Predecessor/Sucessor

[Archiver]

Hello,

I'm new to GAMS (although not new to MIP programming) and hope I can
find help for a problem a currently have.

I have variables with two indices, e.g. x(d,h), where d and h are sets
of days and hours.

My problem is to make a predecessor/sucessor relation between those x
variables. E.g. I have to model the difference between two neighboring
x variables like:

delta(d,h) =e= x(d,h) - x(pred(d,h)) ;

delta(d,) =l= constant ;

Are there any ideas how to make this in an easy and elegant way?

Regards,
Daniel
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[Archiver]

Daniel,

The GAMS lingo for this is lag and lead operators: x(d,h-1) e.g. shows
the previous hour. The '-' is not a numercial minus but a lag. Trouble
is that the predecessor for x(d,'h1') is x(d-1,'h24'). You also have
to decide what predecessor of 'd1','h1' is. If you do a steady state
model you could have 'd365','h24' or you can decide that there is no
predecessor (meaning delta('d1','h1') = x('d1','h1)). I am assuming
your sets look like this

set d / d1*d365 /
h / h1*h24 /

Now here is what you can do:

delta(d,h) =e= x(d,h) - x(d-(1$sameas('h1')),h--1)) ;

Not so elegant, but it will work. I prefer working with an additional
set of all hours in the year:
and a map between d,h and all hours in the year:

sets h /h1*h24/, d /d1*d365/, dh(d,h) /#d.#h/
sets t /t1*t8760/, tdh(t,d,h) /#t:#dh/, dht/#dh:#t/

This matching operators (. and are new syntax and will work with
22.7 and higher. You can do the maps also with older GAMS statements.
Now I would have the variable x and delta over t and then the
constraint looks simple:

delta(t) =e= x(t) - x(t-1) (or x(t--1) for steady state)

In case you have data by d,h you can use the map tdh, for example:

delta(t) =l= sum(tdh(t,d,h), maxdeviation(d,h));

Hope this helps,
Michael Bussieck, GAMSWorld Admin




On Jul 18, 4:24 am, Daniel wrote:
> > Hello,
> >
> > I'm new to GAMS (although not new to MIP programming) and hope I can
> > find help for a problem a currently have.
> >
> > I have variables with two indices, e.g. x(d,h), where d and h are sets
> > of days and hours.
> >
> > My problem is to make a predecessor/sucessor relation between those x
> > variables. E.g. I have to model the difference between two neighboring
> > x variables like:
> >
> > delta(d,h) =e= x(d,h) - x(pred(d,h)) ;
> >
> > delta(d,) =l= constant ;
> >
> > Are there any ideas how to make this in an easy and elegant way?
> >
> > Regards,
> > Daniel
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[Archiver]

Hello,

Thanks for you help. Very nice solution, but I was a little bit short
sighted and therefor I need a little more help.

I have data that is given with respect to sets d and h and my
variables are indexed by d and h, too. I need this because I have
constraints like this

con1(d,h).. xdmin =l= sum(d, x(d,h) ) ;
con2(d,h).. xdmax =g= sum(d, x(d,h) ) ;

on the other hand I also have the already mentionend constraints like,
where the lag/lead operators are needed.

con3a(t).. x(t) =e= x(t-1) + delta_i(t) - delta_d(t) ;
con3b(t).. deltamax =g= delta_i(t) + delta_d(t) ;

Is there a way to use the sets tdt and dht (of the previous message)
to 'convert' the indices?

Regards,
Daniel

On 18 Jul., 11:16, Gamsworld Admin wrote:
> > Daniel,
> >
> > The GAMS lingo for this is lag and lead operators: x(d,h-1) e.g. shows
> > the previous hour. The '-' is not a numercial minus but a lag. Trouble
> > is that the predecessor for x(d,'h1') is x(d-1,'h24'). You also have
> > to decide what predecessor of 'd1','h1' is. If you do a steady state
> > model you could have 'd365','h24' or you can decide that there is no
> > predecessor (meaning delta('d1','h1') = x('d1','h1)). I am assuming
> > your sets look like this
> >
> > set d / d1*d365 /
> > h / h1*h24 /
> >
> > Now here is what you can do:
> >
> > delta(d,h) =e= x(d,h) - x(d-(1$sameas('h1')),h--1)) ;
> >
> > Not so elegant, but it will work. I prefer working with an additional
> > set of all hours in the year:
> > and a map between d,h and all hours in the year:
> >
> > sets h /h1*h24/, d /d1*d365/, dh(d,h) /#d.#h/
> > sets t /t1*t8760/, tdh(t,d,h) /#t:#dh/, dht/#dh:#t/
> >
> > This matching operators (. and are new syntax and will work with
> > 22.7 and higher. You can do the maps also with older GAMS statements.
> > Now I would have the variable x and delta over t and then the
> > constraint looks simple:
> >
> > delta(t) =e= x(t) - x(t-1) (or x(t--1) for steady state)
> >
> > In case you have data by d,h you can use the map tdh, for example:
> >
> > delta(t) =l= sum(tdh(t,d,h), maxdeviation(d,h));
> >
> > Hope this helps,
> > Michael Bussieck, GAMSWorld Admin
> >
> > On Jul 18, 4:24 am, Daniel wrote:
> >
>> > > Hello,
> >
>> > > I'm new to GAMS (although not new to MIP programming) and hope I can
>> > > find help for a problem a currently have.
> >
>> > > I have variables with two indices, e.g. x(d,h), where d and h are sets
>> > > of days and hours.
> >
>> > > My problem is to make a predecessor/sucessor relation between those x
>> > > variables. E.g. I have to model the difference between two neighboring
>> > > x variables like:
> >
>> > > delta(d,h) =e= x(d,h) - x(pred(d,h)) ;
> >
>> > > delta(d,) =l= constant ;
> >
>> > > Are there any ideas how to make this in an easy and elegant way?
> >
>> > > Regards,
>> > > Daniel
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[Archiver]

