Construct an objective function from a dataframe

Question

I have the following dataframe that contains both indices of three dimensional variables and cost parameters.

Product	Factory	Sub	Cost
A	F1	A1	10
A	F2	A1	8
B	F1	B1	20
C	F2	C2	12

Let say there are 3 types of products, 2 factories, and 4 sub_products. I define the following vectors

Product=["A", "B", "C"]
Factory=["F1","F2"]
Sub=["A1","A2","B1","B2","C1","C2"]

I am trying to construct the following objective function for the variables in the dataframe (ie. the coefficients of the decision variables that are not in the table are zero).

Min 10x[A,F1,A1]+ 8x[A,F2,A1] + 20x[B,F1,B1] + 12*x[C,F2,C2]

How can I write this code using JuMP. I tried the following code

@objective(model, Min, sum(data.Cost[data.Product==product,data.Factory==factory,data.SubProduct==sub]*x[product, factory, sub] 
for product in Product, factory in Factory, sub in Sub))

Answer 1

Create the DataFrame, and then add a new column for the decision variables. Your objective is the sum of the cost and x columns multiplied together:

julia> import DataFrames

julia> using JuMP

julia> df = DataFrames.DataFrame(
           Product = ["A", "A", "B", "C"],
           Factory = ["F1", "F2", "F1", "F2"],
           Sub = ["A1", "A1", "B1", "C2"],
           Cost = [10, 8, 20, 12],
       )
4×4 DataFrame
 Row │ Product  Factory  Sub     Cost  
     │ String   String   String  Int64 
─────┼─────────────────────────────────
   1 │ A        F1       A1         10
   2 │ A        F2       A1          8
   3 │ B        F1       B1         20
   4 │ C        F2       C2         12

julia> model = Model();

julia> df.x = @variable(model, x[1:size(df, 1)]);

julia> @objective(model, Min, sum(df.Cost .* df.x))
10 x[1] + 8 x[2] + 20 x[3] + 12 x[4]

julia> df
4×5 DataFrame
 Row │ Product  Factory  Sub     Cost   x         
     │ String   String   String  Int64  GenericV… 
─────┼────────────────────────────────────────────
   1 │ A        F1       A1         10  x[1]
   2 │ A        F2       A1          8  x[2]
   3 │ B        F1       B1         20  x[3]
   4 │ C        F2       C2         12  x[4]

The JuMP documentation has a number of examples for working with DataFrames:

https://jump.dev/JuMP.jl/stable/tutorials/linear/diet/ https://jump.dev/JuMP.jl/stable/tutorials/linear/factory_schedule/ https://jump.dev/JuMP.jl/stable/tutorials/linear/multi/ https://jump.dev/JuMP.jl/stable/tutorials/linear/multi_commodity_network/

Answer 2

Firstly you need to define the 3 dimensional decision variable. Most likely for your case this could look like this:

julia> @variable(model, x[p=Product,f=Factory,s=Sub])
3-dimensional DenseAxisArray{VariableRef,3,...} with index sets:
    Dimension 1, ["A", "B", "C"]
    Dimension 2, ["F1", "F2"]
    Dimension 3, ["A1", "A2", "B1", "B2", "C1", "C2"]
And data, a 3×2×6 Array{VariableRef, 3}:
[:, :, "A1"] =
 x[A,F1,A1]  x[A,F2,A1]
....

Now for readability assume that you have some function that knows the cost for some values of p, f and s.

function getcost(p,f,s)
    # do some search in DataFrame or better make an index utilizing a Dict
    10 # mockup value
end

You can define now the objective function as:

julia> @objective(model, Min, sum(x[p,f,s]*getcost(p,f,s) for p in Product, f in Factory, s in Sub))
10 x[A,F1,A1] + 10 x[A,F1,A2] + 10 x[A,F1,B1] + 10 x[A,F1,B2] + 10 x[A,F1,C1] + 10 x[A,F1,C2] + 10 x[A,F2,A1] + 10 x[A,F2,A2] + 10 x[A,F2,B1] + 10 x[A,F2,B2] + 10 x[A,F2,C1] + 10 x[A,F2,C2] + 10 x[B,F1,A1] + 10 x[B,F1,A2] + 10 x[B,F1,B1] + 10 x[B,F1,B2] + 10 x[B,F1,C1] + 10 x[B,F1,C2] + 10 x[B,F2,A1] + 10 x[B,F2,A2] + 10 x[B,F2,B1] + 10 x[B,F2,B2] + 10 x[B,F2,C1] + 10 x[B,F2,C2] + 10 x[C,F1,A1] + 10 x[C,F1,A2] + 10 x[C,F1,B1] + 10 x[C,F1,B2] + 10 x[C,F1,C1] + 10 x[C,F1,C2] + 10 x[C,F2,A1] + 10 x[C,F2,A2] + 10 x[C,F2,B1] + 10 x[C,F2,B2] + 10 x[C,F2,C1] + 10 x[C,F2,C2]