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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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:47

  This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  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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