[AMPL 1874] Modeling Non-Integer Discrete Variables in AMPL

[Suleyman Demirel]

Hello Everybody,

Does anyone know how to model non-integer discrete variables in AMPL?
For example, x takes values in the set {0, 0.1, 0.17, 0.29, 0.77,
1.02}.

For a well behaved discrete set, e.g. {0, 0.25, 0.50, 0.75, 1}, this
is easy by letting y=4x and setting y as an integer variable. For
other cases, I don't know if AMPL allows defining discrete variables
over a set.

I would appreciate if anyone lets me know a work-around.

Thanks.
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[Robert Fourer-2]

You could write

   var x in {0, 0.1, 0.17, 0.29, 0.77, 1.02};

and let AMPL convert to an integer program.  Or you could do the conversion
yourself:

   set Sx;              # possible values for x
   var x;
   var xv {Sx} binary;  # x = i iff xv[i] = 1

   subj to AtMostOneValueForX:
      sum {i in Sx} xv[i] = 1;

   subj to ConsistentValueForX:
      x = sum {i in Sx} i * xv[i];

Either way, you would then place x in other objective and/or constraint
expressions, and would use a solver that can handle binary (integer)
variables.

Bob Fourer
4er@...

> -----Original Message-----
> From: ampl@... [mailto:ampl@...] On Behalf Of
> Suleyman Demirel
> Sent: Wednesday, July 23, 2008 11:00 AM
> To: AMPL Modeling Language
> Subject: [AMPL 1874] Modeling Non-Integer Discrete Variables in AMPL
>
>
> Hello Everybody,
>
> Does anyone know how to model non-integer discrete variables in AMPL?
> For example, x takes values in the set {0, 0.1, 0.17, 0.29, 0.77,
> 1.02}.
>
> For a well behaved discrete set, e.g. {0, 0.25, 0.50, 0.75, 1}, this
> is easy by letting y=4x and setting y as an integer variable. For
> other cases, I don't know if AMPL allows defining discrete variables
> over a set.
>
> I would appreciate if anyone lets me know a work-around.
>
> Thanks.

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To post to this group, send email to ampl@...
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[Suleyman Demirel]

Thanks a lot!

On Wed, Jul 23, 2008 at 2:02 PM, Robert Fourer <4er@...> wrote:

You could write

  var x in {0, 0.1, 0.17, 0.29, 0.77, 1.02};

and let AMPL convert to an integer program.  Or you could do the conversion
yourself:

  set Sx;              # possible values for x
  var x;
  var xv {Sx} binary;  # x = i iff xv[i] = 1

  subj to AtMostOneValueForX:
     sum {i in Sx} xv[i] = 1;

  subj to ConsistentValueForX:
     x = sum {i in Sx} i * xv[i];

Either way, you would then place x in other objective and/or constraint
expressions, and would use a solver that can handle binary (integer)
variables.

Bob Fourer
4er@...

> -----Original Message-----
> From: ampl@... [mailto:ampl@...] On Behalf Of
> Suleyman Demirel
> Sent: Wednesday, July 23, 2008 11:00 AM
> To: AMPL Modeling Language
> Subject: [AMPL 1874] Modeling Non-Integer Discrete Variables in AMPL
>
>
> Hello Everybody,
>
> Does anyone know how to model non-integer discrete variables in AMPL?
> For example, x takes values in the set {0, 0.1, 0.17, 0.29, 0.77,
> 1.02}.
>
> For a well behaved discrete set, e.g. {0, 0.25, 0.50, 0.75, 1}, this
> is easy by letting y=4x and setting y as an integer variable. For
> other cases, I don't know if AMPL allows defining discrete variables
> over a set.
>
> I would appreciate if anyone lets me know a work-around.
>
> Thanks.

--
______________________________________________
Suleyman Demirel - Office: [phone]

PhD Candidate in Operations Management
Stephen M. Ross School of Business
University of Michigan, Ann Arbor
Web: http://www.umich.edu/~sdemirel
______________________________________________

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