Trying to Optimize Process Using Linear Programming. Getting error about: IndexError: index 1 is out of bounds for axis 0 with size 1

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英文:

Trying to Optimize Process Using Linear Programming. Getting error about: IndexError: index 1 is out of bounds for axis 0 with size 1

问题

在这行代码中：

  1. prob += lpSum([w[j] * y[j] for j in range(n)])

你遇到了这个错误：

  1. IndexError: index 1 is out of bounds for axis 0 with size 1

这个错误是因为在 w 中的数据是一个一维数组，但你尝试访问索引1，而实际上只有一个元素，索引应为0。你可以尝试将 w 定义为一个标量值而不是一个数组，或者根据你的需求调整代码来解决这个错误。

英文:

I am trying to optimize worker's schedules, based on the following dataframe.

  1.     Time Windows Shift 1 Shift 2 Shift 3 Shift 4  Workers Required
  2. 0    6:00 - 9:00       1       0       0       1              55.0
  3. 1   9:00 - 12:00       1       0       0       0              46.0
  4. 2  12:00 - 15:00       1       1       0       0              59.0
  5. 3  15:00 - 18:00       0       1       0       0              23.0
  6. 4  18:00 - 21:00       0       1       1       0              60.0
  7. 5  21:00 - 24:00       0       0       1       0              38.0
  8. 6   24:00 - 3:00       0       0       1       1              20.0
  9. 7    3:00 - 6:00       0       0       0       1              30.0
  10. 8      Wage_Rate     135     140     190     188               0.0

First (create dataframe):

  1. import pandas as pd
  2. df = pd.read_clipboard(sep='\\s+')
  3. df = pd.DataFrame(df)

Here is the code that I am testing.

  1. import pandas as pd
  2. import pulp
  3. from pulp import LpMaximize, LpMinimize, LpProblem, LpStatus, lpSum, LpVariable
  4. import numpy as np
  7. df = df.fillna(0).applymap(lambda x: 1 if x == "X" else x)
  9. df.set_index('Time Windows')
  10. a = df.drop(columns=["Workers Required"]).values
  11. a
  14. df.drop(df.tail(1).index,inplace=True)
  15. print(df.shape)
  18. df = df.fillna(0).applymap(lambda x: 1 if x == "X" else x)
  19. print(df.shape)
  22. a = df.to_numpy()
  23. a
  26. # number of shifts
  27. n = a.shape[0]
  30. # number of time windows
  31. T = a.shape[0]
  34. # number of workers required per time window
  35. d = df["Workers Required"].values
  38. # wage rate per shift
  39. #Get last row of dataframe
  40. last_row = df.iloc[-1:,1:]
  41. #Get last row of dataframe as numpy array
  42. w = last_row.to_numpy()
  43. w
  46. # Decision variables
  47. y = LpVariable.dicts("num_workers", list(range(n)), lowBound=0, cat="Integer")
  48. y
  51. # Create problem
  52. prob = LpProblem("scheduling_workers", LpMinimize)
  56. prob += lpSum([w[j] * y[j] for j in range(n)])
  59. for t in range(T):
  60.     prob += lpSum([a[t, j] * y[j] for j in range(n)]) >= d[t]
  63. prob.solve()
  64. print("Status:", LpStatus[prob.status])
  67. for shift in range(n):
  68.     print(f"The number of workers needed for shift {shift} is {int(y[shift].value())} workers")

When I get to this line:

  1. prob += lpSum([w[j] * y[j] for j in range(n)])

I get this error.

