How can I add this conditional constraint to my model in Python?

Question

I am creating an optimization model with 2 sets of binary decision variables. The first, site, is regarding which of 380 cities to place manufacturing sites in, and the second, ASSG is regarding which of 12 cities each manufacturing site will be assigned to service. There will be 3 manufacturing sites total.

I need to add a constraint that the sum of all cities serviced by a potential manufacturing site is the number of cities that need serviced, 12, but this limit needs to be 0 if a manufacturing site is not placed in that location.

This is difficult for me to explain so I've included a screenshot of the Excel model I am trying to scale-up using Python. The "Logical constraint" is what I am trying to code into Python:

I know this code is a bit of a mess, I'm not great with dictionaries and there's too much going on here for me to keep track of it, but this is what I have so far:

site = m.addVars(siteLoc, vtype=GRB.BINARY, name='site')  # siteLoc is a list of 380 potential mfg site locations
ASSG = m.addVars(siteASSG, vtype=GRB.BINARY, name='ASSG') # siteASSG is a gurobi tuplelist of the format: (potential mfg site location, one of 12 cities mfg site will service)
m.update()

m.addConstr(sum(val for key, val in ASSG.items() if key[0] == k for k in site.keys()) <= 12 * val for key, val in site.items())

Answer 1

If I understood the problem correctly, you can have $380$ binary variables $x_{i}$ that can be defined as follows:

$$x_{i}=\begin{cases} 1, & \text{If location}\,\,i \,\,\text{has been selected for a manufacturing site}\\ 0, & \text{Otherwise} \\ \end{cases}$$

and for the chosen sites:

$$y_{ij}=\begin{cases} 1, & \text{If site}\, \, i \, \, \text{serves city} \, j\\ 0, & \text{Otherwise} \\ \end{cases}$$

then you need to add the following constraints to your model:

\begin{cases}\sum\limits_i x_{i}=3 \ \ \forall i \in \{1,2,\dots,380\}\\\sum\limits_j y_{ij} \le 12 \ \ \forall i \in \{\text{chosen sites}\}\\\sum\limits_i y_{ij}=1 \ \ \forall i \in \{\text{chosen sites}\}\,\,\text{and} \ \ \forall j \in \{1,2,\cdots,12\}\end{cases}

first and second constraints can be combined to force the model to assign the $12$ cities to those $3$ cities (out of $380$ potentials) that have a manufacturing site placed in. The constraint would be as follow:

$$\sum_j y_{ij} \le 12 \times x_i \ \ \forall i$$

Now, to define the aforementioned constraint in Python (the code is based on Pyomo but I believe it is almost the same if you use solver interfaces as well):

import numpy as np
from pyomo.environ import *
model.sites = set(np.arange(1,381)) #Index for the potential locations
model.cities  = set(np.arange(1,13)) #Index for the 12 cities with demands
cons = pyomo.constraint((sum y[i,j] for j in model.cities) <= 12*x[i] for i in model.sites) 

Answer 2

My answer was longer than I could put it in a comment:

I don't know how you defined your variables site and ASSG, so here is what I think should be your constraint (I based it on @Oguz formulation):

from gurobipy import * # I assume this is how you imported

SITES = range(380)  # index i
CITIES = range(12)  # index j
m.addConstrs((quicksum(ASSG[i,j] for j in CITIES) <= 12 * site[i] for i in SITES), 'site-city-relation')

Note that I'm using addConstrs (plural)