204 lines
7.5 KiB
Python
Executable File
204 lines
7.5 KiB
Python
Executable File
#!/usr/bin/env python3
|
|
# Copyright 2010-2021 Google LLC
|
|
# Licensed under the Apache License, Version 2.0 (the "License");
|
|
# you may not use this file except in compliance with the License.
|
|
# You may obtain a copy of the License at
|
|
#
|
|
# http://www.apache.org/licenses/LICENSE-2.0
|
|
#
|
|
# Unless required by applicable law or agreed to in writing, software
|
|
# distributed under the License is distributed on an "AS IS" BASIS,
|
|
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
# See the License for the specific language governing permissions and
|
|
# limitations under the License.
|
|
"""Solves a flexible jobshop problems with the CP-SAT solver.
|
|
|
|
A jobshop is a standard scheduling problem when you must sequence a
|
|
series of task_types on a set of machines. Each job contains one task_type per
|
|
machine. The order of execution and the length of each job on each
|
|
machine is task_type dependent.
|
|
|
|
The objective is to minimize the maximum completion time of all
|
|
jobs. This is called the makespan.
|
|
"""
|
|
|
|
# overloaded sum() clashes with pytype.
|
|
# pytype: disable=wrong-arg-types
|
|
|
|
import collections
|
|
|
|
from ortools.sat.python import cp_model
|
|
|
|
|
|
class SolutionPrinter(cp_model.CpSolverSolutionCallback):
|
|
"""Print intermediate solutions."""
|
|
|
|
def __init__(self):
|
|
cp_model.CpSolverSolutionCallback.__init__(self)
|
|
self.__solution_count = 0
|
|
|
|
def on_solution_callback(self):
|
|
"""Called at each new solution."""
|
|
print('Solution %i, time = %f s, objective = %i' %
|
|
(self.__solution_count, self.WallTime(), self.ObjectiveValue()))
|
|
self.__solution_count += 1
|
|
|
|
|
|
def flexible_jobshop():
|
|
"""Solve a small flexible jobshop problem."""
|
|
# Data part.
|
|
jobs = [ # task = (processing_time, machine_id)
|
|
[ # Job 0
|
|
[(3, 0), (1, 1), (5, 2)], # task 0 with 3 alternatives
|
|
[(2, 0), (4, 1), (6, 2)], # task 1 with 3 alternatives
|
|
[(2, 0), (3, 1), (1, 2)], # task 2 with 3 alternatives
|
|
],
|
|
[ # Job 1
|
|
[(2, 0), (3, 1), (4, 2)],
|
|
[(1, 0), (5, 1), (4, 2)],
|
|
[(2, 0), (1, 1), (4, 2)],
|
|
],
|
|
[ # Job 2
|
|
[(2, 0), (1, 1), (4, 2)],
|
|
[(2, 0), (3, 1), (4, 2)],
|
|
[(3, 0), (1, 1), (5, 2)],
|
|
],
|
|
]
|
|
|
|
num_jobs = len(jobs)
|
|
all_jobs = range(num_jobs)
|
|
|
|
num_machines = 3
|
|
all_machines = range(num_machines)
|
|
|
|
# Model the flexible jobshop problem.
|
|
model = cp_model.CpModel()
|
|
|
|
horizon = 0
|
|
for job in jobs:
|
|
for task in job:
|
|
max_task_duration = 0
|
|
for alternative in task:
|
|
max_task_duration = max(max_task_duration, alternative[0])
|
|
horizon += max_task_duration
|
|
|
|
print('Horizon = %i' % horizon)
|
|
|
|
# Global storage of variables.
|
|
intervals_per_resources = collections.defaultdict(list)
|
|
starts = {} # indexed by (job_id, task_id).
|
|
presences = {} # indexed by (job_id, task_id, alt_id).