  1. Traceback (most recent call last):
  3.   Cell In[197], line 1
  4.     prob += lpSum([w[j] * y[j] for j in range(n)])
  6.   Cell In[197], line 1 in <listcomp>
  7.     prob += lpSum([w[j] * y[j] for j in range(n)])
  9. IndexError: index 1 is out of bounds for axis 0 with size 1

The example I am trying to follow is from the link below.

https://towardsdatascience.com/how-to-solve-a-staff-scheduling-problem-with-python-63ae50435ba4

答案1

得分: 1

你的问题主要是因为对 Pandas 的误用。正确使用切片，它将正常工作：

  1. from io import StringIO
  2. import pandas as pd
  3. import pulp
  5. with StringIO(
  6.     '''Time Windows,Shift 1,Shift 2,Shift 3,Shift 4,Workers Required
  7.     6:00 - 9:00,      1,      0,      0,      1,            55.0
  8.    9:00 - 12:00,      1,      0,      0,      0,            46.0
  9.   12:00 - 15:00,      1,      1,      0,      0,            59.0
  10.   15:00 - 18:00,      0,      1,      0,      0,            23.0
  11.   18:00 - 21:00,      0,      1,      1,      0,            60.0
  12.   21:00 - 24:00,      0,      0,      1,      0,            38.0
  13.    24:00 - 3:00,      0,      0,      1,      1,            20.0
  14.     3:00 - 6:00,      0,      0,      0,      1,            30.0
  15.       Wage_Rate,    135,    140,    190,    188,             0.0''') as f:
  16.     df = pd.read_csv(f, skipinitialspace=True, index_col='Time Windows')
  18. is_shift = df.columns.str.startswith('Shift')
  19. is_wage = df.index == 'Wage_Rate'
  20. shifts = df.loc[~is_wage, is_shift]
  21. wage_rate = df.loc[is_wage, is_shift].squeeze()
  22. workers_req = df.loc[~is_wage, 'Workers Required']
  24. workers_per_shift = pulp.LpVariable.dicts(name='workers_per', indices=shifts.columns, lowBound=0, cat=pulp.LpInteger)
  25. prob = pulp.LpProblem(name='scheduling_workers', sense=pulp.LpMinimize)
  26. prob.objective = pulp.lpDot(wage_rate, workers_per_shift.values())
  28. for (time, shift), worker_req in zip(shifts.iterrows(), workers_req):
  29.     prob.addConstraint(name=f'workers_min_{time}', constraint=pulp.lpDot(shift, workers_per_shift.values()) >= worker_req)
  31. print(prob)
  32. prob.solve()
  34. for k, v in workers_per_shift.items():
  35.     print(f'{k} has {v.value():.0f} workers')
  1. scheduling_workers:
  2. MINIMIZE
  3. 135*workers_per_Shift_1 + 140*workers_per_Shift_2 + 190*workers_per_Shift_3 + 188*workers_per_Shift_4 + 0
  4. SUBJECT TO
  5. workers_min_6:00___9:00: workers_per_Shift_1 + workers_per_Shift_4 >= 55
  7. workers_min_9:00___12:00: workers_per_Shift_1 >= 46
  9. workers_min_12:00___15:00: workers_per_Shift_1 + workers_per_Shift_2 >= 59
  11. workers_min_15:00___18:00: workers_per_Shift_2 >= 23
  13. workers_min_18:00___21:00: workers_per_Shift_2 + workers_per_Shift_3 >= 60
  15. workers_min_21:00___24:00: workers_per_Shift_3 >= 38
  17. workers_min_24:00___3:00: workers_per_Shift_3 + workers_per_Shift_4 >= 20
  19. workers_min_3:00___6:00: workers_per_Shift_4 >= 30
  21. VARIABLES
  22. 0 <= workers_per_Shift_1 Integer
  23. 0 <= workers_per_Shift_2 Integer
  24. 0 <= workers_per_Shift_3 Integer
  25. 0 <= workers_per_Shift_4 Integer
  27. 欢迎使用 CBC MILP 求解器
  28. 版本：2.10.3