Daniel,

These statement would not compile (summation set d already controlled
on the equation index):

con1(d,h).. xdmin =l= sum(d, x(d,h) ) ;
con2(d,h).. xdmax =g= sum(d, x(d,h) ) ;

I guess you have

con1(h).. xdmin =l= sum(d, x(d,h) ) ;
con2(h).. xdmax =g= sum(d, x(d,h) ) ;

(don't know if this makes sense).

You have to select one domain for your variable x. You used t and d,h.
I think you can savely work with just t. Assuming that the change from
above makes sense, you can rewrite these as follows:

con1(h).. xdmin =l= sum(tdh(t,d,h), x(t) ) ;
con2(h).. xdmax =g= sum(tdh(t,d,h), x(d,h) ) ;

Hope this makes sense to you.

Regards,
Michael Bussieck, GAMSWorld Coordinator
On Jul 23, 9:24 am, Daniel Wagner wrote:
> > Hello,
> >
> > Thanks for you help. Very nice solution, but I was a little bit short
> > sighted and therefor I need a little more help.
> >
> > I have data that is given with respect to sets d and h and my
> > variables are indexed by d and h, too. I need this because I have
> > constraints like this
> >
> > con1(d,h).. xdmin =l= sum(d, x(d,h) ) ;
> > con2(d,h).. xdmax =g= sum(d, x(d,h) ) ;
> >
> > on the other hand I also have the already mentionend constraints like,
> > where the lag/lead operators are needed.
> >
> > con3a(t).. x(t) =e= x(t-1) + delta_i(t) - delta_d(t) ;
> > con3b(t).. deltamax =g= delta_i(t) + delta_d(t) ;
> >
> > Is there a way to use the sets tdt and dht (of the previous message)
> > to 'convert' the indices?
> >
> > Regards,
> > Daniel
> >
> > On 18 Jul., 11:16, Gamsworld Admin wrote:
> >
> >
> >
>> > > Daniel,
> >
>> > > The GAMS lingo for this is lag and lead operators: x(d,h-1) e.g. shows
>> > > the previous hour. The '-' is not a numercial minus but a lag. Trouble
>> > > is that the predecessor for x(d,'h1') is x(d-1,'h24'). You also have
>> > > to decide what predecessor of 'd1','h1' is. If you do a steady state
>> > > model you could have 'd365','h24' or you can decide that there is no
>> > > predecessor (meaning delta('d1','h1') = x('d1','h1)). I am assuming
>> > > your sets look like this
> >
>> > > set d / d1*d365 /
>> > > h / h1*h24 /
> >
>> > > Now here is what you can do:
> >
>> > > delta(d,h) =e= x(d,h) - x(d-(1$sameas('h1')),h--1)) ;
> >
>> > > Not so elegant, but it will work. I prefer working with an additional
>> > > set of all hours in the year:
>> > > and a map between d,h and all hours in the year:
> >
>> > > sets h /h1*h24/, d /d1*d365/, dh(d,h) /#d.#h/
>> > > sets t /t1*t8760/, tdh(t,d,h) /#t:#dh/, dht/#dh:#t/
> >
>> > > This matching operators (. and are new syntax and will work with
>> > > 22.7 and higher. You can do the maps also with older GAMS statements.
>> > > Now I would have the variable x and delta over t and then the
>> > > constraint looks simple:
> >
>> > > delta(t) =e= x(t) - x(t-1) (or x(t--1) for steady state)
> >
>> > > In case you have data by d,h you can use the map tdh, for example:
> >
>> > > delta(t) =l= sum(tdh(t,d,h), maxdeviation(d,h));
> >
>> > > Hope this helps,
>> > > Michael Bussieck, GAMSWorld Admin
> >
>> > > On Jul 18, 4:24 am, Daniel wrote:
> >
>>> > > > Hello,
> >
>>> > > > I'm new to GAMS (although not new to MIP programming) and hope I can
>>> > > > find help for a problem a currently have.
> >
>>> > > > I have variables with two indices, e.g. x(d,h), where d and h are sets
>>> > > > of days and hours.
> >
>>> > > > My problem is to make a predecessor/sucessor relation between those x
>>> > > > variables. E.g. I have to model the difference between two neighboring
>>> > > > x variables like:
> >
>>> > > > delta(d,h) =e= x(d,h) - x(pred(d,h)) ;
> >
>>> > > > delta(d,) =l= constant ;
> >
>>> > > > Are there any ideas how to make this in an easy and elegant way?
> >
>>> > > > Regards,
>>> > > > Daniel- Hide quoted text -
> >
> > - Show quoted text -
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[Archiver]

