Issue with Adding Constraints for Binary Variables
AnsweredHi all!
I am working on a model in Python that uses binary variables with indices i, j, and k. "i" represents rushees, "j" represents active members, and "k" represents events. Rushees "i" are preassigned to events "k", so I have already added a constraint that states that the binary variables for rushees "i" equal zero for all events "k" that they are not assigned to.
I am having issues adding two of my constraints:
- Each rushee "i" must be assigned to an active member "j" for their assigned event "k"
- Each active member "j" can be assigned to a maximum of 1 rushee "i" for each event "k"
I have copied my code down below.
Note: the list "K" is a list of the number of events
# Create variables Xijk
var_dict = {}
for x in i:
for y in j:
for z in K:
var_dict[x,y,z] = mod.addVar(vtype="B",obj=scores_dict[x,y],name=f"X[{x},{y},{z}]")
mod.update()
# Rushees (i) must be in their assigned event (k)
for x in i:
for y in j:
for z in K:
if pnm_party_list[x] != z:
mod.addConstr(var_dict[x,y,z] == 0)
# Active members (j) can't be paired with more than one rushee (i) in each event (k)
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for y in j) <= 1 for z in K for y in j)
# Rushees (i) must be paired with exactly one active member (j) for their assigned event (k)
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for x in i) == 1 for z in K for y in j)
Any help would be appreciated!
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Official comment
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Gurobi Staff
This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try Gurobot? -
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Hi Katherine,
You could write your model to an LP file
mod.write("myModel.lp")and analyze the constraints by hand to check whether they look as expected.
I think that the constraints
# Active members (j) can't be paired with more than one rushee (i) in each event (k)
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for y in j) <= 1 for z in K for y in j)should read
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for x in i) <= 1 for z in K for y in j)
So for a fixed event and active member the sum over all rushees cannot exceed 1. With the description you provided, I am not sure about the event condition. Maybe you have to move the \(\texttt{for z in K}\) loop into the \(\texttt{quicksum}\).
I think that the constraints
# Rushees (i) must be paired with exactly one active member (j) for their assigned event (k)
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for x in i) == 1 for z in K for y in j)should read
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for y in j) == 1 for z in K for x in i)
So for a fixed event and a fixed rushee, the number of active member is exactly 1. Again, with the description you provided, I am not sure about the event condition. Maybe you have to move the \(\texttt{for z in K}\) loop into the \(\texttt{quicksum}\).
Best regards,
Jaromił0 -
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Hi,
I have tried both of your suggestions, but both return that the model in infeasible. I have included my model down below for clarification.
import pandas as pd
num_parties = 23
# Import PNM data, then parse the data into lists
rusheedata = pd.read_excel(r"FinalFinalData.xlsx", sheet_name = "Rushee Data",dtype=int)
i = rusheedata["i"].tolist()
k = rusheedata["k"].tolist()
K = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
memberdata = pd.read_excel(r"FinalFinalData.xlsx", sheet_name = "Member Data",dtype=int)
j = memberdata["j"].tolist()
# Creating dictionary of rushees i and what party k they are in
rushee_party_list = dict(zip(rusheedata.i, rusheedata.k))
## START MODEL
import gurobipy as gb
from gurobipy import *
# Create model
mod = Model("Model 1")
# Create variables Xijk
var_dict = {}
for x in i:
for y in j:
for z in K:
var_dict[x,y,z] = mod.addVar(vtype="B",name=f"X[{x},{y},{z}]")
mod.update()
# Constraints
# Rushees must be in their assigned parties (k)
for x in i:
for y in j:
for z in K:
if rushee_party_list[x] != z:
mod.addConstr(var_dict[x,y,z] == 0)
# Active members can't be paired with more than one rushee each party
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for x in i for z in K) <= 1 for y in j)
# Rushees must be paired with exactly one active member
mod.addConstrs(gb.quicksum(var_dict[x,y,z] for y in j for z in K) == 1 for x in i)0 -
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Please note that your code snippet does not help because I don't have access to the file \( \texttt{FinalFinalData.xlsx} \).
In order to resolve the infeasibility, please refer to How do I determine why my model is infeasible?
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I have included a screenshot example of my data below to clarify.
i = 1, 2, 3, ..., 1610
j = 1, 2, 3, ..., 100
k is in range(1 - 23), randomly assigned to each i value
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A screenshot is not helpful as it is not possible to copy+paste the data into your code snippet. If you want to provide the data, please either rewrite as a Python data structure which you can add to your code snippet or upload the data file as described in Posting to the Community Forum.
Note that it would be best if you first try to determine the source of infeasibility yourself as described in How do I determine why my model is infeasible?
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I have figured out my issue, I needed to include "rushee_party_list[x] == z" in my constraint that limits rushees to exactly 1 event.
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