Pulp Python - How to define a constraint with different indexes of variables

Question

I am new to modeling LP with Pulp in Python and I need some help with defining a constraint with multiple variables with different indexes. Please see below.

1. The constraint is defined on A, B, C indexes.
2. Start_Inv and End_Inv variables are again defined on A, B, C indexes.
3. Production variable is defined on A, B, C, D indexes.

I want Production variable to be summed by A, B, C and enter the constraint.

Below is what I wrote and of course it doesn't work.

for A, B, C in Start_Inv_DF.index:

    model += Start_Inv[(A, B, C)] + Production[(A, B, C, D)] == End_Inv[(A, B, C)]

Is there an easy way to model this? Probably, I need a coefficient to do "SUM Production group by A, B, C", can you please advise how to create one?

Adding more details. 1/13/2022

I have tried lpSUM and it works for two indexes but not for three or more. Can you please see what I am doing wrong?

1. This 2 indexes case works.

import pandas as pd 
import pulp as plp

tuples1 = [('DE', 'Apple'),
          ('DE', 'Orange'),
          ('PA', 'Apple'),
          ('PA', 'Orange')]

index1 = pd.MultiIndex.from_tuples(tuples1, names=["Location", "Product"])
DF1 = pd.DataFrame({'Count A': [12., 70., 30., 20.], 'Count B': [12., 70., 30., 20.]}, index=index1)

Production1 = plp.LpVariable.dicts("Production1",
                              ((Location, Product) for Location, Product in DF1.index),
                              lowBound=0,
                              cat='Continuous')

Products = ['Apple', 'Orange']

for Location, Product in DF1.index:
    print(plp.lpSum(Production1[(Location, Product)] for Product in Products))

2. This 3 indexes case errors out.

import pandas as pd 
import pulp as plp

tuples1 = [('DE', 'Apple'),
          ('DE', 'Orange'),
          ('PA', 'Apple'),
          ('PA', 'Orange')]

index1 = pd.MultiIndex.from_tuples(tuples1, names=["Location", "Product"])
DF1 = pd.DataFrame({'Count A': [12., 70., 30., 20.], 'Count B': [12., 70., 30., 20.]}, index=index1)

tuples2 = [('DE', 'Apple', 'Truck'),
           ('DE', 'Orange', 'Rail'),
           ('DE', 'Apple', 'Rail'),
           ('DE', 'Orange', 'Truck'),
           ('PA', 'Apple', 'Truck'),
           ('PA', 'Orange', 'Rail')]

index2 = pd.MultiIndex.from_tuples(tuples2, names=["Location", "Product", "Mode"])
DF2 = pd.DataFrame({'Count A': [12., 70., 30., 20., 20., 40], 'Count B': [12., 70., 30., 20., 80., 30.]}, index=index2)

Production2 = plp.LpVariable.dicts("Production2",
                              ((Location, Product, Mode) for Location, Product, Mode in DF2.index),
                              lowBound=0,
                              cat='Continuous')

Modes = ['Truck', 'Rail']

for Location, Product in DF1.index:
    print(plp.lpSum(Production2[(Location, Product, Mode)] for Mode in Modes))

Answer 1

I assume when you say "it doesn't work" you're getting a KeyError which is expected in your 3-index model. Because you have 2 locations, 2 products, and 2 modes. Your 2-index tuple with product and location has all 4 indexes, but your 3-index tuple has 6, missing ('PA', 'Apple', 'Rail') and ('PA, 'Orange', 'Truck').

If this was a mistake, correct your 3-index tuple and your KeyError will be fixed. If not a mistake, then one way to fix this is to change your last line of code to the following, which checks if the key exists in Production2 and if it's not, replaces it with 0:

print(plp.lpSum(Production2.get((Location, Product, Mode), 0) for Mode in Modes))