我已成功实施了一项计划,在该计划中,我为一周中的每一天分配Ntruck drivers
到Mgathering hubs
。我实施的约束条件包括:
该计划运行平稳,满足总体目标,并为每个轮毂驱动器对输出以下形式的时间表:
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Hub Driver
Hub 1 Driver_20 1 0 0 0 0 0 0
Hub 2 Driver_20 0 0 0 0 0 0 0
Hub 3 Driver_20 0 0 0 0 0 0 0
Hub 4 Driver_20 0 0 0 0 0 0 0
Hub 5 Driver_20 0 1 0 0 0 0 0
Hub 6 Driver_20 0 0 0 0 1 0 0
Hub 7 Driver_20 0 0 0 1 0 1 1
但是,我想添加一个额外约束,强制驾驶员在一个中心工作,如果可能的话,而不是将他们的工作日分成多个中心,即在将驾驶员分配到不同的中心之前,最大限度地提高在一个中心的工作效率
例如,在上面的输出中,我们看到驱动程序在不同的中心工作3天,在中心7工作3天。我们如何编写一个约束,使驱动程序被分配(如果可能的话)在一个中心工作(如果可能的话)
请在下面找到我的代码
多谢各位
import pulp
import pandas as pd
import numpy as np
pd.set_option('display.max_rows', None)
pd.set_option('display.max_columns', None)
pd.set_option('display.width', 2000)
pd.set_option('display.float_format', '{:20,.2f}'.format)
pd.set_option('display.max_colwidth', None)
day_requirement = [[2, 2, 3, 2, 5, 2, 2],
[2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2],
[3, 3, 3, 3, 3, 3, 3],
[2, 2, 2, 2, 2, 2, 2],
[2, 2, 2, 2, 2, 2, 2],
[4, 4, 4, 4, 4, 4, 4],
]
total_day_requirements = ([sum(x) for x in zip(*day_requirement)])
hub_names = {0: 'Hub 1',
1: 'Hub 2',
2: 'Hub 3',
3: 'Hub 4',
4: 'Hub 5',
5: 'Hub 6',
6: 'Hub 7'}
total_drivers = max(total_day_requirements) # number of drivers
total_days = 7 # The number of days in week
total_hubs = len(day_requirement) # number of hubs
def schedule(drivers, days, hubs):
driver_names = ['Driver_{}'.format(i) for i in range(drivers)]
var = pulp.LpVariable.dicts('VAR', (range(hubs), range(drivers), range(days)), 0, 1, 'Binary')
problem = pulp.LpProblem('shift', pulp.LpMinimize)
obj = None
for h in range(hubs):
for driver in range(drivers):
for day in range(days):
obj += var[h][driver][day]
problem += obj
# schedule must satisfy daily requirements of each hub
for day in range(days):
for h in range(hubs):
problem += pulp.lpSum(var[h][driver][day] for driver in range(drivers)) == \
day_requirement[h][day]
# a driver cannot work more than 6 days
for driver in range(drivers):
problem += pulp.lpSum([var[h][driver][day] for day in range(days) for h in range(hubs)]) <= 6
# if a driver works one day at a hub, he cannot work that day in a different hub obviously
for driver in range(drivers):
for day in range(days):
problem += pulp.lpSum([var[h][driver][day] for h in range(hubs)]) <= 1
# Solve problem.
status = problem.solve(pulp.PULP_CBC_CMD(msg=0))
idx = pd.MultiIndex.from_product([hub_names.values(), driver_names], names=['Hub', 'Driver'])
col = ['Monday', 'Tuesday', 'Wednesday', 'Thursday', 'Friday', 'Saturday', 'Sunday']
dashboard = pd.DataFrame(0, idx, col)
for h in range(hubs):
for driver in range(drivers):
for day in range(days):
if var[h][driver][day].value() > 0.0:
dashboard.loc[hub_names[h], driver_names[driver]][col[day]] = 1
driver_table = dashboard.groupby('Driver').sum()
driver_sums = driver_table.sum(axis=1)
# print(driver_sums)
day_sums = driver_table.sum(axis=0)
# print(day_sums)
print("Status", pulp.LpStatus[status])
if (driver_sums > 6).any():
print('One or more drivers have been allocated more than 6 days of work so we must add one '
'driver: {}->{}'.format(len(driver_names), len(driver_names) + 1))
schedule(len(driver_names) + 1, days, hubs)
else:
print(dashboard)
print(driver_sums)
print(day_sums)
for driver in range(drivers):
driver_name = 'Driver_{}'.format(driver)
print(dashboard[np.in1d(dashboard.index.get_level_values(1), [driver_name])])
schedule(total_drivers, total_days, total_hubs)
您可以添加二进制变量
z
,指示集线器上的驱动程序是否处于活动状态:然后将您的目标更改为(最小化集线器上活动的驱动程序总数):
添加约束以将
z
与var
连接:然而,该模型更为复杂,寻找最优解似乎需要一段时间。您可以设置超时(此处为10秒)以获得解决方案:
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