I’ve some model which i would like to implement in GAMS.
Unfortunately there are some issues regarding the domain restriction of a sum.
This is the Equation, which i would like to implement:
I’ve tried: sum((j$(ord(j) ne ord(i))),x1(j,i,g)) but i get Error 8,10,119,149.
If anyone could help me with this one i would really appreciate it 
Please attach a minimal code that can reproduce this issue. Error 8 looks like missing parenthesis which must be coming from some other statement in the code. There is nothing too suspicious about the summation you mention (what you have tried). But it would be good to know how you define j (is a subset of i, alias for i?) How you define your equation (you should define it over i). If the sets are defined correctly, the summation looks fine to me.
The errors seem to be coming from some other part of the code (you can click on the error and it will take the cursor to the statement where the error occurs). It will also be helpful if you mention error message instead of codes as users don’t remember the error codes.
Please also look at the documentation where common compilation errors and ways to fix those are mentioned: https://www.gams.com/33/docs/UG_FixingErrors.html#UG_FixingErrors_ErrorH
Thank you for your prompt reply!
Here is my code, i’ve attached also a screenshot of the whole model:
set i 'inbound trucks ’ / 1*10 /;
Alias (i,j);
Set
i0 ‘i=0 in res2’ / 0 /
n1 ‘n+1 inbound for res3’ / 111 /
o ‘outbound’ / 15 /
g ‘inbound doors available for processing inbound’ / 1*2 /
;
Parameter
p(i) ‘processing time for unloading inbound truck i’
d(o) ‘departure time of outbound truck o’
t(g,o) ‘transshipment time from inbound dock g to the dock where outbound truck o is processed’
w(i,o) ‘weight, e.g., the number of products, of a shipment delivered by inbound truck i dedicated to outbound truck o’
sum_i ‘# of i’
sum_g ‘# of g’;
sum_i = card (i);
sum_g = card (g);
p(i) = normal(30,6);
d(o) = (sum(i,p(i))/sum_g)*uniform(0.5,0.9);
w(i,o) = uniform (1,10);
t(g,o) = uniform (1,10);
Variable
Z ‘ZFW’;
Positive Variable
C(i) ‘completion time of inbound i’;
Binary Variable
x1(j,i,g) ‘res1’
x2(i0,j,g) ‘binary variable: 1, if inbound i is processed first at gate g; 0, otherwise’
x3(i,j,g) ‘res3’
y(i,o) ‘ZF’;
Scalar BIGM;
BIGM = sum(i, p(i))+ smax((g,o),t(g,o));
Equation
ZF ‘ZF’
res1 (i,g) ‘every truck is scheduled’
res2 (g) ‘one truck per gate’
res3 (i,g) ‘’
res4 (i,j,g) ‘’
res5 (i,o) ‘’
;
ZF … Z =e= sum((i,o), w(i,o)*y(i,o));
res1(i,g) … sum(j$(ord(j) ne ord(i)) ,x1(j,i,g)) =e= 1 ;
res2(g) … sum((j,i0),x2(i0,j,g)) =l= 1 ;
res3(i,g) … sum(j$(ord(j) ne ord(i)), x3(i,j,g)) =e= sum(j$(ord(j) ne ord(i)),x1(j,i,g)) ;
res4(i,j,g) … C(i) =g= C(j) +p(i) - BIGM * (1-x1(j,i,g)) ;
res5(i,o) … y(i,o) * BIGM =g= C(i)-d(o)+sum(g,t(g,o))*sum((j$(ord(j) ne ord(i))),x1(j,i,g)) ;
Greetings
Lukas
As I suspected, the error was coming from a different equation res5 where some unnecessary parenthesis were present. If you replace res5 with the following equation, you will not see any compilation errors:
res5(i,o) .. y(i,o) * BIGM =g= C(i)-d(o)+sum(g,t(g,o)*sum(j$(ord(j) ne ord(i)),x1(j,i,g))) ;
Please note that the inner sum over j is inside the outer sum over g. If you don’t do that, x1^g has no meaning.
Please use code blocks to provide codes for future communication as I have used.
Again, thank you very much for your help!
But if i do it like that, i get the errors that ‘set is under control already’:
res5(i,o) .. y(i,o) * BIGM =g= C(i)-d(o)+sum(g,t(g,o)*sum((g,j$(ord(j) ne ord(i))),x1(j,i,g))) ;
The equation I showed and the one you show are different. I don’t sum over g twice.
I’m sorry, i got an infeasible solution and thought naively that would help.
In restriction1 there is a sum first over g and then over j but when i code it in that way below i get an error message: 'expected ‘,’ and ‘)’ and '=l=# or similar. I thought when you’ve multiple sums that would be the right syntax?
res1(i) .. sum((g,j$ord(j) ne ord(i)),x1(j,i,g)) =e= 1 ;
-Lukas
Please follow GAMS tutorials and read about these compilation errors. Again in this equation you have incorrect parentheses.
