[Scip] why the optimal solution has varaible with negative reduced cost

[lixiangyong at 163.com]

Dear Ambros:

Attached please find the attach node lp.
The optimal solution has non basic variable z_7_6 =1 with reduced cost  -0.008333. It is strange!!     
Actually for my model, there several variables with negative reduced cost.

Thanks,


Xiangyong


 
From: Ambros Gleixner
Date: 2014-08-12 15:45
To: scip
Subject: Re: [Scip] why the optimal solution has varaible with negative reduced cost
Dear Xiangyong,
 
Are the reduced costs very negative or only slightly?  They are allowed 
to be negative up to minus the value given by the parameter 
numerics/dualfeastol, i.e., -1e-7 by default (in SCIP 3.1).
 
This is because standard floating-point LP solvers can in general not 
guarantee exact (primal and dual) feasibility.
 
Kind regards,
Ambros
 
 
Am 12.08.2014 02:14, schrieb lixiangyong at 163.com:
> Dear all,
>
>
> I am using SCIP with cplex to implement the branch and price for
> minimization problem.
>
> I found after several columns were added at each round,  the resulting
> model has an optimal solution of which some variables have negative
> reduced cost (min problem).
>
> Thanks,
>
> Xiangyong
>
>
> _______________________________________________
> Scip mailing list
> Scip at zib.de
> http://listserv.zib.de/mailman/listinfo/scip
>
 
-- 
____________________________________________________________
Ambros M. Gleixner
Zuse Institute Berlin - Matheon - Berlin Mathematical School
http://www.zib.de/gleixner
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