Dual Variable for Facility Loaction Problem
Hello,
I am trying to solve the Facility Location Problem using Benders Decomposition. However, I noticed that the FLP is not particularly in standard form. I want to use .getAttr("Pi") to get the dual variable of the subproblem. However, I am unsure if I can retrieve the dual variable for such problems. In addition, is it possible to get the dual variable with equality and inequality constraints?
Is there a workaround or what should I do?
Here is the code if it helps:
import gurobipy as gp
from gurobipy import GRB
from itertools import product
import numpy as np
import matplotlib.pyplot as plt
class Benders_FLP():
def __init__(self, num_customers, num_facilities, customers, facilities, setup_cost) > None:
self.cartesian_prod = list(product(range(num_customers), range(num_facilities)))
self.shipping_cost = {(c,f) : compute_distance(customers[c], facilities[f]) for c, f in self.cartesian_prod}
self.num_customers = num_customers
self.num_facilities = num_facilities
self.customers = customers
self. facilities = facilities
self.setup_cost = setup_cost
def RMP(self):
model = gp.Model()
model.setParam("LogToConsole", 0)
select_facilities = model.addVars(self.num_facilities, vtype=GRB.BINARY)
theta = model.addMVar(1, lb = 0, vtype=GRB.CONTINUOUS)
model.setObjective(select_facilities.prod(self.setup_cost)+ theta, GRB.MINIMIZE)
model.update()
model.optimize()
select = get_selected_locations(select_facilities, self.num_facilities)
return model.ObjVal, select_facilities, theta.x, select
def SP(self, select_facilities):
sub = gp.Model()
sub.setParam("LogToConsole", 0)
assign_customers = sub.addVars(self.cartesian_prod,ub=1,lb=0, vtype=GRB.CONTINUOUS)
sub.addConstrs((assign_customers[(c,f)] <= select_facilities[f] for c,f in self.cartesian_prod), name='Setup2ship')
sub.addConstrs((gp.quicksum(assign_customers[(c,f)] for f in range(self.num_facilities)) == 1 for c in range(self.num_customers)), name='Demand')
sub.setObjective(assign_customers.prod(self.shipping_cost), GRB.MINIMIZE)
return sub.ObjVal, assign_customers

Your subproblem is a Linear Program (LP), which is advantageous because dual values (pi values) can be retrieved for convex, continuous models. This capability applies to both equality and inequality constraints. This is true whether or not the model is written in standard or cononical form.
To retrieve the dual values, the model must be optimized and have a feasible solution. In your code, it's important to ensure that the
sub.optimize()
method is called after setting the objective function in your subproblem.To retrieve pi values
 Define your model
 Optimize it using the Model.optimize() method
 Retrieve the dual values using the Constraint.getAttr("Pi") method.
Example with
afiro.mps
Here is an example using the
afiro.mps
model, which comes prepackaged with Gurobi:import gurobipy as gp
from gurobipy import GRB
# Read/build model
# Here I am using the example LP model afiro that comes prepackaged with Gurobi
m = gp.read('afiro.mps')
# Optimize model
m.optimize()
# Print all dual values
for c in m.getConstrs():
print(f"Constraint '{c.ConstrName}' has a pi value of {c.getAttr('Pi')}")For more details on the pi attribute, see Pi  Gurobi Optimization.
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