Permutation flow shop example

examples/contrib/permutation_flow_shop.py

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+#!/usr/bin/env python3
+# Copyright 2010-2024 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.
+
+"""This model implements the permutation flow shop problem (PFSP).
+
+In the PFSP, a set of jobs has to be processed on a set of machines. Each job
+must be processed on each machine in sequence and all jobs have to be processed
+in the same order on every machine. The objective is to minimize the makespan.
+"""
+
+import argparse
+from dataclasses import dataclass
+from itertools import product
+
+import numpy as np
+from ortools.sat.python import cp_model
+
+
+@dataclass
+class TaskType:
+    """
+    Small wrapper to hold the start, end, and interval variables of a task.
+    """
+
+    start: cp_model.IntVar
+    end: cp_model.IntVar
+    interval: cp_model.IntervalVar
+
+
+def permutation_flow_shop(
+    processing_times: np.ndarray,
+    time_limit: float = float("inf"),
+    log: bool = False,
+):
+    """
+    Solves the given permutation flow shop problem instance with OR-Tools.
+
+    Parameters
+    ----------
+    processing_times
+        An n-by-m matrix of processing times of the jobs on the machines.
+    time_limit
+        The time limit in seconds. If not set, the solver runs until an
+        optimal solution is found.
+    log
+        Whether to log the solver output. Default is False.
+
+    Raises
+    ------
+    ValueError
+        If the number of lines is greater than 1, i.e., the instance is a
+        distributed permutation flow shop problem.
+    """
+    m = cp_model.CpModel()
+    num_jobs, num_machines = processing_times.shape
+    horizon = processing_times.sum()
+
+    # Create interval variables for all tasks (each job/machine pair).
+    tasks = {}
+    for job, machine in product(range(num_jobs), range(num_machines)):
+        start = m.new_int_var(0, horizon, "")
+        end = m.new_int_var(0, horizon, "")
+        duration = processing_times[job][machine]
+        interval = m.new_interval_var(start, duration, end, "")
+        tasks[job, machine] = TaskType(start, end, interval)
+
+    # No overlap for all job intervals on this machine.
+    for machine in range(num_machines):
+        intervals = [tasks[job, machine].interval for job in range(num_jobs)]
+        m.add_no_overlap(intervals)
+
+    # Add precedence constraints between tasks of the same job.
+    for job, machine in product(range(num_jobs), range(num_machines - 1)):
+        pred = tasks[job, machine]
+        succ = tasks[job, machine + 1]
+        m.add(pred.end <= succ.start)
+
+    # Create arcs for circuit constraints.
+    arcs = []
+    for idx1 in range(num_jobs):
+        arcs.append((0, idx1 + 1, m.new_bool_var("start")))
+        arcs.append((idx1 + 1, 0, m.new_bool_var("end")))
+
+    lits = {}
+    for idx1, idx2 in product(range(num_jobs), repeat=2):
+        if idx1 != idx2:
+            lit = m.new_bool_var(f"{idx1} -> {idx2}")
+            lits[idx1, idx2] = lit
+            arcs.append((idx1 + 1, idx2 + 1, lit))
+
+    m.add_circuit(arcs)
+
+    # Enforce that the permutation of jobs is the same on all machines.
+    for machine in range(num_machines):
+        starts = [tasks[job, machine].start for job in range(num_jobs)]
+        ends = [tasks[job, machine].end for job in range(num_jobs)]
+
+        for idx1, idx2 in product(range(num_jobs), repeat=2):
+            if idx1 == idx2:
+                continue
+
+            # Since all machines share the same arc literals, if the literal
+            # i -> j is True, this enforces that job i is always scheduled
+            # before job j on all machines.
+            lit = lits[idx1, idx2]
+            m.add(ends[idx1] <= starts[idx2]).only_enforce_if(lit)
+
+    # Set minimizing makespan as objective.
+    obj_var = m.new_int_var(0, horizon, "makespan")
+    completion_times = [
+        tasks[(job, num_machines - 1)].end for job in range(num_jobs)
+    ]
+    m.add_max_equality(obj_var, completion_times)
+    m.minimize(obj_var)
+
+    solver = cp_model.CpSolver()
+    solver.parameters.log_search_progress = log
+    solver.parameters.max_time_in_seconds = time_limit
+
+    status_code = solver.Solve(m)
+    status = solver.StatusName(status_code)
+
+    print(f"Status: {status}")
+    print(f"Makespan: {solver.ObjectiveValue()}")
+
+    if status in ["OPTIMAL", "FEASIBLE"]:
+        start = [solver.Value(tasks[job, 0].start) for job in range(num_jobs)]
+        solution = np.argsort(start) + 1
+        print(f"Solution: {solution}")
+
+
+def parse_args():
+    parser = argparse.ArgumentParser("Solve a permutation flow shop problem.")
+
+    msg = "Time limit in seconds. Default is no time limit."
+    parser.add_argument(
+        "--time-limit", type=float, default=float("inf"), help=msg
+    )
+
+    msg = "Whether to log the solver output."
+    parser.add_argument("--log", action="store_true", help=msg)
+
+    return parser.parse_args()
+
+
+if __name__ == "__main__":
+    # VRF_10_5_2 instance from http://soa.iti.es/problem-instances.
+    # Optimal makespan is 698.
+    PROCESSING_TIMES = [
+        [79, 67, 10, 48, 52],
+        [40, 40, 57, 21, 54],
+        [48, 93, 49, 11, 79],
+        [16, 23, 19, 2, 38],
+        [38, 90, 57, 73, 3],
+        [76, 13, 99, 98, 55],
+        [73, 85, 40, 20, 85],
+        [34, 6, 27, 53, 21],
+        [38, 6, 35, 28, 44],
+        [32, 11, 11, 34, 27],
+    ]
+
+    args = parse_args()
+
+    permutation_flow_shop(
+        np.array(PROCESSING_TIMES), args.time_limit, args.log
+    )