Оптимизация транспорта (PuLP)

В задаче транспортной оптимизации PuLP:

from pulp import *
Warehouses = ["A","B"]

# Creates a dictionary for the number of units of supply for each supply node
supply = {"A": 1000,
        "B": 4000}

# Creates a list of all demand nodes
Bars = ["1", "2", "3", "4", "5"]

# Creates a dictionary for the number of units of demand for each demand node
demand = {"1": 500,
        "2": 900,
        "3": 1800,
        "4": 200,
        "5": 700}
# Creates a list of costs of each transportation path
costs = [   #Bars
        #1 2 3 4 5
         [2,4,5,2,1],#A  Warehouses
        [3,1,3,2,3] #B
         ]
# Creates the prob variable to contain the problem data
prob = LpProblem("Beer Distribution Problem",LpMinimize)
# Creates a list of tuples containing all the possible routes for transport
Routes = [(w,b) for w in Warehouses for b in Bars]
# A dictionary called route_vars is created to contain the referenced variables (the routes)
route_vars = LpVariable.dicts("Route",(Warehouses,Bars),0,None,LpInteger)

Во время работы следующий код:

# The objective function is added to prob first
prob += lpSum([route_vars[w][b]*costs[w][b] for (w,b) in Routes]), "Sum of Transporting Costs"

Я получаю следующую ошибку:

TypeError: индексы списка должны быть целыми числами, а не str