[Clp] Behavior of Clp when many variables are optimal simultaneously

[Arno Schödl]

Hello,

I am a practitioner, so please excuse any inaccuracies in my exposition.

I am repeatedly solving an LP problem, and after each run, want to eliminate those constraints that are limiting the current objective. As an example:

(0) a <= 15
(1) b-a <= 15

(2) a >= g
(3) b-a >= g
(4) 100-b >= g

maximize g

In this case, I would like to identify (2) and (3) as the two constraints that limit further growth of g. When I feed this into Clp, I get g==15 and dual[2]=1, identifying (2) as limiting, but dual[3]=0, although the problem seems entirely symmetrical to me. Interestingly, if (0) and (1) are not limiting, for example by setting their bound to 100, I get dual[2]=dual[3]=dual[4]=.333

My understanding of the simplex is poor. Is there any way to get what I want, or is that beyond what the simplex can tell me in a single solve?

TIA,

Arno

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