基于CPLEX与Pyomo的库存优化建模索引错误排查求助

我尝试用Pyomo结合CPLEX求解该模型，但运行代码时出现错误：Index '0' is not valid for indexed component 'inv'，代码如下：

import pyomo.environ as pyo
from pyomo.environ import *
from pyomo.opt import SolverFactory
import numpy as np

model=pyo.ConcreteModel() 
T=10
cap=1000
inflow=500
outflow=250
demand=300
cost=25
model.inv=pyo.Var(range(1,T+1),within=Integers, bounds=(0,np.inf))
inv=model.inv

model.c0=pyo.Constraint(expr=inv[0]==300)
model.c1=pyo.ConstraintList()
for t in range(0,(T)):
    model.c1.add(expr=inv[t]<=cap)
model.c2=pyo.ConstraintList()
for t in range(0,(T)):
    model.c2.add(expr=inv[t]+inflow-outflow<=inv[t+1])
model.c3=pyo.ConstraintList()
for t in range(0,(T)):
    model.c3.add(inv[t]>=demand)


model.obj=pyo.Objective(expr=sum(inv[t]*cost for t in range(1,(T+1))),sense=minimize)

opt=SolverFactory('cplex')
opt.solve(model)

model.pprint()

for t in range(1,T+1):
    print(pyo.value(inv[t]))
print(pyo.value(model.obj))

问题原因 #

代码中model.inv的索引范围是1到T，但约束c0、c1、c2、c3中都使用了inv[0]，而0不在变量的索引范围内，导致索引无效错误。

修正方案 #

将model.inv的索引范围扩展为0到T，包含初始库存的索引，同时调整相关约束和目标函数的索引逻辑：

import pyomo.environ as pyo
from pyomo.environ import *
from pyomo.opt import SolverFactory
import numpy as np

model = pyo.ConcreteModel() 
T = 10
cap = 1000
inflow = 500
outflow = 250
demand = 300
cost = 25

# 调整变量索引为0到T，包含初始库存点
model.inv = pyo.Var(range(0, T+1), within=Integers, bounds=(0, np.inf))
inv = model.inv

# 初始库存约束
model.c0 = pyo.Constraint(expr=inv[0] == 300)

# 库存容量约束：覆盖t=0到t=T
model.c1 = pyo.ConstraintList()
for t in range(0, T+1):
    model.c1.add(expr=inv[t] <= cap)

# 库存递推约束：t从0到T-1，关联inv[t]和inv[t+1]
model.c2 = pyo.ConstraintList()
for t in range(0, T):
    model.c2.add(expr=inv[t] + inflow - outflow <= inv[t+1])

# 满足需求约束：覆盖t=0到t=T
model.c3 = pyo.ConstraintList()
for t in range(0, T+1):
    model.c3.add(expr=inv[t] >= demand)

# 目标函数：计算t=1到T的库存持有成本
model.obj = pyo.Objective(expr=sum(inv[t] * cost for t in range(1, T+1)), sense=minimize)

opt = SolverFactory('cplex')
result = opt.solve(model)

# 输出结果
model.pprint()

print("各期库存值：")
for t in range(0, T+1):
    print(f"t={t}: {pyo.value(inv[t])}")
print(f"最小持有总成本：{pyo.value(model.obj)}")

说明 #

• 扩展变量索引后，inv[0]作为初始库存变量，符合模型的递推逻辑
• 修正了c1和c3的循环范围，确保所有时间点的库存都满足容量和需求约束
• 目标函数保持计算t=1到T的持有成本，与原模型一致

内容的提问来源于stack exchange，提问作者Salman M Sulphi