How to put lpSum in lpSum for Objective Function ?

[Kudadas]

I'm trying to use PuLP to minimize total cost to find quantity to produce of each product and quantity to order more for material.

The code below are input for product ,material , margin and material usage of each product. and I have defined variable already.

but I don't know how to create objective function for Total_Excess cost. because normally we use lpsum but our constraint need sum in sum as equation in the picture. I tried to code as below but It showed error when I did.

List

product = ['S1', 'S2', 'S3', 'S4'] # i

material list

material = ['A', 'B', 'C', 'D', 'E', 'F', 'I', 'G', 'H', 'J', 'K', 'L', 'M'] # m

Dictionary

margin = {'S1': 25.68, 'S2': 25.68,
'S3': 25.68, 'S4': 25.68}
capacity = 300
inv_bf = 42753.63
product_cost = {'S1': 4.28, 'S2': 4.28,
'S3': 4.28, 'S4': 4.28}

usage = {'S1': {'A': 12.24,
'D': 12.24,
'E': 0.014,
'F': 0.095,
'G': 12.24,
'H': 0.589,
'J': 24.24,
'K': 0.005,
'L': 0.0105},
'S2': {'A': 12.24,
'D': 12.24,
'E': 0.014,
'F': 0.095,
'G': 12.24,
'H': 0.589,
'J': 24.24,
'K': 0.005,
'L': 0.0105},
'S3': {'H': 0.26,
'K': 0.014,
'B': 12.24,
'C': 12.24,
'I': 0.624,
'G': 12.18,
'J': 24.24,
'M': 0.005},
'S4': {'H': 0.26,
'K': 0.014,
'B': 12.24,
'C': 12.24,
'I': 0.624,
'G': 12.18,
'J': 24.24,
'M': 0.005}}

inv = {'A': 7645.8, 'B': 2470, 'C': 4526,
'D': 6678, 'J': 4180.92, 'G': 6879,
'E': 159.5, 'F': 717.4, 'I': 764.1,
'H': 1302.69, 'K': 248.79, 'L': 235,
'M': 179.4}

cost = {'A': 0.03, 'B': 0.03, 'C': 0.056,
'D': 0.151, 'J': 0.024, 'G': 0.88,
'E': 5.156, 'F': 13.04, 'I': 11.09,
'H': 6.833, 'K': 11.261, 'L': 10.118,
'M': 11.914}

Define variables

How many unit will produce ?

produce = LpVariable.dicts("produce", product, lowBound=0, cat='Integer')

How many quantity of material to order more ?

order = LpVariable.dicts("order", material, lowBound=0, cat='Continuous')

Define and initialize model

model = LpProblem("total_cost", LpMinimize)```

Objective Function

Total_ProCost = lpSum(product_cost[i]*produce[i] for i in product)
Total_MatCost = lpSum(order[m]*cost[m] for m in material)
Total_ExcessCost = lpSum((inv[m]+order[m] for m in material - lpSum(produce[i]*usage[i][m] for m in material for i in product))
* cost[m] for m in material)

objective = Total_ProCost + Total_MatCost + Total_ExcessCost

model.setObjective(objective)

Define Constraints

Material Quantity used

for m in material:
model += lpSum(produce[i]*usage[i][m]for m in material for i in product) <= lpSum(inv[m]+order[m] for m in material)

Capacity limited

for i in product:
model += lpSum(produce[i]) <= capacity

Profit

for i in product:
model += lpSum(produce[i]*margin[i]) >= Total_ProCost + Total_MatCost

Reduce inv cost

for i in product:
model += lpSum(inv[m]+order[m] - produce[i]*usage[i][m] for m in material for i in product) <= inv_bf

model.solve()

#Output

for v in model.variables():
print(v.name,'=',v.varValue)

produce = [v.varValue for v in model.variables()]

The optimised objective function value is printed to the console

print("Total cost = ", pulp.value(model.objective))

What am I missing here?
Thank you for your answers in advance.