Variate Piece-wise Linear Function

Answered

Natalie Tam

August 03, 2023 15:27

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My modelling problem consists of finding a minimized cost for the model, and finding xij the decision variable. I want to apply a piece-wise linear function on it like so: 

But I can only find examples when the functions in the linear functions are constant. Even then, I tried putting dummy values for the y points

 

y = model.addVar(name='y')
xpts = [0, 4800, 15000, 30000 ]
ypts = [50000, 345000, 444000]

model.addGenConstrPWL(x, y, xpts, ypts)
K = 46.35
objective_expr = gp.LinExpr()
for i in I:
  for j in J:
    objective_expr += K*((x[i, j])) + (shipping_cost_matrix[i][j] * dist_matrix[i][j] - cost_per_state[j]) * x[i, j]

model.setObjective(objective_expr, gp.GRB.MINIMIZE)
model.optimize()

 

 

But I get a type error TypeError: {(0, 0): <gurobi.Var *Awaiting Model Update*>, (0, 1), ... (2, 4): <gurobi.Var *Awaiting Model Update*>} is not a variable

 

 

 

Related to

• Piecewise Linear

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:39

  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.
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  w sj

  August 05, 2023 16:12

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  If your function is continuous, perhaps you can first convert it into a linear function and then use addconstr

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  Jaromił Najman

  • Gurobi Staff

  August 07, 2023 06:54

  Hi Natalie,

  In your code snippet, the definition of \(x\) variables is missing.

  Note that the size of the \(\texttt{xpts}\) and \(\texttt{ypts}\) lists has to be the same, see addGenConstrPWL and the documentation on PWL.

  In your case, you want the \(\texttt{ypts}\) to hold the values at break points of you function, i.e.,

  xpts = [0, 4800, 15000, 30000 ]
  ypts = [0, 24960, 75960, 144960]

  With the \(x\) points and \(y\) points Gurobi is able to compute the PWL segments that you define via linear terms in your function.

  Best regards, 
  Jaromił

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