  29. 构建日期：2019年12月15日
  31. 命令行 - C:\Users\gtoom\src\stackexchange\.venv\lib\site-packages\pulp\solverdir\cbc\win\cbc.exe C:\Users\gtoom\AppData\Local\Temp759563a6c3439b8221b857b9f617af-pulp.mps timeMode elapsed branch printingOptions all solution C:\Users\gtoom\AppData\Local\Temp759563a6c3439b8221b857b9f617af-pulp.sol (默认策略 1)
  32. 第2行 NAME          MODEL
  33. 第3行 ROWS
  34. 第13行 COLUMNS
  35. 第38行 RHS
  36. 第47行 BOUNDS
  37. 第52行 ENDATA
  38. 问题 MODEL 共有 8 行，4 列，12 个元素
  39. Coin0008I 以 0 个错误读取模型
  40. 将 timeMode 选项从 CPU 更改为经过的时间
  41. 连续目标值为 22290 - 0.00 秒
  42. Cgl0004I 处理后的模型有 0 行，0 列（0 个整数（其中 0 个是二进制））和 0 个元素
  43. Cbc3007W 没有整数变量 - 无事可做
  44. 根节点处的切割将目标从 22290 更改为 -1.79769e+308
  45. 探测尝试了 0 次，并在添加切割回合后创建了 0 个切割，其中 0 个活跃（0.000 秒）
  46. Gomory 尝试了 0 次，并在添加切割回合后创建了 0 个切割，其中 0 个活跃（0.000 秒）
  47. 尝试了 0 次的背包问题，并创建了 0 个切割，其中 0 个在添加切割回合后是活跃的（0.000 秒）
  48. 尝试了 0 次的团问题，并创建了 0 个切割，其中 0 个在添加切割回合后是活跃的（0.000 秒）
  49. 尝试了 0 次的混合整数舍入问题，并创建了 0 个切割，其中 0 个在添加切割回合后是活跃的（0.000 秒）
  50. FlowCover 尝试了 0 次，并创建了 0 
  52. <details>
  53. <summary>英文:</summary>
  55. Your problems mostly come from misuse of Pandas. Use sane slicing, and it works fine:
  57. ```python
  58. from io import StringIO
  60. import pandas as pd
  61. import pulp
  63. with StringIO(
  64. &#39;&#39;&#39;Time Windows,Shift 1,Shift 2,Shift 3,Shift 4,Workers Required
  65.     6:00 - 9:00,      1,      0,      0,      1,            55.0
  66.    9:00 - 12:00,      1,      0,      0,      0,            46.0
  67.   12:00 - 15:00,      1,      1,      0,      0,            59.0
  68.   15:00 - 18:00,      0,      1,      0,      0,            23.0
  69.   18:00 - 21:00,      0,      1,      1,      0,            60.0
  70.   21:00 - 24:00,      0,      0,      1,      0,            38.0
  71.    24:00 - 3:00,      0,      0,      1,      1,            20.0
  72.     3:00 - 6:00,      0,      0,      0,      1,            30.0
  73.       Wage_Rate,    135,    140,    190,    188,             0.0&#39;&#39;&#39;) as f:
  74.     df = pd.read_csv(f, skipinitialspace=True, index_col=&#39;Time Windows&#39;)
  76. is_shift = df.columns.str.startswith(&#39;Shift&#39;)
  77. is_wage = df.index == &#39;Wage_Rate&#39;
  78. shifts = df.loc[~is_wage, is_shift]
  79. wage_rate = df.loc[is_wage, is_shift].squeeze()
  80. workers_req = df.loc[~is_wage, &#39;Workers Required&#39;]
  82. workers_per_shift = pulp.LpVariable.dicts(name=&#39;workers_per&#39;, indices=shifts.columns, lowBound=0, cat=pulp.LpInteger)
  83. prob = pulp.LpProblem(name=&#39;scheduling_workers&#39;, sense=pulp.LpMinimize)
  84. prob.objective = pulp.lpDot(wage_rate, workers_per_shift.values())
  86. for (time, shift), worker_req in zip(shifts.iterrows(), workers_req):
  87.     prob.addConstraint(name=f&#39;workers_min_{time}&#39;, constraint=pulp.lpDot(shift, workers_per_shift.values()) &gt;= worker_req)
  89. print(prob)
  90. prob.solve()
  92. for k, v in workers_per_shift.items():
  93.     print(f&#39;{k} has {v.value():.0f} workers&#39;)
  1. scheduling_workers:
  2. MINIMIZE
  3. 135*workers_per_Shift_1 + 140*workers_per_Shift_2 + 190*workers_per_Shift_3 + 188*workers_per_Shift_4 + 0
