<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<style type="text/css" style="display:none"><!--P{margin-top:0;margin-bottom:0;} .ms-cui-menu {background-color:#ffffff;border:1px rgb(171, 171, 171) solid;font-family:'Segoe UI WPC', 'Segoe UI', Tahoma, 'Microsoft Sans Serif', Verdana, sans-serif;font-size:11pt;color:rgb(51, 51, 51);} .ms-cui-menusection-title {display:none;} .ms-cui-ctl {vertical-align:text-top;text-decoration:none;color:rgb(51, 51, 51);} .ms-cui-ctl-on {background-color:rgb(223, 237, 250);opacity: 0.8;} .ms-cui-img-cont-float {display:inline-block;margin-top:2px} .ms-cui-smenu-inner {padding-top:0px;} .ms-owa-paste-option-icon {margin: 2px 4px 0px 4px;vertical-align:sub;padding-bottom: 2px;display:inline-block;} .ms-rtePasteFlyout-option:hover {background-color:rgb(223, 237, 250) !important;opacity:1 !important;} .ms-rtePasteFlyout-option {padding:8px 4px 8px 4px;outline:none;} .ms-cui-menusection {float:left; width:85px;height:24px;overflow:hidden}.wf {speak:none; font-weight:normal; font-variant:normal; text-transform:none; -webkit-font-smoothing:antialiased; vertical-align:middle; display:inline-block;}.wf-family-owa {font-family:'o365Icons'}@font-face { font-family:'o365IconsIE8'; src:url('prem/15.0.898.11/resources/styles/office365icons.ie8.eot?#iefix') format('embedded-opentype'), url('prem/15.0.898.11/resources/styles/office365icons.ie8.woff') format('woff'), url('prem/15.0.898.11/resources/styles/office365icons.ie8.ttf') format('truetype'); font-weight:normal; font-style:normal;}@font-face { font-family:'o365IconsMouse'; src:url('prem/15.0.898.11/resources/styles/office365icons.mouse.eot?#iefix') format('embedded-opentype'), url('prem/15.0.898.11/resources/styles/office365icons.mouse.woff') format('woff'), url('prem/15.0.898.11/resources/styles/office365icons.mouse.ttf') format('truetype'); font-weight:normal; font-style:normal;}.wf-family-owa {font-family:'o365IconsMouse'}.ie8 .wf-family-owa {font-family:'o365IconsIE8'}.ie8 .wf-owa-play-large:before {content:'\e254';}.notIE8 .wf-owa-play-large:before {content:'\e054';}.ie8 .wf-owa-play-large {color:#FFFFFF/*$WFWhiteColor*/;}.notIE8 .wf-owa-play-large {border-color:#FFFFFF/*$WFWhiteColor*/; width:1.4em; height:1.4em; border-width:.1em; border-style:solid; border-radius:.8em; text-align:center; box-sizing:border-box; -moz-box-sizing:border-box; padding:0.1em; color:#FFFFFF/*$WFWhiteColor*/;}.ie8 .wf-size-play-large {width:40px; height:40px; font-size:30px}.notIE8 .wf-size-play-large {width:40px; height:40px; font-size:30px}
<!--
p
{margin-top:0;
margin-bottom:0}
.ms-cui-menu
{background-color:#ffffff;
border:1px rgb(171,171,171) solid;
font-family:'Segoe UI WPC','Segoe UI',Tahoma,'Microsoft Sans Serif',Verdana,sans-serif;
font-size:11pt;
color:rgb(51,51,51)}
.ms-cui-ctl
{vertical-align:text-top;
text-decoration:none;
color:rgb(51,51,51)}
.ms-cui-ctl-on
{background-color:rgb(223,237,250)}
.ms-cui-img-cont-float
{display:inline-block;
margin-top:2px}
.ms-cui-smenu-inner
{padding-top:0px}
.ms-owa-paste-option-icon
{margin:2px 4px 0px 4px;
vertical-align:sub;
padding-bottom:2px;
display:inline-block}
.ms-rtePasteFlyout-option
{padding:8px 4px 8px 4px;
outline:none}
.ms-cui-menusection
{float:left;
width:85px;
height:24px;
overflow:hidden}
.wf
{speak:none;
font-weight:normal;
font-variant:normal;
text-transform:none;
vertical-align:middle;
display:inline-block}
.wf-family-owa
{font-family:'o365Icons'}
@font-face
{font-family:'o365IconsIE8';
font-weight:normal;
font-style:normal}
@font-face
{font-family:'o365IconsMouse';
font-weight:normal;
font-style:normal}
.wf-family-owa
{font-family:'o365IconsMouse'}
.ie8 .wf-family-owa
{font-family:'o365IconsIE8'}
.notIE8 .wf-owa-play-large
{border-color:#FFFFFF;
width:1.4em;
height:1.4em;
border-width:.1em;
border-style:solid;
text-align:center;
padding:0.1em;
color:#FFFFFF}
.ie8 .wf-size-play-large
{width:40px;
height:40px;
