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(2x_1+4x_2+4y_1-2y_2+3*y_3<=12)

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

my_bdrex.add_constraint(x_1<=2)

my_bdrex.add_constraint(x_2<=2)

Defining the objective function

objective_bdrex=4x_1+7x_2+2y_1-3y_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…………