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Re: [Help-glpk] Modeling SOS1

From: Andrew Makhorin
Subject: Re: [Help-glpk] Modeling SOS1
Date: Fri, 06 Jul 2012 15:57:58 +0400

> I would like to model an SOS1 constraints in GLPK . 
> In my case, {U, B} and {V, X} are SOS1 sets. U,B are non-negative
> variables and X is a boolean variable.

SOS1(x1, x2, ..., xn) means that at most one of the variables can be

If all the variables are binary, SOS1 is equivalent to

   x[1] + x[2] + ... + x[n] <= 1

If the variables are continuous, assuming that 0 <= x[j] <= u[j], where
u[j] is an upper bound of x[j], SOS1 can be modeled as follows:

   x[j] <= u[j] * z[j]  for j = 1,...,n,

   z[1] + ... + z[n] <= 1,

where z[j] are auxiliary binary variables.

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