Doubt regarding adding a constraint with difference of summations using quicksum

Answered

Yaswanth Bangaru

May 19, 2021 21:03 Edited

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Hey folks, firstly, thanks for taking the time to read the question, I am looking for some clarification on the ways to approach adding a constraint that involves the difference between summations.

so, this is the constraint I am trying to add to my model, the idea is to go through all i one at a time and make sure the difference between the summations of xij an xji over j is equal to zero, I added the constraint using the following line of code,

 

mdl.addConstrs(((quicksum(x[i,j] for j in I if j!=i)) - (quicksum(x[j,i] for j in I if j!=i)))==0for i in I);

 

I am just not sure if it's the right way to do it since I have a feeling that I might be iterating over j twice instead of being able to do that by iterating over j just once, can someone please help me figure out if I am doing this the right way? Thank you

1

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:54 Edited

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• 

  Jaromił Najman

  • Gurobi Staff

  May 21, 2021 09:27

  Hi,

  You could write your constraint as

  \[ \sum_j (x_{ij} - x_{ji}) =0 \quad \forall \, i \]

  mdl.addConstrs( (quicksum(x[i,j] - x[j,i] for j in I if j!=i)) == 0 for i in I )

  Best regards,
  Jaromił

  1

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