126434 1469241744 201981955 201981957 201981953 201981955 201981957 201981953 201981955 201981957;}
@list l0:level1
{mso-level-number-format:bullet;
mso-level-text:\F0B7;
mso-level-tab-stop:18.0pt;
mso-level-number-position:left;
margin-left:18.0pt;
text-indent:-18.0pt;
font-family:Symbol;
color:windowtext;}
ol
{margin-bottom:0cm;}
ul
{margin-bottom:0cm;}
-->
</style>
</head>
<body lang=ES link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>We are using SYMPHONY’s version 5.1.8, for
solving a MIP problem with warm start, and we have found the following problem:<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt;text-indent:-18.0pt;mso-list:l0 level1 lfo1'><![if !supportLists]><font
size=2 face=Symbol><span lang=EN-GB style='font-size:10.0pt;font-family:Symbol'><span
style='mso-list:Ignore'>·<font size=1 face="Times New Roman"><span
style='font:7.0pt "Times New Roman"'>
</span></font></span></span></font><![endif]><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>We do a first solving
keeping warm-start information and once a feasible solution is found, we modify
the objective function and call sym_warm_solve with a certain Gap_limit>=0.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>If we set a Gap_limit>0
the call to sym_warm_solve returns immediately with the message of “Optimal
solution found” and the same initial solution without further optimization.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>If we run the same case with
Gap_Limit= -1 the solver iterates several times with gaps in each iteration
much greater than the Gap_limit parameter.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>I have traced the problem
comparing execution with and without Gap_limit and everything is the same up to
the first call to function “shall_we_dive” were the tm->ub=1e7
and the tm->lb=infinity.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>At the beginning of the
function the call to find_tree_lb(tm) makes tm->lb=tm->ub.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>Having ub and lb equal
and Gap_limit>=0 makes always the function return the value DO_NOT_DIVE and
stopping the optimization, does not matter with value of Gap_limit you use.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>If Gap_limit=-1 the
function returns CHECK_BEFORE_DIVE and optimization continues.<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I have also tested the last version 5.1.10 and the
same problem appears.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>The only way I have found of solving the problem is
modifying the function “shall_we_dive” included in the file “tm_func.c”
of the TreeManager directory.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I include adjoin the modification proposed marked
with ‘>>>’.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-indent:35.4pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>________________________________________________________<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>char
shall_we_dive(tm_prob *tm, double objval)<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>{<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> char dive;<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> int i, k;<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> double
rand_num, average_lb;<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> double cutoff
= 0;<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>
find_tree_lb(tm);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> if
(tm->par.time_limit >= 0.0 &&<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> wall_clock(NULL)
- tm->start_time >= tm->par.time_limit){<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> return(FALSE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> }<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> if
(tm->par.node_limit >= 0 && tm->stat.analyzed >=
tm->par.node_limit){<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> return(FALSE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> }<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> <o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> if
(tm->has_ub && (tm->par.gap_limit >= 0.0)){<o:p></o:p></span></font></p>
<p class=MsoNormal><b><font size=2 face="Courier New"><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New";font-weight:bold'>>>> </span></font></b><font
size=2 face="Courier New"><span lang=EN-GB style='font-size:10.0pt;font-family:
"Courier New"'> <b><span style='font-weight:bold'>if
(tm->ub>tm->lb) {// PVJ 13/04/2009<o:p></o:p></span></b></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> if
(100*(tm->ub-tm->lb)/tm->ub <= tm->par.gap_limit){<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> return(FALSE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> }<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Courier New"><span lang=EN-GB
style='font-size:10.0pt;font-family:"Courier New"'>>>> <b><span
style='font-weight:bold'>}<o:p></o:p></span></b></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'> }<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'>_______________________________________________________________<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:18.0pt'><font size=2 face=Arial><span
lang=EN-GB style='font-size:10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>I also included detail of the calling program.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>int error_user =
sym_explicit_load_problem(env, n_cols, n_rows, start, index, value, col_lb, <o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>
col_ub, int_vars, objective1, NULL, row_sense, <o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>
row_rhs, row_range, TRUE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_str_param(env,"gap_limit",gap_limit);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,
"keep_warm_start", TRUE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,
"find_first_feasible", TRUE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,
"node_selection_strategy", DEPTH_FIRST_SEARCH);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>int cp_num;<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>int ncutpools =