|
|
job_ends = []
|
|
|
|
# Scan the jobs and create the relevant variables and intervals.
|
|
for job_id in all_jobs:
|
|
job = jobs[job_id]
|
|
num_tasks = len(job)
|
|
previous_end = None
|
|
for task_id in range(num_tasks):
|
|
task = job[task_id]
|
|
|
|
min_duration = task[0][0]
|
|
max_duration = task[0][0]
|
|
|
|
num_alternatives = len(task)
|
|
all_alternatives = range(num_alternatives)
|
|
|
|
for alt_id in range(1, num_alternatives):
|
|
alt_duration = task[alt_id][0]
|
|
min_duration = min(min_duration, alt_duration)
|
|
max_duration = max(max_duration, alt_duration)
|
|
|
|
# Create main interval for the task.
|
|
suffix_name = '_j%i_t%i' % (job_id, task_id)
|
|
start = model.NewIntVar(0, horizon, 'start' + suffix_name)
|
|
duration = model.NewIntVar(min_duration, max_duration,
|
|
'duration' + suffix_name)
|
|
end = model.NewIntVar(0, horizon, 'end' + suffix_name)
|
|
interval = model.NewIntervalVar(start, duration, end,
|
|
'interval' + suffix_name)
|
|
|
|
# Store the start for the solution.
|
|
starts[(job_id, task_id)] = start
|
|
|
|
# Add precedence with previous task in the same job.
|
|
if previous_end is not None:
|
|
model.Add(start >= previous_end)
|
|
previous_end = end
|
|
|
|
# Create alternative intervals.
|
|
if num_alternatives > 1:
|
|
l_presences = []
|
|
for alt_id in all_alternatives:
|
|
alt_suffix = '_j%i_t%i_a%i' % (job_id, task_id, alt_id)
|
|
l_presence = model.NewBoolVar('presence' + alt_suffix)
|
|
l_start = model.NewIntVar(0, horizon, 'start' + alt_suffix)
|
|
l_duration = task[alt_id][0]
|
|
l_end = model.NewIntVar(0, horizon, 'end' + alt_suffix)
|
|
l_interval = model.NewOptionalIntervalVar(
|
|
l_start, l_duration, l_end, l_presence,
|
|
'interval' + alt_suffix)
|
|
l_presences.append(l_presence)
|
|
|
|
# Link the master variables with the local ones.
|
|
model.Add(start == l_start).OnlyEnforceIf(l_presence)
|
|
model.Add(duration == l_duration).OnlyEnforceIf(l_presence)
|
|
model.Add(end == l_end).OnlyEnforceIf(l_presence)
|
|
|
|
# Add the local interval to the right machine.
|
|
intervals_per_resources[task[alt_id][1]].append(l_interval)
|
|
|
|
# Store the presences for the solution.
|
|
presences[(job_id, task_id, alt_id)] = l_presence
|
|
|
|
# Select exactly one presence variable.
|
|
model.AddExactlyOne(l_presences)
|
|
else:
|
|
intervals_per_resources[task[0][1]].append(interval)
|
|
presences[(job_id, task_id, 0)] = model.NewConstant(1)
|
|
|
|
job_ends.append(previous_end)
|
|
|
|
# Create machines constraints.
|
|
for machine_id in all_machines:
|
|
intervals = intervals_per_resources[machine_id]
|
|
if len(intervals) > 1:
|
|
model.AddNoOverlap(intervals)
|
|
|
|
# Makespan objective
|
|
makespan = model.NewIntVar(0, horizon, 'makespan')
|
|
model.AddMaxEquality(makespan, job_ends)
|
|
model.Minimize(makespan)
|
|
|
|
# Solve model.
|
|
solver = cp_model.CpSolver()
|
|
solution_printer = SolutionPrinter()
|
|
status = solver.Solve(model, solution_printer)
|
|
|
|
# Print final solution.
|
|
for job_id in all_jobs:
|
|
print('Job %i:' % job_id)
|
|
for task_id in range(len(jobs[job_id])):
|
|
start_value = solver.Value(starts[(job_id, task_id)])
|
|
machine = -1
|
|
duration = -1
|
|
selected = -1
|
|
for alt_id in range(len(jobs[job_id][task_id])):
|
|
if solver.Value(presences[(job_id, task_id, alt_id)]):
|
|
duration = jobs[job_id][task_id][alt_id][0]
|
|
machine = jobs[job_id][task_id][alt_id][1]
|
|
selected = alt_id
|
|
print(
|
|
' task_%i_%i starts at %i (alt %i, machine %i, duration %i)' %
|
|
(job_id, task_id, start_value, selected, machine, duration))
|
|
|
|
print('Solve status: %s' % solver.StatusName(status))
|
|
print('Optimal objective value: %i' % solver.ObjectiveValue())
|
|
print('Statistics')
|
|
print(' - conflicts : %i' % solver.NumConflicts())
|
|
print(' - branches : %i' % solver.NumBranches())
|
|
print(' - wall time : %f s' % solver.WallTime())
|
|
|
|
|
|
flexible_jobshop()
|