Note

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Retrieve master and sub problems¶

This example shows how to obtain the master and sub problems from a complete mathematical programming model. This functionality is useful for users who have implemented a complete model (usually for comparison purposes) and want to implement a Benders decomposition method based on that model without manually defining the master and sub problems.

Create the original problem.

from gurobipy import Model, GRB
from benderslib import AnnotatedBenders
from benderslib.solvers import Gurobi


def make_original_problem():
    model = Model("Original")

    n_vars = 20
    y = model.addVars(n_vars, name="y", lb=1, ub=40, vtype=GRB.INTEGER)
    z = model.addVars(n_vars, name="z", lb=1, ub=40, vtype=GRB.CONTINUOUS)

    model.addConstr(y.sum() + z.sum() <= 50 * n_vars, "main_constr")
    model.addConstrs((2 * y[i] <= 2 * (i + 1) for i in range(n_vars)), name="constr_y")
    model.addConstrs((2 * y[i] + z[i] >= i for i in range(n_vars)), name="constr_yz")
    model.addConstrs((3 * z[i] <= 15 for i in range(n_vars)), name="constr_zx")

    model.setObjective(2 * y.sum() + 3 * z.sum(), sense=GRB.MINIMIZE)

    model.Params.OutputFlag = 0
    model.Params.LogToConsole = 0

    model.update()
    complicating_vars = [v.VarName for v in y.values()]
    return model, complicating_vars

Obtain the master and sub problems.

model, complicating_vars = make_original_problem()
master, sub = AnnotatedBenders.decompose(
    original_problem=model,
    solver=Gurobi,
    master_vars=complicating_vars,
    # True: return solver model instances;
    # False: return benderslib MasterProblem and SubProblem instances.
    solver_model=True
)
master.update()
print(master)