Problem with transfering a constraint into GAMS language

GAMS
1

Dear all,
I have a problem with tranfering a constraint of my optimization problem into GAMS language. It is part of a kind of a Job-Shop Scheduling Problem. Maybe you can help me?

I want to manipulate the index t of the paramter e(ijt) and subtract (ts(ij)+1) from t. ts(ij) and x(ijkt) are variables, e_strich is a parameter.



In GAMS this looks like this, but it seems as if it doesn’t work like this. Any ideas?



E_Mittel(t) =e= sum( (i,j,k) , e(i,j,t-ts(i,j)+1 )* x(i,j,k,t) ) - e_strich;



Second problem with this constraint is, that e(i,j,t-ts(ij)+1)*x(i,j,k,t) should be only summed up if the value of t is between the variables ts(ij) [t_start] and te(ij) [t_end].



In GAMS it looks like this, but GAMS doesn’t like variables in the -operator. Again: Any ideas? \ \ \ E_Mittel(t) =e= sum( (i,j,k) , (e(i,j,t-ts(i,j)+1 )* x(i,j,k,t)(ord(t)>=ts(i,j) and ord(t)<=te(i,j) ) ) - e_strich;



So I would like to know whether there is a simple solution for my problems or wheter I have to change my contraint completely.



Many thanks in advance and kind regards

Christian

–
To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/DVkCZwNxwcAJ.
To post to this group, send email to gamsworld@googlegroups.com.
To unsubscribe from this group, send email to gamsworld+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/gamsworld?hl=en.

2

Hi Christian

It looks like you don’t want to sum over the whole 3-dimensional space of I,j,k.

What I often do is define a parameter over i,j and k that is 1 if one should use this combination of I,j,k in the summation and otherwise zero.
This makes it easier to check, which elements will be used or not.

Say, in a 2-dimensional setting, you want to sum over the combinations that look like this
ixj matrix
1 2
1 1 0
2 1 1
3 1 1
4 0 1


The code would like this
set i /14/,
j /13/;
parameter summittel(i,j);

  • I first initialize all elements to 1
    Summittel(i,j) = 1;
  • Then I change all the values in the rows that should be zero
    Summittel(i,j)$(ord(i) lt ord(j)) = 0;
  • The same for the columns
    Summittel(i,j)$(ord(i) gt ord(j) +2) = 0;

display summittel

For your problem the $-statements would look a little bit nastier, but this should finally work and lets you check easily, if you are summing over the right elements.

Good luck!

Renger

\

Modelworks
Gewerbestrasse 15
3600 Thun - Switzerland
+41 79 818 53 73
Info@modelworks.ch
blog.modelworks.ch




From: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] On Behalf Of scboening@gmail.com
Sent: Mittwoch, 23. Januar 2013 11:21
To: gamsworld@googlegroups.com
Subject: Problem with transfering a constraint into GAMS language

Dear all,
I have a problem with tranfering a constraint of my optimization problem into GAMS language. It is part of a kind of a Job-Shop Scheduling Problem. Maybe you can help me?


I want to manipulate the index t of the paramter e(ijt) and subtract (ts(ij)+1) from t. ts(ij) and x(ijkt) are variables, e_strich is a parameter.

In GAMS this looks like this, but it seems as if it doesn’t work like this. Any ideas?

E_Mittel(t) =e= sum( (i,j,k) , e(i,j,t-ts(i,j)+1 )* x(i,j,k,t) ) - e_strich;

Second problem with this constraint is, that e(i,j,t-ts(ij)+1)*x(i,j,k,t) should be only summed up if the value of t is between the variables ts(ij) [t_start] and te(ij) [t_end].

In GAMS it looks like this, but GAMS doesn’t like variables in the $-operator. Again: Any ideas?

E_Mittel(t) =e= sum( (i,j,k) , (e(i,j,t-ts(i,j)+1 )* x(i,j,k,t)$(ord(t)>=ts(i,j) and ord(t)<=te(i,j) ) ) - e_strich;

So I would like to know whether there is a simple solution for my problems or wheter I have to change my contraint completely.

Many thanks in advance and kind regards
Christian

3

Hi Renger,
many thanks for your quick response.


I’m not quite sure whether this could help me.
Perhaps I haven’t described my problem very well.


I noticed you are sitting in Switzerland.
Is it possible to continue our conversation in german?

Greetings
Christian (From Germany :slight_smile:)



\

To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/KbJlKocQ0UgJ.
To post to this group, send email to gamsworld@googlegroups.com.
To unsubscribe from this group, send email to gamsworld+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/gamsworld?hl=en.

4

Selbstverständlich, Holländisch ware auch ok J. Du kannst mich auch direkt anmailen.

Renger



Von: gamsworld@googlegroups.com [mailto:gamsworld@googlegroups.com] Im Auftrag von scboening@gmail.com
Gesendet: Donnerstag, 24. Januar 2013 10:51
An: gamsworld@googlegroups.com
Betreff: Re: Problem with transfering a constraint into GAMS language



Hi Renger,

many thanks for your quick response.



I’m not quite sure whether this could help me.

Perhaps I haven’t described my problem very well.



I noticed you are sitting in Switzerland.

Is it possible to continue our conversation in german?



Greetings

Christian (From Germany :slight_smile:)




\

To view this discussion on the web visit https://groups.google.com/d/msg/gamsworld/-/KbJlKocQ0UgJ.
To post to this group, send email to gamsworld@googlegroups.com.
To unsubscribe from this group, send email to gamsworld+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/gamsworld?hl=en.

–
To post to this group, send email to gamsworld@googlegroups.com.
To unsubscribe from this group, send email to gamsworld+unsubscribe@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/gamsworld?hl=en.