Besides, while declaring equation, you have res1(i,g) but while defining you have res1(i).
In this case, you are having trouble defining a sum over two sets. You can check it here: https://www.gams.com/latest/docs/UG_Parameters.html#INDEX_indexed_21_operations_22_sum
Second, there is some confusion about how $ conditions are written, what is the correct syntax etc. You can check it here: https://www.gams.com/latest/docs/UG_CondExpr.html#UG_CondExpr_TheDollarCondition
Here is your fixed equation:
res1(i) .. sum((g,j)$(ord(j) ne ord(i)),x1(j,i,g)) =e= 1 ;
Thank you for your help, i really appreciate it!
I’ve corrected my mistakes and i get no compilation error, thank you!
Unfortunately, the solution is still infeasible. I’ve tried to set the variable C to zero as described in the model but that didn’t worked either.
I’ve asked you very much, but again, do you probably know why i still can’t get a solution?
$title TSFD
$onText
Beschreibung
$offText
set i 'inbound trucks ' / 1*5 /;
Alias (i,j);
Set
i0 'i=0 in res2' / 0 /
n1 'n+1 inbound trucks; für res3 benötigt' / 1*6 /
o 'outbound trucks' / 1*2 /
g 'inbound doors available for processing inbound trucks' / 1*2 /
;
display i0;
Parameter
p(i) 'processing time for unloading inbound truck i'
d(o) 'departure time of outbound truck o'
t(g,o) 'transshipment time from inbound dock g to the dock where outbound truck o is processed'
w(i,o) 'weight, e.g., the number of products, of a shipment delivered by inbound truck i dedicated to outbound truck o'
sum_i 'Anzahl der Elemente in der Indexmenge i'
sum_g 'Anzahl der Elemente in der Indexmenge g'
;
sum_i = card (i);
sum_g = card (g);
$onText
generate pseudorandom numbers for p(i), d(o), t(g,o), w(i,o)
execseed = 1 + gmillised(jnow);
$offText
p(i) = normal(30,6);
d(o) = (sum(i,p(i))/sum_g)*uniform(0.5,0.9);
w(i,o) = uniform (1,10);
t(g,o) = uniform (1,10);
display p,d,w,t;
Variable
Z 'ZFW'
C(i0) 'starting C';
Positive Variable
C(i) 'completion time of inbound i';
Binary Variable
x1(j,i,g) 'res1'
x2(i0,j,g) 'binary variable: 1, if inbound i is processed first at gate g; 0, otherwise'
x3(i,j,g) 'res3'
y(i,o) 'ZF';
Scalar BIGM;
BIGM = sum(i, p(i))+ smax((g,o),t(g,o));
display BIGM;
Equation
ZF 'Zielfunktion'
res1 (i) 'every truck is schedulded'
res2 (g) 'one truck per gate at the same time'
res3 (i,g) ''
res4 (i,j,g) ''
res5 (i,o) ''
res6 (i0)
;
ZF .. Z =e= sum((i,o), w(i,o)*y(i,o));
res1(i) .. sum((g,j)$(ord(j) ne ord(i)),x1(j,i,g)) =e= 1 ;
res2(g) .. sum((j,i0),x2(i0,j,g)) =l= 1 ;
res3(i,g) .. sum(j$(ord(j) ne ord(i)), x1(j,i,g)) =e= sum(j$(ord(j) ne ord(i)),x3(i,j,g)) ;
res4(i,j,g) .. C(i) =g= C(j) +p(i) - BIGM * (1-x1(j,i,g)) ;
res5(i,o) .. y(i,o) * BIGM =g= C(i)-d(o)+sum(g,t(g,o)*sum(j$(ord(j) ne ord(i)),x1(j,i,g))) ;
res6(i0).. C(i0) =e= 0;
$onText
option optCr = 0.0, optCa = 0.0;
$offText
Model TSFD / all /;
solve TSFD using mip minimizing Z;
display z.l;
-Lukas
Sorry but your model doesn’t compile without errors. Besides the model you show in the picture and the one you attach are two different models.
If you see summation over j in the model, you will see that it is I U {0} or I U {n + 1}. You are not doing this anywhere in the model.
You are defining C over i0 as well as i. When you are writing a mathematical model, all small details matter and any change can make the model infeasible.
There is n in the model you attach but there is no n in your GAMS code. So why is this difference? You can try to make sense of your model only when you have modelled “exactly” what you wanted to model.
In this particular case, you need to read about subsets. https://www.gams.com/latest/docs/UG_SetDefinition.html#UG_SetDefinition_Subsets
Because you alias j with i but if in the model, j is I U {0} or I U anything, it is “more than” i. So you really need to create a set that is a superset of i.
I can’t suggest everything but this should be a good starting point.