Hi, I'm affraid that I'm not who answer the message, there must be another Daniel at Gamsworld
Best regards

2008/7/25 Gamsworld Admin


Daniel,

These statement would not compile (summation set d already controlled
on the equation index):

con1(d,h).. xdmin =l= sum(d, x(d,h) ) ;
con2(d,h).. xdmax =g= sum(d, x(d,h) ) ;

I guess you have

con1(h).. xdmin =l= sum(d, x(d,h) ) ;
con2(h).. xdmax =g= sum(d, x(d,h) ) ;

(don't know if this makes sense).

You have to select one domain for your variable x. You used t and d,h.
I think you can savely work with just t. Assuming that the change from
above makes sense, you can rewrite these as follows:

con1(h).. xdmin =l= sum(tdh(t,d,h), x(t) ) ;
con2(h).. xdmax =g= sum(tdh(t,d,h), x(d,h) ) ;

Hope this makes sense to you.

Regards,
Michael Bussieck, GAMSWorld Coordinator
On Jul 23, 9:24 am, Daniel Wagner wrote:
> Hello,
>
> Thanks for you help. Very nice solution, but I was a little bit short
> sighted and therefor I need a little more help.
>
> I have data that is given with respect to sets d and h and my
> variables are indexed by d and h, too. I need this because I have
> constraints like this
>
> con1(d,h).. xdmin =l= sum(d, x(d,h) ) ;
> con2(d,h).. xdmax =g= sum(d, x(d,h) ) ;
>
> on the other hand I also have the already mentionend constraints like,
> where the lag/lead operators are needed.
>
> con3a(t).. x(t) =e= x(t-1) + delta_i(t) - delta_d(t) ;
> con3b(t).. deltamax =g= delta_i(t) + delta_d(t) ;
>
> Is there a way to use the sets tdt and dht (of the previous message)
> to 'convert' the indices?
>
> Regards,
> Daniel
>
> On 18 Jul., 11:16, Gamsworld Admin wrote:
>
>
>
> > Daniel,
>
> > The GAMS lingo for this is lag and lead operators: x(d,h-1) e.g. shows
> > the previous hour. The '-' is not a numercial minus but a lag. Trouble
> > is that the predecessor for x(d,'h1') is x(d-1,'h24'). You also have
> > to decide what predecessor of 'd1','h1' is. If you do a steady state
> > model you could have 'd365','h24' or you can decide that there is no
> > predecessor (meaning delta('d1','h1') = x('d1','h1)). I am assuming
> > your sets look like this
>
> > set d / d1*d365 /
> > h / h1*h24 /
>
> > Now here is what you can do:
>
> > delta(d,h) =e= x(d,h) - x(d-(1$sameas('h1')),h--1)) ;
>
> > Not so elegant, but it will work. I prefer working with an additional
> > set of all hours in the year:
> > and a map between d,h and all hours in the year:
>
> > sets h /h1*h24/, d /d1*d365/, dh(d,h) /#d.#h/
> > sets t /t1*t8760/, tdh(t,d,h) /#t:#dh/, dht/#dh:#t/
>
> > This matching operators (. and are new syntax and will work with
> > 22.7 and higher. You can do the maps also with older GAMS statements.
> > Now I would have the variable x and delta over t and then the
> > constraint looks simple:
>
> > delta(t) =e= x(t) - x(t-1) (or x(t--1) for steady state)
>
> > In case you have data by d,h you can use the map tdh, for example:
>
> > delta(t) =l= sum(tdh(t,d,h), maxdeviation(d,h));
>
> > Hope this helps,
> > Michael Bussieck, GAMSWorld Admin
>
> > On Jul 18, 4:24 am, Daniel wrote:
>
> > > Hello,
>
> > > I'm new to GAMS (although not new to MIP programming) and hope I can
> > > find help for a problem a currently have.
>
> > > I have variables with two indices, e.g. x(d,h), where d and h are sets
> > > of days and hours.
>
> > > My problem is to make a predecessor/sucessor relation between those x
> > > variables. E.g. I have to model the difference between two neighboring
> > > x variables like:
>
> > > delta(d,h) =e= x(d,h) - x(pred(d,h)) ;
>
> > > delta(d,) =l= constant ;
>
> > > Are there any ideas how to make this in an easy and elegant way?
>
> > > Regards,
> > > Daniel- Hide quoted text -
>
> - Show quoted text -




--
Daniel Andrés Navia López
Mg.Sc.(c) Ciencias de la Ingeniería Mención Ingeniería Química
89674421

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