tabulated values for a gurobi variable

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Federico Mungari

2023年07月04日 07:23 編集済み

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Dear all,

I am trying to assign to a continuous variable (vtype = gp.GRB.CONTINUOUS) a value chosen from a series of pre-calculated values. This decision/attribution takes place in light of the decision made, during the optimization process, about a set of binary decision variables.

In particular, I will therefore have decision variables such as:

z = {}

for k in K:

    z[k] = m.addVar(vtype = gp.GRB.BINARY, name = 'z_%s' % (k))

and the variables

x = {}

for q in Q:

    x[q] = m.addVar(vtype = gp.GRB.CONTINUOUS, name = 'z_%s' % (q))

take values extracted from a dictionary Q_vals[{x}].

 

Is it possible to model such a system in gurobi?

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• Modeling

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  Maliheh Aramon

  • Gurobi Staff

  2023年07月05日 01:31

  Hi Federico, 

  I am not sure I fully understood your question. I guess you mean that the continuous variable \(x\) can be assigned to a value from the set \(\{a_1, a_2, \ldots, a_k\}\). To model this, you can define binary decision variables \(z_i\) which equals 1 if the value \(a_i\) is assigned to variable \(x\) and equals 0 otherwise. You would then need to define the constraints below:

  \[\begin{align} & \sum_{i=1}^{k} z_i = 1 & \\ & x =  \sum_{i=1}^{k} a_i z_i &  \end{align}\]

  The first constraint ensures that exactly one of the \(z\) variables is assigned to 1 and the second constraint ensures that \(x\) variable is assigned to exactly one value from the predetermined set.

  Hope this helps. Let me know if I misunderstood your question. 

  Best regards,

  Maliheh 

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