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I'm working on a decomposition model using column generation. When generate a new column, I'd like to check it's reduced cost using CPLEX function. I did read a post here, however the sign of the reduced cost obtain by this method is always negative (in my case), since the new columns are stated as nonbasis (according to the accepted answer).

Edit 1: So the purpose of checking these values is that I have trouble running my code. My master problem is to maximize an objective function. The pricing problems keep generating new column with positive reduce cost, however, after added new columns to the master and reoptimize, the objective function didn't improve at all, and this cycle keep going on for 30 minutes. So I decide to look into each detail to see what is the problem.

Nguyen Quang Anh
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  • That may well be correct. Note that adding a column does not change the size of the basis. So making this column non-basic seems the right thing to do. If minimizing, this negative reduced cost will make the new column a candidate to enter the basis in the next simplex iteration. You may want to state more carefully why you think that is wrong and what you did expect. – Erwin Kalvelagen Aug 19 '21 at 05:34
  • @ErwinKalvelagen I've updated my question. I hope it is more clear now. – Nguyen Quang Anh Aug 19 '21 at 05:42
  • It may be easier to make the master a minimization problem so you can use more standard sign conventions. – Erwin Kalvelagen Aug 19 '21 at 05:53

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