[SCIP] MILP how to make constraints numbers as a decision variable

[berthold at zib.de]

Dear David,

it is my understanding that this mailing list is intended for SCIP
specific questions rather than for general modelling discussions.

For such questions I would recommend or-exchange, the sci.op-research
google group or even a general platform like stackoverflow.

As a starter, you might want to search for indicator constraints and big-M
formulations.

Good luck,
Timo

> Hi,
>
>
>
> I am trying to build a MILP.
>
>
>
> I need to set the number of linear constraints in the model as a decision
> variable.
>
>
>
> For example:
>
>
>
> max 8* x1 + 6 * x2  - x3
>
> s.t.
>
>       constraint 1 : x1 + x2 <= 29
>
>       constraint 2 : x1 - x2 <= 5
>
>       constraint 3 : x2 + x3 <= 56
>
>
>
> I would like to make the all three constraints as candidates such that
>
>
>
> 1. the objective maximized.
>
> 2. At least one constraint must be active
>
> 3. How many of candidate constraints are active depends on the objective
> optimization value.
>
>
>
> I know this may have exponential complexity because for 3 candidates, I
> can
> have 2^3 = 8 combinations of constraints.
>
>
>
> Are there some ways to out all candidate in the model and solve it for one
> run to get the optimal solution and let the model decide which candidates
> should be active  /
>
>
>
> thanks
>
>
>
> David
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