Flow conservation constraint

Hi there! I’m trying to write a flow conservation constrains. Yet it says key not found

``````# this is the constraint I'd like to write   (and α(i,j) is a binary variable  and A1 is a subset of nodes)
∑ᵢ α[i,j] = ∑ₖ α[j,k]   ∀ j ∈ A1   # flow conservation on all nodes belong to  A1

``````

using JuMP, CPLEX

``````
m = Model(CPLEX.Optimizer)
A1 = [1,2,5]
Arcs = ((3, 1), (1, 2), (2, 5), (7, 7), (4, 2))

@variable(m, α[i in Arcs]>= 0, Bin)

``````

Do you know why the above is not working? any suggestion to write it the other way?

1 Like

Hi @gdalle Thanks for your advice. I’ve made some change. Basically, there are some arcs in a newtrok and I need to ensure that for a subset of nodes (A1); flow conservation constraints hold.
They require that, for each node in ` A1`, the sum of the flow into the node must be equal to the sum of the flow out of the node.

Something like this?

``````@constraint(
model,
[jj in A1],
sum(α[(i, j)] for (i, j) in Arcs if j == jj) == sum(α[(j, k)] for (j, k) in Arcs if j == jj),
)
``````
1 Like