Re: [Help-glpk] [Fwd: I: Modelling binary variable]

[Nigel Galloway]

Change N to create a larger array. I present test results for all
combinations when N is 3. I leave it to readers to convince themselves
that it works for all combinations for any given N.

/*
  Set Z to 1 if one and only one of an array of binary variables is 1.

  address@hidden
  October 7th., 2013
*/

param N := 3;
var x{n in 1..N} , binary;
var Q{n in 1..N} , binary;

st1 : sum{n in 1..N} x[n] = sum{n in 1..N} Q[n];
st2 {n in 1..N-1} : 0 <= Q[n] - Q[n+1];

st90 : x[1] = 1;
st91 : x[2] = 1;
st92 : x[3] = 1;
solve;

printf "x[1] = %d, x[2] = %d, x[3] = %d, and Z =
%d\n",x[1],x[2],x[3],Q[1] - Q[2];

end;

/*

Changing st90, st91 and st92 for the eight possible combinations
produces:

INTEGER OPTIMAL SOLUTION FOUND BY MIP PREPROCESSOR
Time used:   0.0 secs
Memory used: 0.1 Mb (104314 bytes)
x[1] = 1, x[2] = 1, x[3] = 1, and Z = 0
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (119549 bytes)
x[1] = 1, x[2] = 1, x[3] = 0, and Z = 0
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (119549 bytes)
x[1] = 1, x[2] = 0, x[3] = 1, and Z = 0
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (119549 bytes)
x[1] = 0, x[2] = 1, x[3] = 1, and Z = 0
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (119549 bytes)
x[1] = 0, x[2] = 1, x[3] = 0, and Z = 1
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND
Time used:   0.0 secs
Memory used: 0.1 Mb (119549 bytes)
x[1] = 1, x[2] = 0, x[3] = 0, and Z = 1
Model has been successfully processed

INTEGER OPTIMAL SOLUTION FOUND BY MIP PREPROCESSOR
Time used:   0.0 secs
Memory used: 0.1 Mb (104314 bytes)
x[1] = 0, x[2] = 0, x[3] = 0, and Z = 0
Model has been successfully processed
*/


-- 
  Nigel Galloway
  address@hidden

On Wed, Oct 2, 2013, at 11:41 AM, Andrew Makhorin wrote:
> -------- Forwarded Message --------
> From: Pietro Scionti <address@hidden>
> To: address@hidden <address@hidden>
> Subject: I: Modelling binary variable
> Date: Wed, 2 Oct 2013 17:52:19 +0200
> 
> Hi Andrew,
> 
> I sent this message to the list but I’ve never seen it appear in the
> digest or the online archives. Is the address changed since the last
> time I used it?
> 
> Thank you very much
> 
> Pietro
> 
>  
> 
> Da: Pietro Scionti 
> Inviato: lunedì 23 settembre 2013 10:50
> A: 'address@hidden'
> Oggetto: Modelling binary variable
> 
> 
>  
> 
> Hi everyone,
> 
> I need help to model this situation: I have a series of binary decision
> variables
> 
> var x{o in O, t in T, g in G}
> 
> and I want to introduce a new binary variable
> 
> var z{o in O, t in T}
> 
> which takes 1 if and only if
> 
> sum{g in G} x[o,t,g] = 1
> 
>  
> 
> I tried using a Big-M approach but it only covered one of the two
> implications.
> 
> Any suggestions?
> 
>  
> 
> Thanks,
> 
> Pietro
> 
> 
> 
> 
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