sym_create_permanent_cut_pools(env, &cp_num);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>int rvalue =
sym_solve(env);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>ws =
sym_get_warm_start(env,true);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,
"node_selection_strategy", LOWEST_LP_FIRST);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,"do_reduced_cost_fixing",FALSE);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>sym_set_int_param(env,
"find_first_feasible", FALSE); <o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>rvalue =
sym_set_int_param(env, "node_limit", -1);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>for (int i=0;
i<n_cols; i++){<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>
sym_set_obj_coeff(env, i, objective2[i]);<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>}<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-left:35.4pt'><font size=2 face="Courier New"><span
lang=EN-GB style='font-size:10.0pt;font-family:"Courier New"'>rvalue =
sym_warm_solve(env);<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Please if posible confirm if there is any other possible
way of avoiding the problem without modifying the code or if considered
adecuate include the correction in next version.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Please contact me for any further clarification.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Thanks for the help and the excelent work done in
the library.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-GB style='font-size:
10.0pt;font-family:Arial'>Best Regards.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span lang=EN-GB
style='font-size:12.0pt'><o:p> </o:p></span></font></p>
<table class=MsoNormalTable border=0 cellpadding=0 align=left width=2036
style='width:1527.0pt'>
<tr>
<td width=10 style='width:7.2pt;padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><font size=3
face="Times New Roman"><span lang=EN-GB style='font-size:12.0pt'><o:p> </o:p></span></font></p>
</td>
<td style='padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:9.0pt;font-family:Verdana;color:navy;
font-weight:bold'>Juan Prieto Vivanco</span></font></b><o:p></o:p></p>
</td>
</tr>
<tr>
<td width=10 style='width:7.2pt;padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'> <o:p></o:p></span></font></p>
</td>
<td style='padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span lang=EN-GB style='font-size:7.5pt;font-family:Verdana;
color:navy;font-weight:bold'>Forecast & Optimization Manager<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span lang=EN-GB style='font-size:7.5pt;font-family:Verdana;
color:navy;font-weight:bold'>Energy Technologies.<o:p></o:p></span></font></b></p>
</td>
</tr>
<tr height=20 style='height:15.0pt'>
<td width=2032 colspan=2 height=20 style='width:1524.0pt;padding:.75pt .75pt .75pt .75pt;
height:15.0pt'>
<p class=MsoNormal style='mso-element:frame'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'><img width=156
height=75 id="_x0000_i1025" src="cid:image001.jpg@01C9BF45.D69EF4C0"><font
color=navy><span style='color:navy'><o:p></o:p></span></font></span></font></p>
</td>
</tr>
<tr>
<td width=10 style='width:7.2pt;padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'> <o:p></o:p></span></font></p>
</td>
<td valign=top style='padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>Parque empresarial <st1:PersonName ProductID="La Finca"
w:st="on">La Finca</st1:PersonName>, Edificio 4<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>Avda de <st1:PersonName ProductID="La Finca" w:st="on">la
Finca</st1:PersonName> s/n<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>28223 Pozuelo de Alarcon<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>MADRID <o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>SPAIN<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>Tlf directo : 912 579 023<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>Móvil: 691 513 017<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:navy;
font-weight:bold'>Tlf centralita: 912 102 000 (ext: 49023).<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 color=navy
face=Verdana><span lang=FR style='font-size:7.5pt;font-family:Verdana;
color:navy;font-weight:bold'>Fax: 91 210 20 10<o:p></o:p></span></font></b></p>
<p class=MsoNormal style='mso-element:frame'><b><font size=1 face=Verdana><span
style='font-size:7.5pt;font-family:Verdana;font-weight:bold'><a
href="mailto:jprietov@indra.es" title="mailto:jprietov@indra.es"><span
lang=FR><span title="mailto:jprietov@indra.es">jprietov@indra.es</span></span></a></span></font></b><span
lang=FR><o:p></o:p></span></p>
<p class=MsoNormal style='mso-element:frame'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'><a
href="http://www.indra.es/" title="http://www.indra.es/"><strong><b><font
size=1 face=Verdana><span lang=FR style='font-size:7.5pt;font-family:Verdana;
text-decoration:none'><span title="http://www.indra.es/"><span
title="http://www.indra.es/">www.indra.es</span></span></span></font></b></strong></a></span></font><strong><b><font
color=navy face=Verdana><span lang=FR style='font-family:Verdana;color:navy'>
</span></font></b></strong><span lang=FR><o:p></o:p></span></p>
<p class=MsoNormal style='mso-element:frame'><strong><b><font size=6
color=green face=Webdings><span style='font-size:24.0pt;font-family:Webdings;
color:green'>P</span></font></b></strong><strong><b><font size=1 color=green
face=Verdana><span style='font-size:7.5pt;font-family:Verdana;color:green'> </span></font></b></strong><strong><b><font
size=1 color=green face=Tahoma><span style='font-size:7.5pt;font-family:Tahoma;
color:green'>Por favor, considere su responsabilidad medioambiental antes de
imprimir este e-mail</span></font></b></strong><strong><b><font color=navy
face=Verdana><span style='font-family:Verdana;color:navy'>
</span></font></b></strong><strong><b><font size=1 color=navy face=Verdana><span
style='font-size:7.5pt;font-family:Verdana;color:navy'><o:p></o:p></span></font></b></strong></p>
</td>
</tr>
</table>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
</body>
</html>