Re: [Help-glpk] [Fwd: Either...or logic]

[Alexandre Saidi]

Hi,
If a boolean tells you either you must have 
sum{i in S} x[i] = N or  sum{i in S} x[i] = 0 

like in :

X =1 --> sum{i in S} x[i] = N

then you can use the transformation of an "implication" into GLPK (by the 
so-called Big-M method OR Convex  Hull).
Many GLPK (Andrew too) users don't like Big-M method.

regards

Alex



Le 19 juin 2013 à 13:27, Andrew Makhorin a écrit :

> -------- Forwarded Message --------
> From: Alan Zinober <address@hidden>
> To: address@hidden
> Subject: Either...or logic
> Date: Wed, 19 Jun 2013 09:54:28 +0100
> 
> 
> Suppose
> 
> set S;   #  eg S = {1,3,4,6,8}
> 
> N = card(S);
> 
> var x{i in S} binary;   # x = 1 if the item i is active   ;     x = 0 if
> no items are included
> 
> 
> 
> I have a logical constraint having the form:
> 
> either
> sum{i in S} x[i] = N
> 
> or
> 
>    sum{i in S} x[i] = 0 
> 
> 
> In words either all the items x[i] are included or none are.
> 
> This will be repeated many times in my model. What is the optimal manner of 
> implementing this in the model?
> 
>   Alan
> -- 
> Sent from my MacBook Pro 
> 
> 
> 
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 -------------------------------
Alexandre Saidi
Maitre de Conférences
Ecole Centrale de Lyon-Dép. MI
LIRIS-CNRS UMR 5205
Tél : 0472186530, Fax : 0472186443