Nested loop for sum of variables

Answered

Eugene Parus

March 11, 2025 05:59 Edited

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Hi team,

I am new to Gurobi.

I have problem with sum of variables for constraints.

Let we have 3 hours H=[1,2,3]. For each hour we have one variable [V1,V2,V3] and maximum of sum for current and previous hours [K1,K2,K3].

It is necessary to create such a system of restrictions:

V1              <=K1

V1+V2       <=K2

V1+V2+V3<=K3

How do I declare a nested loop to create such a restriction system?

Related to

• Model Building

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• 

  Ronald van der Velden

  • Gurobi Staff

  March 11, 2025 08:01

  Hi Eugene,

  You could do something like this:

  import gurobipy as gp
  from gurobipy import GRB
  
  H = range(3)
  K = [7, 13, 16]
  
  with gp.Env() as env, gp.Model(env=env) as model:
      V = model.addVars(H, name='V')
      for h in H:
          model.addConstr(gp.quicksum(V[i] for i in range(h+1)) <= K[h])
      model.write('temp.lp') # To inspect the resulting model

  There are ways to speed this (model-building) up in case you're looking at thousands of hours, e.g.

  • Build the left-hand-side expression iteratively. After adding the constraint for K1, add V2 to the expression. After adding the constraint for K2, add V3 etcetera.
  • Alternatively, you could introduce variables containing the cumulative values for the left-hand-side, e.g. C1=V1, C2=C1+V2, C3=C2+V3. You should test what performs best when solving the model.

  Kind regards,
  Ronald

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  Eugene Parus

  March 30, 2025 14:52

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  many thanks

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