# Issue

*This Content is from Stack Overflow. Question asked by Mohammad Samiullah *

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 got the error: CPLEX Error 2002: Invalid Benders decomposition.

I request here to the community please help me to solve it by using the Benders decomposition approach.

Thanks…………

# Solution

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

This Question was asked in StackOverflow by Mohammad Samiullah and Answered by Alex Fleischer It is licensed under the terms of CC BY-SA 2.5. - CC BY-SA 3.0. - CC BY-SA 4.0.