font-size:30px}
.notIE8 .wf-size-play-large
{width:40px;
height:40px;
font-size:30px}
-->
--></style>
</head>
<body>
<div style="font-size:12pt;color:#000000;background-color:#FFFFFF;font-family:Calibri,Arial,Helvetica,sans-serif;">
<p><span style="font-size: 12pt;">Dear Ambros, </span><br>
</p>
<div style="color: #282828;">
<div>
<div style="font-size: 12pt; color: #000000; background-color: #ffffff; font-family: calibri, arial, helvetica, sans-serif;">
<p><br>
</p>
<p>Thank you for your prompt reply. As you suggested, I am resending my previous email. <br>
</p>
<p><br>
</p>
<p>I am writing this email about the problem we have faced with SCIP. <br>
</p>
<p><span style="font-size: 12pt;">As Mahdi reported yesterday (please </span><span style="font-size: 12pt;">s</span><span style="font-size: 12pt;">ee his email </span><span style="font-size: 12pt;">b</span><span style="font-size: 12pt;">elow), we have checked
the </span><br>
</p>
<p>code several <span style="font-size: 12pt;">times, and even t</span><span style="font-size: 12pt;">rie</span><span style="font-size: 12pt;">d</span><span style="font-size: 12pt;"> to run its alternative formulation but the problem </span></p>
<p><span style="font-size: 12pt;"></span><span style="font-size: 12pt;">remains the </span><span style="font-size: 12pt;">same. I have also attached the output of three instances of the model. </span></p>
<p><span style="font-size: 12pt;">I hope </span><span style="font-size: 12pt;">this helps you to identify the problem. </span></p>
<p><span style="font-size: 12pt;"><br>
We use column generation procedure where continuous variables are added into the </span></p>
<p><span style="font-size: 12pt;">master problem and branch and bound procedure is used to solve the master problem. </span></p>
<p><span style="font-size: 12pt;">But after some iterations it cannot be improved. For example, as you will see from </span></p>
<p><span style="font-size: 12pt;">log file.rtf, we have the following output. </span></p>
<p><span style="font-size: 12pt;"><br>
</span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;">I am looking forward to receiving your reply and suggestions. </span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;"><br>
</span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;">Thank you for your help at advance. </span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;"><br>
</span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;">Best regards</span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;"><br>
</span></p>
<p style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;"><span style="font-size: 12pt;">Nalan </span></p>
<div style="font-family: calibri, arial, helvetica, sans-serif; font-size: 16px;">
<p><br>
</p>
<div style="font-family: tahoma; font-size: 13px;">_____________________________________________<br>
Nalan Gulpinar, Ph.D. <br>
Associate Professor of Operational Research<br>
Warwick Business School<br>
The University of Warwick, Coventry, CV4 7AL, UK.<br>
Tel: +44 (0) 24 7652 4491<br>
Fax: +44 (0) 24 7652 4539<br>
Email: Nalan.Gulpinar@wbs.ac.uk<br>
_____________________________________________<br>
</div>
</div>
<p><span style="font-size: 12pt;"><br>
</span></p>
<p><span style="color: #20124d; font-family: georgia, serif;">leastJ/leastT= 0,0, minRedCost: -43.3</span><span style="color: #20124d; font-family: georgia, serif;">117</span><span style="font-size: 12pt;"><br>
</span></p>
<div style="font-size: 16px; background-color: #ffffff; font-family: georgia, serif; color: #20124d;">
<p>total cost= 1173.06, 10.84, 882.22, 280, z_134</p>
<p>134, add new variables</p>
<p> 0.1s| 1 | 0 | 203 | - | 725k| 0 | 33 | 206 | 115 | 205 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap
</p>
<p> 0.1s| 1 | 0 | 205 | - | 725k| 0 | 36 | 206 | 115 | 206 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> </p>
<p> leastJ/leastT= 2,0, minRedCost: -90.6829</p>
