# How to create multidimensional sets in JuMP/Julia as in GAMS
**URL:** https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581
**Category:** Optimization (Mathematical)
**Tags:** jump, syntax, optimization, set
**Created:** [February 18, 2021, 10:21pm UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581 "2021-02-18T22:21:33Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@GraceMabele](https://discourse.julialang.org/u/GraceMabele)
#### Post date: [February 18, 2021, 10:21pm UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/1 "2021-02-18T22:21:33Z")
In GAMS, we can create multidimensional sets as follows
```julia
Set i "mining regions" / china, ghana, ee+ussr, s-leone /
n "ports" / accra, freetown, leningrad, shanghai /
in(i,n) "mines to ports map" / china .shanghai
ghana .accra
ee+ussr.leningrad
s-leone.freetown /;
```
How can I do the same in JuMP/Julia?
---
### Author:  [@NiclasMattsson](https://discourse.julialang.org/u/NiclasMattsson)
#### Post date: [February 18, 2021, 10:49pm UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/2 "2021-02-18T22:49:45Z")
Usually I’d suggest a vector of symbols, but since your regions contain characters like `+` and `-` probably a vector of strings is better in your case. Then the mines to ports map could be a dictionary, like so:
```julia
regions = ["china", "ghana", "ee+ussr", "s-leone"]
ports = ["accra", "freetown", "leningrad", "shanghai"]
links = Dict("china" => "shanghai",
"ghana" => "accra",
"ee+ussr" => "leningrad",
"s-leone" => "freetown")
```
I teach an introductory course in energy system LP modeling. The first assignment is to build (or rather modify) a very simple model of a district heating system. The model was originally written in GAMS but I recently converted it to Julia/JuMP - you might find it useful to see how things can translate. Both versions (and the assignment itself) are available here:
> **[GitHub - niclasmattsson/LPtown: A simple LP model of a district heating...](https://github.com/niclasmattsson/LPtown)**
>
> A simple LP model of a district heating system, written in Julia/JuMP. - GitHub - niclasmattsson/LPtown: A simple LP model of a district heating system, written in Julia/JuMP.
---
### Author:  [@GraceMabele](https://discourse.julialang.org/u/GraceMabele)
#### Post date: [February 19, 2021, 4:44am UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/3 "2021-02-19T04:44:22Z")
When I index it in a constraint, I obtain a key error.
Is it not better to have it as a vector of symbols?
---
### Author:  [@NiclasMattsson](https://discourse.julialang.org/u/NiclasMattsson)
#### Post date: [February 19, 2021, 9:30am UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/4 "2021-02-19T09:30:14Z")
It’s very hard to say without seeing the error in context, but key error means you’re trying to look up an element in the dictionary that doesn’t exist. Wild guess: are you doing something like `links[x]` where `x` is an integer?
```julia
julia> links["china"]
"shanghai"
julia> links[23]
ERROR: KeyError: key 23 not found
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [February 19, 2021, 7:53pm UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/5 "2021-02-19T19:53:23Z")
```nohighlight
julia> using JuMP
julia> regions = ["china", "ghana", "ee+ussr", "s-leone"]
4-element Array{String,1}:
"china"
"ghana"
"ee+ussr"
"s-leone"
julia> ports = ["accra", "freetown", "leningrad", "shanghai"]
4-element Array{String,1}:
"accra"
"freetown"
"leningrad"
"shanghai"
julia> links = [
"china" => "shanghai",
"ghana" => "accra",
"ee+ussr" => "leningrad",
"s-leone" => "freetown"
]
4-element Array{Pair{String,String},1}:
"china" => "shanghai"
"ghana" => "accra"
"ee+ussr" => "leningrad"
"s-leone" => "freetown"
julia> model = Model()
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: NO_OPTIMIZER
Solver name: No optimizer attached.
julia> @variable(model, arcs[r=regions, p=ports; (r => p) in links])
JuMP.Containers.SparseAxisArray{VariableRef,2,Tuple{String,String}} with 4 entries:
[s-leone, freetown] = arcs[s-leone,freetown]
[china, shanghai] = arcs[china,shanghai]
[ee+ussr, leningrad] = arcs[ee+ussr,leningrad]
[ghana, accra] = arcs[ghana,accra]
julia> arcs["s-leone", "freetown"]
arcs[s-leone,freetown]
```
---
### Author:  [@sylvaticus](https://discourse.julialang.org/u/sylvaticus)
#### Post date: [February 20, 2021, 10:49am UTC](https://discourse.julialang.org/t/how-to-create-multidimensional-sets-in-jump-julia-as-in-gams/55581/6 "2021-02-20T10:49:38Z")
See also this implementation in JuMP of the classical transport problem in GAMS:
> **[Jupyter Notebook Viewer](https://nbviewer.org/github/sylvaticus/juliatutorial/blob/master/assets/JuMP.ipynb)**
>
> Check out this Jupyter notebook!