如何为 Google 的 OR-Tools Job Shop 问题添加空闲时间？

Question

我是 Google OR-Tools（以及一般的约束编程）的新手，我正在尝试向 Jobshop 示例添加空闲时间。

我的工作车间示例可以在这里找到： https://developers.google.com/optimization/scheduling/job_shop#entire-program

我做了一些修改，因为我包含了一个截止日期变量。 现在我唯一想添加到程序中的是一个空闲变量。 例如，完成一项任务的机器在开始下一项任务之前必须有一定的空闲时间。 我如何在代码中实现它？ 我的代码：

import collections

# Import Python wrapper for or-tools CP-SAT solver.
from ortools.sat.python import cp_model


def MinimalJobshopSat():
"""Minimal jobshop problem."""
# Create the model.
    model = cp_model.CpModel()

    jobs_data = [  # task = (machine_id, processing_time,deadline).
    [(0, 3, 7), (1, 2, 7), (2, 2, 7)],  # Job0
    [(0, 2, 13), (2, 1, 13), (1, 4, 13)],  # Job1
    [(1, 4, 13), (2, 3, 13)]  # Job2
]


#counts the number of machines (3 in this case)
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)

# Named tuple to store information about created variables.
task_type = collections.namedtuple('task_type', 'start end deadline 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]
        deadline = task[2]
        suffix = '_%i_%i' % (job_id, task_id)
        
        start_var = model.NewIntVar(0, horizon, 'start' + suffix)
        
        end_var = model.NewIntVar(0, deadline, 'end' + suffix)
    
        interval_var = model.NewIntervalVar(start_var, duration, end_var,
                                            'interval' + suffix)
        deadline_var = model.NewIntVar(deadline, deadline,
                                            'deadline' + suffix)
       
        all_tasks[job_id, task_id] = task_type(
            start=start_var, end=end_var, deadline=deadline_var, interval=interval_var)
        
        machine_to_intervals[machine].append(interval_var)
        
# 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)

for job_id, job in enumerate(jobs_data):
    for task_id in range(len(job) - 1):
        model.Add(all_tasks[job_id, task_id].end <= all_tasks[job_id, task_id].deadline)
        
    
# 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)

# Solve model.
solver = cp_model.CpSolver()
status = solver.Solve(model)

if status == cp_model.OPTIMAL:
    # 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_%i' % (assigned_task.job, assigned_task.index)
            # Add spaces to output to align columns.
            sol_line_tasks += '%-10s' % 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 += '%-10s' % sol_tmp

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

    # Finally print the solution found.
    print('Optimal Schedule Length: %i' % solver.ObjectiveValue())
    print(output)


MinimalJobshopSat()

Answer 1

您可以更改此约束：

# 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)

到

model.Add(all_tasks[job_id, task_id +
                            1].start >= all_tasks[job_id, task_id].end + idle_time)

有关更复杂的示例（任务之间的距离），请参阅： https://github.com/google/or-tools/blob/stable/examples/python/jobshop_ft06_distance_sat.py