How to implement a max over constraint considering an array of variables
Ongoing
I would like to implement this constraint using gurobi in Java.
The L_op array is a set of constants, while the z_opw array consists of a set of binary variables.
Due to the fact that z_opw is a variable I cannot use the Math.max function, how can I otherwise implement such constraint?
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You can use a max general constraint for this. Such a max constraint states that one variable should equal the maximum of a set of other variables (and a constant).
Note that since the arguments for the max constraint need to be variables and not linear expressions you need to define some auxiliary variables $$\mathrm{aux}_{op} = L_{op} \ast z_{op1}.$$ Then you can define $$m_{o1} = \max_{p}(\mathrm{aux}_{op})$$ and finally $$t_{o1}^{walk} \leq m_{o1}.$$
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Thank you for your help, I tried to structure the code following the structure you provided, although I do not know how to fill the arguments of the addGenConstrMax(). I leave here the code snippet
// Constraint 1: aux_ow1 = L_op * z_op1 for all o, for all p
GRBVar[][] aux_op1 = new GRBVar[O][P];
for (int i=0; i<O;i++) {
for (int j=1; j<P; j++) {
expr = new GRBLinExpr();
expr.addTerm(L_op[i][j],z_opw[i][j][0]);
model.addConstr(expr, GRB.EQUAL,aux_op1[i][j], "constraint8["+i+"]["+j+"]");
}
}
// Constraint 2: m_o1 = max over p (aux_op1) for all o
GRBVar[] m_o1 = new GRBVar[O];
for (int i=0; i<O;i++) {
model.addGenConstrMax();
}
// Constraint 3: t_walk_o1 = m_o1 for all o
for (int i=0; i<O;i++) {
expr = new GRBLinExpr();
expr.addTerm(1,m_o1[i]);
model.addConstr(expr, GRB.EQUAL,t_walk_ow[i][0], "constraint8["+i+"]");
}
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