'How to have conditions for constraints?

How can I code a constraint like this in JUMP?

Suppose i,j,k,m are indices and capital letters associated with them are set, like J.

x_{i,j,k,m'} + sum((j in J, k in K), y_{j,k,m})<= z_{i,m} for all i in I and for all m and m' in M  ; m !=m'

just like the photo

julia julia-jump

Solution 1:^[1]

I understand that you want a multi-dimensional constraint loop with filtering. I get this to a minimal working example:

M=1:10
model = Model(HiGHS.Optimizer)
@variable(model, y[1:lenght(M),1:lenght(M)] >= 0)
z = rand(lenght(M))

Having this values you can have the constraint with filtering as:

@constraint(model, [m1 in M, m2 in M], y[m1,m2] >= z[m1]*(m1 !== m2))

Note that constructing variable as y[1:lenght(M),1:lenght(M)] produces a regular Matrix while y[M,M] would yield a DenseAxisArray.

Solution 2:^[2]

Your math formulation is wrong, because the j and k indices on x are not defined. Is the summation in the wrong place?

Assuming it is, one option is:

for i in I
    for (m, m2) in M
        if m != m2
            @constraint(model, sum(x[i,j,k,m2] + y[j,j,k] for j in J, k in K) <= z[i, m, m2])
        end
    end
end

Another is

@constraint(
    model,
    [i in I, (m, m2) in M; m != m2],
    sum(x[i,j,k,m2] + y[j,j,k] for j in J, k in K) <= z[i, m, m2]),
)

Sources

This article follows the attribution requirements of Stack Overflow and is licensed under CC BY-SA 3.0.

Source: Stack Overflow

Solution	Source
Solution 1	Przemyslaw Szufel
Solution 2	Oscar Dowson

'How to have conditions for constraints?

Solution 1:[1]

Solution 2:[2]

Sources

Related Questions

Solution 1:^[1]

Solution 2:^[2]