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<div><span></span>Dear Ambros:</div><div><br></div><div>Attached please find the attach node lp.</div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;">The optimal solution has non basic variable z_7_6 =1 with reduced cost -0.008333. It is strange!! </span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;">Actually for my model, there several variables with negative reduced cost.</span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;"><br></span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;">Thanks,</span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;"><br></span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;"><br></span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;">Xiangyong</span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;"><br></span></div><div><span style="font-size: 12pt; line-height: 1.5; background-color: window;"><br></span></div>
<blockquote style="margin-top: 0px; margin-bottom: 0px; margin-left: 0.5em;"><div> </div><div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm"><div style="PADDING-RIGHT: 8px; PADDING-LEFT: 8px; FONT-SIZE: 12px;FONT-FAMILY:tahoma;COLOR:#000000; BACKGROUND: #efefef; PADDING-BOTTOM: 8px; PADDING-TOP: 8px"><div><b>From:</b> <a href="mailto:gleixner@zib.de">Ambros Gleixner</a></div><div><b>Date:</b> 2014-08-12 15:45</div><div><b>To:</b> <a href="mailto:scip@zib.de">scip</a></div><div><b>Subject:</b> Re: [Scip] why the optimal solution has varaible with negative reduced cost</div></div></div><div><div>Dear Xiangyong,</div>
<div> </div>
<div>Are the reduced costs very negative or only slightly? They are allowed </div>
<div>to be negative up to minus the value given by the parameter </div>
<div>numerics/dualfeastol, i.e., -1e-7 by default (in SCIP 3.1).</div>
<div> </div>
<div>This is because standard floating-point LP solvers can in general not </div>
<div>guarantee exact (primal and dual) feasibility.</div>
<div> </div>
<div>Kind regards,</div>
<div>Ambros</div>
<div> </div>
<div> </div>
<div>Am 12.08.2014 02:14, schrieb lixiangyong@163.com:</div>
<div>> Dear all,</div>
<div>></div>
<div>></div>
<div>> I am using SCIP with cplex to implement the branch and price for</div>
<div>> minimization problem.</div>
<div>></div>
<div>> I found after several columns were added at each round, the resulting</div>
<div>> model has an optimal solution of which some variables have negative</div>
<div>> reduced cost (min problem).</div>
<div>></div>
<div>> Thanks,</div>
<div>></div>
<div>> Xiangyong</div>
<div>></div>
<div>></div>
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<div> </div>
<div>-- </div>
<div>____________________________________________________________</div>
<div>Ambros M. Gleixner</div>
<div>Zuse Institute Berlin - Matheon - Berlin Mathematical School</div>
<div>http://www.zib.de/gleixner</div>
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