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

Answered

Vusal Babashov

March 16, 2023 13:33 Edited

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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

Related to

• gurobipy-pandas

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• 

  Riley Clement

  • Gurobi Staff

  March 17, 2023 03:48 Edited

  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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