Solving the integer programming problem using the Benders decomposition approach

Mohammad Samiullah 0
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I wanted to solve the simple example, given below, using the Benders decomposition approach.

from docplex.mp.model import Model

# Creating model

    my_bdrex=Model('My Benders Model',log_output=True)
 
# Defining variables

    x_1=my_bdrex.integer_var(name='x_1', lb=0)

x_2=my_bdrex.integer_var(name='x_2', lb=0)

y_1=my_bdrex.integer_var(name='y_1', lb=0)

y_2=my_bdrex.integer_var(name='y_2', lb=0)

y_3=my_bdrex.integer_var(name='y_3', lb=0)

# Adding constraints
my_bdrex.add_constraint(2*x_1+4*x_2+4*y_1-2*y_2+3*y_3<=12)

my_bdrex.add_constraint(3*x_1+5*x_2+2*y_1+3*y_2-y_3<=10)

my_bdrex.add_constraint(x_1<=2)

my_bdrex.add_constraint(x_2<=2)

# Defining the objective function
objective_bdrex=4*x_1+7*x_2+2*y_1-3*y_2+y_3

# Solving the Model
my_bdrex.maximize(objective_bdrex)

my_bdrex.parameters.benders.strategy = 1

x_1.benders_annotation=0

x_2.benders_annotation=0

y_1.benders_annotation=1

y_2.benders_annotation=1

y_3.benders_annotation=1

my_bdrex_MP.print_information()

print(my_bdrex_MP.export_as_lp_string())

my_bdrex_MP.solve(clean_before_solve=True)

my_bdrex_MP.print_solution()

The above problem is an integer programming problem. I want to solve it by putting some variables in the master problem and remaining in the subproblem. But when I run the code I get the error: CPLEX Error 2002: Invalid Benders decomposition.

cplex python
1 Answers

In documentation Benders decomposition: CPLEX default

CPLEX implements a default Benders decomposition in certain situations.

We can read

if there are no continuous variables in your model, CPLEX raises an error stating that it cannot automatically decompose the model to apply a Benders strategy.

There is no continuous variable in your model, which explains why you got an error

Alex Fleischer0
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