  4. SUBJECT TO
  5. workers_min_6:00___9:00: workers_per_Shift_1 + workers_per_Shift_4 &gt;= 55
  7. workers_min_9:00___12:00: workers_per_Shift_1 &gt;= 46
  9. workers_min_12:00___15:00: workers_per_Shift_1 + workers_per_Shift_2 &gt;= 59
  11. workers_min_15:00___18:00: workers_per_Shift_2 &gt;= 23
  13. workers_min_18:00___21:00: workers_per_Shift_2 + workers_per_Shift_3 &gt;= 60
  15. workers_min_21:00___24:00: workers_per_Shift_3 &gt;= 38
  17. workers_min_24:00___3:00: workers_per_Shift_3 + workers_per_Shift_4 &gt;= 20
  19. workers_min_3:00___6:00: workers_per_Shift_4 &gt;= 30
  21. VARIABLES
  22. 0 &lt;= workers_per_Shift_1 Integer
  23. 0 &lt;= workers_per_Shift_2 Integer
  24. 0 &lt;= workers_per_Shift_3 Integer
  25. 0 &lt;= workers_per_Shift_4 Integer
  27. Welcome to the CBC MILP Solver 
  28. Version: 2.10.3 
  29. Build Date: Dec 15 2019 
  31. command line - C:\Users\gtoom\src\stackexchange\.venv\lib\site-packages\pulp\solverdir\cbc\win\cbc.exe C:\Users\gtoom\AppData\Local\Temp759563a6c3439b8221b857b9f617af-pulp.mps timeMode elapsed branch printingOptions all solution C:\Users\gtoom\AppData\Local\Temp759563a6c3439b8221b857b9f617af-pulp.sol (default strategy 1)
  32. At line 2 NAME          MODEL
  33. At line 3 ROWS
  34. At line 13 COLUMNS
  35. At line 38 RHS
  36. At line 47 BOUNDS
  37. At line 52 ENDATA
  38. Problem MODEL has 8 rows, 4 columns and 12 elements
  39. Coin0008I MODEL read with 0 errors
  40. Option for timeMode changed from cpu to elapsed
  41. Continuous objective value is 22290 - 0.00 seconds
  42. Cgl0004I processed model has 0 rows, 0 columns (0 integer (0 of which binary)) and 0 elements
  43. Cbc3007W No integer variables - nothing to do
  44. Cuts at root node changed objective from 22290 to -1.79769e+308
  45. Probing was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  46. Gomory was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  47. Knapsack was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  48. Clique was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  49. MixedIntegerRounding2 was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  50. FlowCover was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  51. TwoMirCuts was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  52. ZeroHalf was tried 0 times and created 0 cuts of which 0 were active after adding rounds of cuts (0.000 seconds)
  54. Result - Optimal solution found
  56. Objective value:                22290.00000000
  57. Enumerated nodes:               0
  58. Total iterations:               0
  59. Time (CPU seconds):             0.00
  60. Time (Wallclock seconds):       0.00
  62. Option for printingOptions changed from normal to all
  63. Total time (CPU seconds):       0.01   (Wallclock seconds):       0.01
  65. Shift 1 has 46 workers
  66. Shift 2 has 23 workers
  67. Shift 3 has 38 workers
  68. Shift 4 has 30 workers

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  • 本文由 发表于 2023年4月4日 07:54:41
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  • linear-programming
  • optimization
  • python
  • python-3.x
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