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Re[2]: [Help-glpk] Variables with different cardinalities

From: Andrew Makhorin
Subject: Re[2]: [Help-glpk] Variables with different cardinalities
Date: Tue, 18 Jan 2005 11:35:40 +0300

> It sounds like you must be using a MIP, since variables have a finite
> number of possible values.  All you need to do is declare a variable to 
> be integer and give appropriate lower and upper bounds.  This will limit 
> the values it can take.  It is perfectly fine to have variables with 
> different bounds.
> I think something like the following would work, thought I didn't test 
> it myself:
> var One >=0, <= 3, integer;
> var Two >=0, <= 2, integer;

To model a discrete variable which takes its values on an arbitrary
finite domain { a[1], a[2], ..., a[n] } the following standard technique
may be used:

var x;
var z{1..n}, binary; /* auxiliary decision variables */
s.t. sum{j in 1..n} z[j] = 1;
s.t. x = sum{j in 1..n} a[j] * z[j];

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