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Objective function result

Answered
Sab
Gurobi-versary
First Comment
First Question

Hi!

I am currently working on optimizing the average coverage of different locations. 

The sets are:

Ict = [ "1","5","4"] #, "77003", "77063"] # Candidate  locations
It = [ "9","6","8" ] #"77005","77004","77010"] # Existing locations
Ic = [ "2","3","7"] #"77020", "77502" , "77503"] #In-clinic locations
Ictt = ["1","5","4", "9","6","8"] # candidate and existing 
I = ["1","5","4", "9","6","8","2","3","7"] #all locations

J = ["4","11","7"] #demand locations
K = ["African", "Hispanic", "Asian", "White"] #population 

Constant parameters:

l = 10 # number of patients for each available location
b = 6 # new locations that are going to be chosen
n = 20 # Number of patients

model = Model("Base Model")

Variables:

x = model.addVars(I, vtype=GRB.BINARY, name = "x")  # locations 
#E = model.addVars(I, I, vtype=GRB.BINARY, name = "E")  #auxiliary variable 

Contraints: 

a = model.addConstr((sum(x[i] for i in Ict) <= b), name="a")

for i in Ictt:
     model.addConstr(quicksum(n * (1 - q[i,j,k])
     for j in J for k in K) >= l * x[i])

Ict_1 = ["2"]
for i in Ict_1:
        model.addConstr(x["1"]+ x[i] <= 1)

for i in It:
     model.addConstr(x[i] == 1 , name = "d")

for i in Ic:
     model.addConstr(x[i] == 1 , name = "e")

As of know for simplicity, I am setting the obj function to zero:

obj = 0

model.setObjective( obj, GRB.MAXIMIZE)

model.optimize()

If I only evaluate variable x, then the answer is:

x[1] 0
x[5] 1
x[4] 1
x[9] 1
x[6] 1
x[8] 1
x[2] 1
x[3] 1
x[7] 1
Obj: -0

which makes sense x[1] is being limited by constraint 3 so it should be giving 0. 

Nevertheless, as soon as I add the auxiliary variable E, the answer changes to:

x[1] 0
x[5] 0
x[4] 0
x[9] 1
x[6] 1
x[8] 1
x[2] 1
x[3] 1
x[7] 1
E[1,1] 1
E[1,5] 1
E[1,4] 1
E[1,9] 1
E[1,6] 1
E[1,8] 1
E[1,2] 1
E[1,3] 1
E[1,7] 1
E[5,1] 1
...
E[7,5] 1
E[7,4] 1
E[7,9] 1
E[7,6] 1
E[7,8] 1
E[7,2] 1
E[7,3] 1
E[7,7] 1
Obj: -0

My question is why as soon as I included E, the candidate locations x[5] and x[4] changed to zero even when the constraints remained the same? What is this variable doing that is limiting the candidate locations?

 

0

Comments

2 comments

Date Votes
  • Official comment
    Simranjit Kaur
    Gurobi Staff Gurobi Staff
    This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
  • Eli Towle
    Gurobi Staff Gurobi Staff
    • Edited

    Hi Sab,

    The additional variables don't limit the candidate locations. Because your objective is \( 0 \), Gurobi just looks for a feasible solution. There is no incentive in the objective function to utilize additional candidate locations.

    If you solve the exact same model using the exact same parameters, Gurobi should return the same result. Although the \( \texttt{E} \) variables don't show up in any constraints, adding them results in a different model. Thus, Gurobi will not necessarily return the exact same solution as it did when you solved the problem without these variables. You can read more about this in the article Is Gurobi Optimizer deterministic?.

    Thanks,

    Eli

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