conditionally apply constraints in optimization problems
AnsweredIm working on a problem and chose guroby as a tool for it, however i am going through an issue. I want to apply a constraint if and only if one of the variables exceeds a certain threshold. Variables are integers, and my desired constraint is the following;
with variables x[0] x[1] x[2] x[3] being the load of products 1-4 carried by a truck x, if x[2] is above 3, make x[1] be at least 4. Otherwise if x[2] isnt >=3 ignore this constraint.
How could this be done through using gurobi?
m = gp.Model()
# Define the decision variables
x = m.addVars(4, name="x", ub=5)
y = m.addVars(4, name="y",ub=5)
z = m.addVars(4, name="z",ub=5)
w = m.addVars(4, name="w",ub=5)
#trucks
xtot = x[0]+x[1]+x[2]+x[3]
ytot = y[0]+y[1]+y[2]+y[3]
ztot = z[0]+z[1]+z[2]+z[3]
wtot = w[0]+w[1]+w[2]+w[3]
#box types:
foods=x[0]+y[0]+z[0]+w[0]
meds=x[1]+y[1]+z[1]+w[1]
surgs=x[2]+y[2]+z[2]+w[2]
cloths=x[3]+y[3]+z[3]+w[3]
# Define the objective function
m.setObjective(xtot + ytot + ztot + wtot, sense=gp.GRB.MAXIMIZE)
# Define the constraints
# max bus load
m.addConstr(xtot <= 10)
m.addConstr(ytot <= 10)
m.addConstr(ztot <= 9)
m.addConstr(wtot <= 9)
#boxes available
m.addConstr(foods <= 12)
m.addConstr(meds <= 17)
m.addConstr(surgs <= 11)
m.addConstr(cloths <= 18)
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Gurobi Staff
Have you seen our Knowledge Base article How do I model conditional statements in Gurobi? This may be useful to you.
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Thanks for the suggestion! I did read that one previously, and all the documentation i could find in gurobi, but it showed a result which differs with the one i need in the sense that:
1- it is continuous rather than discrete values
2- the condition compares the value of two variables rather than comparing a single variable to a threshold value.
Tryed to apply it to my code but i couldnt make it work, im sure the result is close to what that one article promotes, but im having a hard time adapting it to my case.
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this is how i applyed it:
eps = 0.0001
M = 5 + eps
xb = m.addVar(vtype=gp.GRB.BINARY)
m.addConstr(x[2] >= 3 + eps - M * (1 - xb))
m.addConstr(x[2] <= 3 + M * xb)
m.addConstr((xb == 1) >> (x[1] >= 4))0 -
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ok im so sorry for the dumb question, found out all i had to do is take out the 3 in the second constraint and substitute by a 2 since both statements were triggered with a x[2] == 3, thank you so much for the help, have a great day.
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Since your x[2] variable is integer, you do not need the eps value in the first constraint, it might even lead to numerical issues (or forbid x[2] == 3 in some cases).
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