尝试弄清楚如何使用 Python 优化员工的日程安排

Question

我有工人时间、班次和工资率的基本情况（如下所述）。我了解如何将其作为线性规划问题来解决，但我如何使用 SciPy Optimize 来解决/最小化支付给工人的金额？

import pandas as pd
import numpy as np
import scipy.optimize as sco
from io import StringIO



with StringIO(
'''Time Windows,Shift 1,Shift 2,Shift 3,Shift 4,Workers Required
    6:00 - 9:00,      1,      0,      0,      1,            55.0
   9:00 - 12:00,      1,      0,      0,      0,            46.0
  12:00 - 15:00,      1,      1,      0,      0,            59.0
  15:00 - 18:00,      0,      1,      0,      0,            23.0
  18:00 - 21:00,      0,      1,      1,      0,            60.0
  21:00 - 24:00,      0,      0,      1,      0,            38.0
   24:00 - 3:00,      0,      0,      1,      1,            20.0
    3:00 - 6:00,      0,      0,      0,      1,            30.0
      Wage_Rate,    135,    140,    190,    188,             0.0''') as f:
    df = pd.read_csv(f, skipinitialspace=True, index_col='Time Windows')

is_shift = df.columns.str.startswith('Shift')
is_wage = df.index == 'Wage_Rate'
shifts = df.loc[~is_wage, is_shift]
wage_rate = df.loc[is_wage, is_shift].squeeze()
workers_req = df.loc[~is_wage, 'Workers Required']

# create arrays
min_wages = wage_rate.values
min_workers = workers_req.values


# add constraints
constraints = (min_workers, min_wages)

# min 0 workers and increase in 10% increments up to 100%
# there is no 10% of a worker, but .1 could be multiplied by 'workers_req'
bound = (0.0,.1)

bounds = tuple(bound for item in range(min_workers))
result = sco.minimize(method='SLSQP', bounds=bounds, constraints=constraints)

一切都可以编译，直到最后两行代码。当我尝试将“边界”设置为“min_workers”时，出现此错误。