<p>total cost= 532.45, 1.05, 363.4, 168, z_135</p>
<p>135, add new variables</p>
<p> 0.1s| 1 | 0 | 205 | - | 727k| 0 | 36 | 207 | 115 | 206 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> 0.1s| 1 | 0 | 205 | - | 727k| 0 | 23 | 207 | 115 | 207 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> </p>
<p> leastJ/leastT= 2,0, minRedCost: -90.6829</p>
<p>total cost= 532.45, 1.05, 363.4, 168, z_136</p>
<p>136, add new variables</p>
<p> 0.1s| 1 | 0 | 205 | - | 729k| 0 | 23 | 208 | 115 | 207 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> 0.1s| 1 | 0 | 209 | - | 729k| 0 | 23 | 208 | 115 | 208 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> </p>
<p> leastJ/leastT= 1,0, minRedCost: -88.4043</p>
<p>total cost= 350.84, 31.14, 151.7, 168, z_137</p>
<p>137, add new variables</p>
<p> 0.1s| 1 | 0 | 209 | - | 731k| 0 | 23 | 209 | 115 | 208 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> </p>
<p> leastJ/leastT= 1,0, minRedCost: -88.4043</p>
<p>total cost= 350.84, 31.14, 151.7, 168, z_138</p>
<p>138, add new variables</p>
<p> 0.1s| 1 | 0 | 209 | - | 733k| 0 | 23 | 210 | 115 | 208 | 115 | 0 | 0 | 0 | -- | 7.654555e+03 | Inf
</p>
<p> </p>
<p> leastJ/leastT= 1,0, minRedCost: -88.4043</p>
<p>total cost= 350.84, 31.14, 151.7, 168, z_139</p>
<p>139, add new variables<br>
</p>
<br>
This goes on......<br>
</div>
<div style="color: #282828;">
<div id="divRplyFwdMsg" dir="ltr">
<div> <br>
</div>
</div>
<div>
<div dir="ltr">
<div class="gmail_quote">
<div class="HOEnZb">
<div class="h5">
<div dir="ltr"><br>
<div class="gmail_quote">---------- Forwarded message ----------<br>
From: <b class="gmail_sendername">mahdi noorizadegan</b> <span dir="ltr"><<a href="mailto:m.noorizadegan@gmail.com" target="_blank">m.noorizadegan@gmail.com</a>></span><br>
Date: 31 March 2014 18:37<br>
Subject: Column generation<br>
To: <a href="mailto:Scip@zib.de" target="_blank">Scip@zib.de</a><br>
<div dir="ltr">
<div style="font-family: georgia, serif; color: #20124d;"><br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">Hi,<br>
<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">I have been trying to solve a problem by the column generation method.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">The variables which are being added to the master problem were binary<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">so I had the problem with the branch and bound procedure.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">I changed the formulation and added new dummy binary variables and changed<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">the type of the other variables to continuous.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">So there should not be any problem with the branch and bound producer.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">However, I still have problems. It keeps adding the same column after few iterations!<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">For example for a simple instance, the objective function value is 350.84,<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">the dual value is 439.24 therefore the reduced cost is -439.24+350.84=-88.40.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">When this new variable is added to the problem, in the next iteration this variable is again
<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">identified and added!<br>
<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">I have checked the pricing problem. It seems correct and I could not find any mistake.<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">I was wondering if you could help me and let me know what can be wrong!?<br>
<br>
</div>
<div style="font-family: georgia, serif; color: #20124d;">Thanks and best,<br>
Mahdi<br>
</div>
</div>
</div>
<br>
</div>
</div>
</div>
</div>
<br>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>