Summation

Answered

Trinh Nguyen

July 18, 2022 11:01

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Hello Gurobi team/experts,

How can I code this objective function in gurobi?

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:32

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• 

  Alison Cozad

  • Gurobi Staff

  July 19, 2022 13:25

  There are a few ways you can do this.  Here is one way to accomplish the nested summations using quicksum():

  import gurobipy as gp
  from gurobipy import GRB
  import numpy as np
  
  # Create a new model
  model = gp.Model('Nested Summation')
  
  # Define sets
  H = range(0,2)
  I = range(0,3)
  J = range(0,4)
  K = range(0,5)
  T = range(0,6)
  
  # Define cost[i,j,h]
  cost = np.random.random((len(I), len(J), len(H)))
  
  # Create flow[i,j,t,h,k] variable
  flow = model.addVars(I, J, T, H, K,
                       vtype=GRB.CONTINUOUS, 
                       name="flow")
  
  # Set objective
  model.setObjective(gp.quicksum(cost[i][j][h]*flow[i,j,t,h,k]
                                 for t in T
                                 for k in K
                                 for j in J
                                 for i in I
                                 for h in H
                              ))

  I have assumed that cost is constant here.

   

  Here are some materials that build on this:

  • Python I: Introduction to Modeling with Python - Gurobi. This is your best place to start.  It includes a video tutorial and examples with jupyter notebooks to follow.  It also includes an example of using nested summations.
  • netflow.py: This is a Gurobi example of how to do nested summations in two different ways: (a) using quicksum() and (b) using tupledict.sum()

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