Defining set of decision variables with partially common index sets in gurobi pandas

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Vusal Babashov

2023年03月16日 13:33 編集済み

Good day,

I want to define the following binary decision variables using the pandas dataframe: x_{ik}, y_{ikn}, z_{kn} and w_{is}.

As we see, while index k is the same for first three variables, index n is only applicable for the second and third decision variables and index s is used only in the fourth decision variable. How can I leverage gurobi-pandas to define these variables using pandas multiindex within the same dataframe?

Appreciate your help with a small example in advance.

Best,

Vusal

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Riley Clement

Gurobi Staff

2023年03月17日 03:48 編集済み
Hi Vusal,

If the variables have different indexes then it doesn't make sense to have them in the same dataframe, however this does not mean you cannot use gurobipy-pandas.

Let's start with a simple case, using just the x and z variables from your example. We can create a pandas.Series for each of the variables (a dataframe isn't necessary here):
```
import gurobipy as gp
from gurobipy import GRB
import gurobipy_pandas as gppd
import pandas as pd

i = (1,2)
k = (1,2,3)
n = ("a","b")

model = gp.Model()

x = gppd.add_vars(model, pd.MultiIndex.from_product((i,k), names=("i", "k")), vtype=GRB.BINARY, name="x")
z = gppd.add_vars(model, pd.MultiIndex.from_product((k,n), names=("k", "n")), vtype=GRB.BINARY, name="z")
```
Then let's say you wanted to add constraints of the form:

\[ \sum_{k} C_k x_{i,k} z_{k,n} \geq R_{i,n}, \quad \forall i, n\]

for some constant vectors C and R.
```
import numpy as np
C = pd.Series(
    np.random.randint(1,10, size=len(k)),
    index=pd.Index(k, name="k"),
)
R = pd.Series(
    np.random.randint(1,10, size=len(i)*len(n)),
    pd.MultiIndex.from_product((i,n), names=("i", "n")),
)
```
Adding the constraints can be concisely done with
```
gppd.add_constrs(model, (C*x*z).groupby(["i", "n"]).sum(), ">=", R)
```
The advantage of using gurobipy-pandas is this will be an efficient way of building the model.

The disadvantage is that it may be less readable for those unfamiliar with this style.

- Riley
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