使用 Python pulp 优化背包 - 如何设置约束？

问：

我想开发库存履行优化模型。如果每个 SKU 的WH_Inv配送量低于 SS，我想从 Plt_Inv 到 WH_Inv配送，且总配送量应小于 10000KG。

我按如下方式编写代码并显示结果。但我收到的状态是“不可行”，结果与要求不符。我假设约束模型不正确。谁能帮忙看看哪里有不正确的代码。

import pandas as pd
!pip install pulp
import pulp

数据帧

df1 = pd.DataFrame({'SS':[10,20,100,5,500],'SKU':['A','B','C','D','E']})
df2 = pd.DataFrame({'WH_Inv':[30,15,200,7,300],'SKU':['A','B','C','D','E']})
df3 = pd.DataFrame({'Plt_Inv':[100,0,300,0,100],'SKU':['A','B','C','D','E']})
df4 = pd.DataFrame({'KG':[20,12,10,12,20],'SKU':['A','B','C','D','E']})

定义列表

SKU = df1['SKU'].tolist()
SS =df1['SS'].tolist()
WH =df2['WH_Inv'].tolist()
PLT = df3['Plt_Inv'].tolist()
KG = df4['KG'].tolist()

定义常量

safety = {row.SKU:row.SS for row in df1.itertuples()}
warehouse = {row.SKU:row.WH_Inv for row in df2.itertuples()}
plant = {row.SKU:row.Plt_Inv for row in df3.itertuples()}
kgs = {row.SKU:row.KG for row in df4.itertuples()}

优化模型

problem =pulp.LpProblem('Optimization',pulp.LpMaximize)

设置变量

x={}
 for s in SKU:

  x[s]=pulp.LpVariable(f'x_{s}',cat='Integer')

约束

for s in SKU:
    problem += x[s]>=0
    problem+= x[s]>= safety[s]
    problem+= x[s]<= plant[s]
    problem += pulp.lpDot(x[s],KG)<=10000

目的

problem += pulp.lpDot(x[s],KG)

解决

status = problem.solve()
print('status:',pulp.LpStatus[status])

for s in SKU:
  print(s,x[s].value())
  print('obj=', problem.objective.value())

结果：状态不可行，履行数量与要求不符

状态：不可行 一个 10.0 乙 0.0 C 100.0 深 0.0 东 500.0 obj= 37000.0