def _add_production_variables(num_types: int, num_time_periods: int,
solver: Solver) -> Dict[V, Variable]:
"""Create production variables.
A production variable $x^t_p$ is a binary variable which is one if and only if an item of
type $t$ is produced in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each production variable to its solver variable
"""
production_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(num_time_periods)):
production_vars[V(type=item_type,
period=time_period)] = solver.BoolVar(
name=f'x_{item_type}_{time_period}')
module_logger.info(
f'Created {len(production_vars)} production variables.')
return production_vars
def _add_configuration_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[V, Variable]:
"""Create configuration variables.
A configuration variable $y^t_p$ is a binary variable which is one if and only if the
machine is configured for type $t$ in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each configuration tuple to its solver variable
"""
configuration_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(num_time_periods)):
configuration_vars[V(type=item_type,
period=time_period)] = solver.BoolVar(
name=f'y_{item_type}_{time_period}')
module_logger.info(
f'Created {len(configuration_vars)} configuration variables.')
return configuration_vars
def _add_transition_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[W, Variable]:
"""Create transition variables.
A transition variable $u^ij_p$ is a binary variable which is one if and only if the
machine's configuration changes from type $i$ to type $j$ in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each transition variable to its solver variable
"""
transition_vars = dict()
for type_i, type_j, time_period in product(range(num_types),
range(num_types),
range(1, num_time_periods)):
transition_vars[W(from_type=type_i,
to_type=type_j,
from_period=time_period - 1,
to_period=time_period)] = solver.BoolVar(
name=f'u_{type_i}_{type_j}_{time_period}')
module_logger.info(
f'Created {len(transition_vars)} transition variables.')
return transition_vars