Equation index involved in loops

GAMS
1

Dear all,

I am trying to formulate a model that can add new constraints after each solution, but the GAMS seems to forbid solving model in which equations’ index are involved in loops. The example is shown in the follow, and it is just to show the idea and may not be feasible.

Sets
i / i1i100 /
j / j1j100 / ;

Positive variables
x(i,j)
y(i) ;

Variable
z ;

Equations
EQ1(i,j) Equation 1
EQ2(i) Equation 2
OBJ Objective ;

EQ1(i,j) … y(i) =l= 100 ;

EQ2 (i) … sum(j$(ord(j)=2*ord(i)), x(i,j)) + y(i) =g= 3000 ;

OBJ … z =e= 2*sum((i,j), x(i,j)) + sum(i, y(i)) ;

Model M1 / EQ1, EQ2, OBJ / ;

Solve M1 using LP minimizing z ;

Set
r / r1*r10 / ;

Parameters
a(i) ;

a(i) = 0 ;

Equations
EQ3(r,i) Equation 3 ;

EQ3(r,i)$a(i) … sum(j, x(i,j)) =l= 10000 ;


Model M2 / EQ1, EQ2, EQ3, OBJ / ;

loop(r,
loop(i,
loop(j,
if(x.l(i,j) >= 500,
a(i) = 1 ;
) ;
) ;
) ;
Solve M2 using LP minimizing z ;
) ;

–
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2

Hi Dylan


You almost have the solution. The only thing to do is introducing aliases, so you can loop without running into your problem



Here is the idea (it might not be exactly what you want, but the idea might help you to exactly do what you want)



Parameters

a(i) ,ar(r);



a(i) = 0 ;

ar(r) = 0;



Equations

EQ3(r,i) Equation 3 ;



EQ3(r,i)$(a(i) and ar(r))… sum(j, x(i,j)) =l= 10000 ;





Model M2 / EQ1, EQ2, EQ3, OBJ / ;



alias(i,ii),(j,jj),(r,rr);







loop(rr,

loop(ii,

a(i) = 0;

ar(r) = 0;

loop(jj,

if(x.l(ii,jj) >= 500,

a(i)$(ord(i) = ord(ii)) = 1 ;

ar(r)$(ord(rr) = ord(r)) = 1;

) ;

Solve M2 using LP minimizing z ;

);

) ;

) ;



Cheers

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 Dylan Lan
Sent: Thursday, October 16, 2014 4:15 AM
To: gamsworld@googlegroups.com
Subject: Equation index involved in loops



Dear all,



I am trying to formulate a model that can add new constraints after each solution, but the GAMS seems to forbid solving model in which equations’ index are involved in loops. The example is shown in the follow, and it is just to show the idea and may not be feasible.



Sets

i / i1*i100 /

j / j1*j100 / ;



Positive variables

x(i,j)

y(i) ;



Variable

z ;



Equations

EQ1(i,j) Equation 1

EQ2(i) Equation 2

OBJ Objective ;



EQ1(i,j) … y(i) =l= 100 ;



EQ2 (i) … sum(j$(ord(j)=2ord(i)), x(i,j)) + y(i) =g= 3000 ;



OBJ … z =e= 2sum((i,j), x(i,j)) + sum(i, y(i)) ;



Model M1 / EQ1, EQ2, OBJ / ;



Solve M1 using LP minimizing z ;



Set

r / r1*r10 / ;



Parameters

a(i) ;



a(i) = 0 ;



Equations

EQ3(r,i) Equation 3 ;



EQ3(r,i)$a(i) … sum(j, x(i,j)) =l= 10000 ;





Model M2 / EQ1, EQ2, EQ3, OBJ / ;



loop(r,

loop(i,

loop(j,

if(x.l(i,j) >= 500,

a(i) = 1 ;

) ;

) ;

) ;

Solve M2 using LP minimizing z ;

) ;

–
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–
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3

Hi Renger,

Thank you very much for your help, it really helps a lot.

Best regards,

Dylan

在 2014年10月16日星期四UTC+8下午2时18分54秒，Renger van Nieuwkoop写道：

Hi Dylan


You almost have the solution. The only thing to do is introducing aliases, so you can loop without running into your problem



Here is the idea (it might not be exactly what you want, but the idea might help you to exactly do what you want)



Parameters

a(i) ,ar(r);



a(i) = 0 ;

ar(r) = 0;



Equations

EQ3(r,i) Equation 3 ;



EQ3(r,i)$(a(i) and ar(r))… sum(j, x(i,j)) =l= 10000 ;





Model M2 / EQ1, EQ2, EQ3, OBJ / ;



alias(i,ii),(j,jj),(r,rr);







loop(rr,

loop(ii,

a(i) = 0;

ar(r) = 0;

loop(jj,

if(x.l(ii,jj) >= 500,

a(i)$(ord(i) = ord(ii)) = 1 ;

ar(r)$(ord(rr) = ord(r)) = 1;

) ;

Solve M2 using LP minimizing z ;

);

) ;

) ;



Cheers

Renger

Modelworks

Gewerbestrasse 15

3600 Thun – Switzerland

+41 79 818 53 73

In…@modelworks.ch

blog.modelworks.ch









From: gams...@googlegroups.com [mailto:gams...@googlegroups.com] On Behalf Of Dylan Lan
Sent: Thursday, October 16, 2014 4:15 AM
To: gams...@googlegroups.com
Subject: Equation index involved in loops



Dear all,



I am trying to formulate a model that can add new constraints after each solution, but the GAMS seems to forbid solving model in which equations’ index are involved in loops. The example is shown in the follow, and it is just to show the idea and may not be feasible.



Sets

i / i1*i100 /

j / j1*j100 / ;



Positive variables

x(i,j)

y(i) ;



Variable

z ;



Equations

EQ1(i,j) Equation 1

EQ2(i) Equation 2

OBJ Objective ;



EQ1(i,j) … y(i) =l= 100 ;



EQ2 (i) … sum(j$(ord(j)=2ord(i)), x(i,j)) + y(i) =g= 3000 ;



OBJ … z =e= 2sum((i,j), x(i,j)) + sum(i, y(i)) ;



Model M1 / EQ1, EQ2, OBJ / ;



Solve M1 using LP minimizing z ;



Set

r / r1*r10 / ;



Parameters

a(i) ;



a(i) = 0 ;



Equations

EQ3(r,i) Equation 3 ;



EQ3(r,i)$a(i) … sum(j, x(i,j)) =l= 10000 ;





Model M2 / EQ1, EQ2, EQ3, OBJ / ;



loop(r,

loop(i,

loop(j,

if(x.l(i,j) >= 500,

a(i) = 1 ;

) ;

) ;

) ;

Solve M2 using LP minimizing z ;

) ;

–
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To post to this group, send email to gams...@googlegroups.com.
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For more options, visit https://groups.google.com/d/optout.

–
To unsubscribe from this group and stop receiving emails from it, send an email to gamsworld+unsubscribe@googlegroups.com.
To post to this group, send email to gamsworld@googlegroups.com.
Visit this group at http://groups.google.com/group/gamsworld.
For more options, visit https://groups.google.com/d/optout.