Flow equation

GAMS
1

Hi,
I’m trying to write a code to calculate the flow of a snippet.
The section should receive the flow of the previous sections.
But my problem is the matrix “q(n,np)” depends on itself.
Apresentação1.jpg

Set     n       nodes   / n1 * n48 /
         a(n,n)  arcos   / n1.(n2,n9), n2.(n1,n3), n3.(n2,n4), n4.(n3,n5,n10),
                           n5.(n4,n6,n11), n6.(n5,n7), n7.(n6,n8), n8.(n7,n17),
                           n9.(n1,n13), n10.(n4,n14), n11.(n5,n15), n12.(n8,n16),
                           n13.(n9,n17), n14.(n10,n20), n15.(n11,n21),
                           n16.(n12,n24), n17.(n13,n18,n25), n18.(n17,n19),
                           n19.(n18,n20), n20.(n14,n19,n21,n28),
                           n21.(n15,n20,n22,n29), n22.(n21,n23), n23.(n22,n24),
                           n24.(n16,n23,n33), n25.(n17,n26,n33), n26.(n25,n27),
                           n27.(n26,n28), n28.(n20,n27,n29,n34),
                           n29.(n21,n28,n30,n35), n30.(n29,n31), n31.(n30,n32),
                           n32.(n24,n31,n36), n33.(n25,n37), n34.(n28,n38),
                           n35.(n29,n39), n36.(n32,n40), n37.(n33,n41),
                           n38.(n34,n44), n39.(n35,n45), n40.(n36,n48),
                           n41.(n37,n42), n42.(n41,n43), n43.(n42,n44),
                           n44.(n38,n43,n45), n45.(n39,n44,n46),
                           n46.(n45,n47), n47.(n46,n48), n48.(n40,n47)/
         si(n)   saida   /n48/
         cont(n) contribution; cont(n)=yes; cont(si)=no; display cont;
         alias(n,np);


Scalar q /10/;

Variables ar(n,np)
          qn(n,np)
          xq;

binary variable ar(n,np);

Equation flow
         qalter;

qalter(n,np).. xq(n,np) =l= qn(n,np);

flow(n,np)$ar(n,np)..  qn(n,np) =e= sum(np,xq(n,np)) + q;

Gams Show the Error…

 vazao(n,np)$ar(n,np)..  qn(n,np) =e= sum(np,xq(n,np)) + q;
                                            $125
                                                                  
 125  Set is under control already

**** 1 ERROR(S)   0 WARNING(S)

I tried to use the equation to maintain the linear equation

qalter(n,np).. xq(n,np) =l= qn(n,np);

Please could someone give me some idea

2

Hi
You can use -1 for the previous index and the $-sign to constrain the summation, like this

alias(m, am);

Q(m,n) = sum(am$(ord(am) < ord(m)+1),  Q(am-1,n)X(am-1,n))+ QIN(am,n);

Note, that you have to use an alias, as you can’t sum over m as it is already used for indicating the variable Q(m,n), so Gams complains over using m in two concflicting ways (error 125).

I hope this helps

Cheers
Renger

3

Using this expretion

Q(m,n) = sum(am$(ord(am) < ord(m)+1),  Q(am-1,n)X(am-1,n))

Q(m,n) and Q(am-1,n)

GAMS will use the same matrix of data, in this case, will use the same matriz of the flow data?

4

I think it should be:

alias(np,anp);
flow(n,np)$ar(n,np)..  QN(n,np) =e= sum(anp$(ord(anp) < ord(np), XN(n,anp)) + q;

.
This will take all XN for which the first index is the same as in QN (i.e. ‘n’) and the second index anp goes from the first element of np to the one just before n.
Hope this clarifies it.
CHeers
Renger