# Creating variables using JuMP

**URL:** <https://discourse.julialang.org/t/creating-variables-using-jump/111562>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [March 13, 2024, 11:02am UTC](https://discourse.julialang.org/t/creating-variables-using-jump/111562 "2024-03-13T11:02:34Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![heiwie](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/heiwie/32/208105_2.png) [@heiwie](https://discourse.julialang.org/u/heiwie)\
**Post date:** [March 13, 2024, 11:02am UTC](https://discourse.julialang.org/t/creating-variables-using-jump/111562/1 "2024-03-13T11:02:34Z")

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I am trying to define variables corresponding to nodes in a lattice consisting of one root node and two other time steps with two nodes each. I have defined a 2D list with all the nodes which I want to use for the indexing of my variables:

`nodes = [["T=0: N=1"], ["T=1: N=1", "T=1: N=2"], ["T=2: N=1", "T=2: N=2"]]`

I want to create the variables in the following way:

```julia
for i in range(1, length(time_steps)-1)
    q = @variable(model, 0 <= q[time_steps[i], time_steps[i+1]])
end

```

I understand that it is not possible to add new variables to an existing container as done here, but I have not found a good way of achieving what I want. I appreciate any guidance you may have in this matter.

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**Author:** ![math\_opt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/math_opt/32/25317_2.png) [@math\_opt](https://discourse.julialang.org/u/math_opt)\
**Post date:** [March 13, 2024, 12:27pm UTC](https://discourse.julialang.org/t/creating-variables-using-jump/111562/2 "2024-03-13T12:27:55Z")

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How about this (basically define the indices beforehand):

```julia
using JuMP

model = Model()

# key: time step, value: node
nodes = Dict(1 => [1], 2 => [2, 3], 3 => [4, 5])

# construct indices
indices = [(i, j) for t in 1:length(nodes) - 1 for i in nodes[t] for j in nodes[t + 1]]

@variable(model, q[indices] >= 0)

```

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<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 13, 2024, 8:47pm UTC](https://discourse.julialang.org/t/creating-variables-using-jump/111562/3 "2024-03-13T20:47:58Z")

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I don’t really understand how `nodes` is related to `time_steps`.

But there are many options. @math_opt’s is a good one. Here is another:

```Julia
arcs = [0 => 1, 1=> 1, 1 => 2, 2 => 1, 2 => 2]
model = Model()
@variable(model, q[T in 0:2, N in 1:2; (T => N) in arcs] >= 0)

```

It really depends on: what do you want to do with `q` once it is constructed?

If you find yourself struggled to wrangle variables into appropriate forms for constraints and expressions, it usually means that you could use a different data structure that was more appropriate.

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<div class="post-metadata">

**Author:** ![heiwie](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/heiwie/32/208105_2.png) [@heiwie](https://discourse.julialang.org/u/heiwie)\
**Post date:** [March 18, 2024, 9:40am UTC](https://discourse.julialang.org/t/creating-variables-using-jump/111562/4 "2024-03-18T09:40:35Z")

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Thank you! I managed to define the variables in the wanted string format when I used dictionaries.