Summation

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Trinh Nguyen

2022年07月18日 11:01

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Hello Gurobi team/experts,

How can I code this objective function in gurobi?

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  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:32

  This post is more than three 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.
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  Alison Cozad

  • Gurobi Staff

  2022年07月19日 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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