Adding Quadratic Constraint python

Answered

beray Tuzcu

March 15, 2022 21:14

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Pij = Is a matrix that includes processing times, for order(j) in  truck(i). (integer matrix)

Sik =Is a decision variable that represents the starting time of an order in a truck(i) in truck's slot(k). (cont)

Cj = Decision variable represents the completion time of order(j). (cont or int)

Xijk= Is a binary decision variable (1 if order j assigned to truck i at kth slot)

As can be seen from the above constraint, we need to multiply the Xijk binary decision variable and the continuous decision variable (Sik) and assign it to Cj. 

We are having a problem with adding constraint that has quadratic multiplication expression (binary*cont) , (in a summation). 

 

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:41

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  Jaromił Najman

  • Gurobi Staff

  March 16, 2022 08:51

  It looks like a parentheses issue. Could you try

  model.addConstrs((gurobipy.quicksum(Xijk[truck,order,position] * Sik[truck,position]) == Cj[order] for order in orders), name='Completion Time of Order3')

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  Umurcan Vural

  March 16, 2022 09:20 Edited

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  Thank you for the response! Jaromił Najman
  As we got in our previous attempts, now we get a "Quad Exp. object is not iterable" error.

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  Jaromił Najman

  • Gurobi Staff

  March 16, 2022 09:44

  You are currently using 2 \(\texttt{for}\)-loops to generate the sums. However, the quicksum function does this for you already. The following code should work

  model.addConstrs((gurobipy.quicksum(Xijk[truck,order,position] * Sik[truck,position] for truck in trucks for position in positions) == Cj[order] for order in orders), name='Completion Time of Order3)

  The reason for the error is because the quicksum function requires iterable data as input argument, e.g., a list. However, the object \(\texttt{Xijk * Sik}\) is a QuadExpr. You could have used the 2 \(\texttt{for}\)-loops to construct the sums, but this would make the code more clumsy and harder to read. Thus, using the quicksum function is recommended here.

  Best regards, 
  Jaromił

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  Umurcan Vural

  March 16, 2022 10:40

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  Hi again,
  
  Now it work smoothly, thank you for the detailed explanation!
  
  Regards,
  Umur.

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