minimal_jobshop_sat.py

#!/usr/bin/env python3
# Copyright 2010-2022 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.

# [START program]
"""Minimal jobshop example."""
# [START import]
import collections
from ortools.sat.python import cp_model
# [END import]


def main():
    """Minimal jobshop problem."""
    # Data.
    # [START data]
    jobs_data = [  # task = (machine_id, processing_time).
        [(0, 3), (1, 2), (2, 2)],  # Job0
        [(0, 2), (2, 1), (1, 4)],  # Job1
        [(1, 4), (2, 3)]  # Job2
    ]

    machines_count = 1 + max(task[0] for job in jobs_data for task in job)
    all_machines = range(machines_count)
    # Computes horizon dynamically as the sum of all durations.
    horizon = sum(task[1] for job in jobs_data for task in job)
    # [END data]

    # Create the model.
    # [START model]
    model = cp_model.CpModel()
    # [END model]

    # [START variables]
    # Named tuple to store information about created variables.
    task_type = collections.namedtuple('task_type', 'start end interval')
    # Named tuple to manipulate solution information.
    assigned_task_type = collections.namedtuple('assigned_task_type',
                                                'start job index duration')

    # Creates job intervals and add to the corresponding machine lists.
    all_tasks = {}
    machine_to_intervals = collections.defaultdict(list)

    for job_id, job in enumerate(jobs_data):
        for task_id, task in enumerate(job):
            machine = task[0]
            duration = task[1]
            suffix = '_%i_%i' % (job_id, task_id)
            start_var = model.NewIntVar(0, horizon, 'start' + suffix)
            end_var = model.NewIntVar(0, horizon, 'end' + suffix)
            interval_var = model.NewIntervalVar(start_var, duration, end_var,
                                                'interval' + suffix)
            all_tasks[job_id, task_id] = task_type(start=start_var,
                                                   end=end_var,
                                                   interval=interval_var)
            machine_to_intervals[machine].append(interval_var)
    # [END variables]

    # [START constraints]
    # Create and add disjunctive constraints.
    for machine in all_machines:
        model.AddNoOverlap(machine_to_intervals[machine])

    # Precedences inside a job.
    for job_id, job in enumerate(jobs_data):
        for task_id in range(len(job) - 1):
            model.Add(all_tasks[job_id, task_id +
                                1].start >= all_tasks[job_id, task_id].end)
    # [END constraints]

    # [START objective]
    # Makespan objective.
    obj_var = model.NewIntVar(0, horizon, 'makespan')
    model.AddMaxEquality(obj_var, [
        all_tasks[job_id, len(job) - 1].end
        for job_id, job in enumerate(jobs_data)
    ])
    model.Minimize(obj_var)
    # [END objective]

    # Creates the solver and solve.
    # [START solve]
    solver = cp_model.CpSolver()
    status = solver.Solve(model)
    # [END solve]

    # [START print_solution]
    if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:
        print('Solution:')
        # Create one list of assigned tasks per machine.
        assigned_jobs = collections.defaultdict(list)
        for job_id, job in enumerate(jobs_data):
            for task_id, task in enumerate(job):
                machine = task[0]
                assigned_jobs[machine].append(
                    assigned_task_type(start=solver.Value(
                        all_tasks[job_id, task_id].start),
                                       job=job_id,
                                       index=task_id,
                                       duration=task[1]))

        # Create per machine output lines.
        output = ''
        for machine in all_machines:
            # Sort by starting time.
            assigned_jobs[machine].sort()
            sol_line_tasks = 'Machine ' + str(machine) + ': '
            sol_line = '           '

            for assigned_task in assigned_jobs[machine]:
                name = 'job_%i_task_%i' % (assigned_task.job,
                                           assigned_task.index)
                # Add spaces to output to align columns.
                sol_line_tasks += '%-15s' % name

                start = assigned_task.start
                duration = assigned_task.duration
                sol_tmp = '[%i,%i]' % (start, start + duration)
                # Add spaces to output to align columns.
                sol_line += '%-15s' % sol_tmp

            sol_line += '\n'
            sol_line_tasks += '\n'
            output += sol_line_tasks
            output += sol_line

        # Finally print the solution found.
        print(f'Optimal Schedule Length: {solver.ObjectiveValue()}')
        print(output)
    else:
        print('No solution found.')
    # [END print_solution]

    # Statistics.
    # [START statistics]
    print('\nStatistics')
    print('  - conflicts: %i' % solver.NumConflicts())
    print('  - branches : %i' % solver.NumBranches())
    print('  - wall time: %f s' % solver.WallTime())
    # [END statistics]


if __name__ == '__main__':
    main()
# [END program]