flexible_job_shop_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.

"""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.

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 primary/global 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()