纸浆求解器：如何使用循环设置最小变量产量

Question

I have this Toy factory LP :

# Import the PuLP lib
from pulp import *

# Products list
products = ["car", "bicycle"]

#Profit per product in $
profit = {"car": 8, "bicycle": 12}

# Used resources per product in kgs 
plasticAmount = {"car": 2, "bicycle": 4}
woodAmount    = {"car": 1, "bicycle": 1}
steelAmount   = {"car": 3, "bicycle": 2}


# Setting Problem variables dictionary
x = LpVariable.dicts("products ", products , 0)

# The Objective function : Maximising profit in $
prob += lpSum([profit[i] * x[i] for i in products ]), "Maximise"

# Total Stock amount Constraints in kgs
prob += lpSum([plasticAmount[i] * x[i] for i in  products]) <= 142 ,"MaxPlastic"
prob += lpSum([woodAmount [i]   * x[i] for i in  products]) <= 117 ,"MaxWood"
prob += lpSum([steelAmount[i]   * x[i] for i in  products]) <= 124 ,"MaxSteel"

# This constraints is not working : Minimal production amount should be at least 10 on each products ( need at least 10 Cars and 10 bicycles)
prob += lpSum([x[i] for i in produits]) >= 10 ,"MinProdObjs"

1. How should I set a minimal production value of 10 for each product ?

2. How should I write this in a more elegant manner, in case I have 200 products ?

3. Is the Lp correct ?

The minimal production constraint :

prob += lpSum([x[i] for i in produits]) >= 10 ,"MinProdObjs"

simply means ( in fact, car is an "amount of cars" and bicycle is also 'an amount of bicycles'... Maybe the variables names are not so nice ...)

prob += car + bicycle >= 10

or

prob += x1 + x2 >= 10

But it doesn't work as expected ...

Answer 1

If x[p] is the number of units produced for a product p in P , then you can just add a constraint of the form:

x[p] >= 10  forall p in P

Translated in code:

for p in products:
   prob += x[p] >= 10, f"min production units for product {p}"

With your constraint

prob += lpSum([x[i] for i in produits]) >= 10 ,"MinProdObjs"

what you are saying is that you want a total of at least 10 as production value over all the items.

Note also that your variables are fractional at the moment and that you might want to use Integer ones.