PuLP with Gurobi on the side

Using Gurobi and PuLP for LP:

import pulp

• Retrieves a solver interface for Gurobi using PuLP. It allows one to use Gurobi as the solver when defining optimization problems in PuLP:

  solver = pulp.getSolver('GUROBI')
  

• Silence pulp solving console output:

  pulp.LpSolverDefault.msg = 0
  

• Setup the model with variables, objectives and constraints

  # Initialize the LP model
  K = 3
  B = 4
  model = pulp.LpProblem("model_name", pulp.LpMaximize)
  z = pulp.LpVariable.dicts("z", range(K), lowBound=0)
  
  # Objective function
  model += pulp.lpSum(z), "Objective"        
  
  # Constraints
  model += pulp.lpSum([z[k] for k in range(K)]) <= B, "Budget_Constraint"
  

• Solve the problem and check status

  model.solve()
  print(pulp.LpStatus[self.model.status] == pulp.LpStatus[1])
  

• Variable results:

  for k in range(K):
      print(f"z = {pulp.value(z[k])}")
  

• Constraint slackness:

  if model.constraints["Budget_Constraint"].pi != 0:
      print("The budget constraint is tight.")
  else:
      print("The budget constraint is not tight.")
  

Put together:

import pulp
pulp.LpSolverDefault.msg = 0

K = 3
B = 4

# Initialization
model = pulp.LpProblem("model_name", pulp.LpMaximize)
z = pulp.LpVariable.dicts("z", range(K), lowBound=0)

# Objective function
model += pulp.lpSum(z[k] for k in range(K)), "Objective"

# Constraints
budget_constraint = pulp.lpSum(z[k] for k in range(K)) <= B
model += budget_constraint, "Budget_Constraint"

# Solve the model
model.solve()

# Check if the model is solved optimally
if pulp.LpStatus[model.status] == 'Optimal':
    print("Model solved optimally.")
else:
    print("Model not solved optimally.")

# Print variable values
for k in range(K):
    print(f"z[{k}] = {pulp.value(z[k])}")

# Accessing and printing the dual value of the budget constraint
print("Dual value (shadow price) of the budget constraint:", model.constraints["Budget_Constraint"].pi)