I am running into an error when trying to run my code for this Assignment Cost minimization problem in Python and was hoping someone could illuminate me on what I have done incorrectly here:

The Question:

My code:

import numpy as np
import time

n = 10   # n: number of jobs/workers
cost = np.random.rand(n,n)   # generate an n-by-n random matrix

from scipy.optimize import linprog
c = cost.reshape((n**2,1))   # reshape the cost matrix to a column vector

#row constraints (sum of each row equals 1)
A_eq_rows = np.ones((n, n**2))
b_eq_rows = np.ones(n)

#column constraints (sum of each column equals 1)
A_eq_cols = np.zeros((n, n**2))
for i in range(n):
    A_eq_cols[i, i::n] = 1
b_eq_cols = np.ones(n)

#solve for A_eq and 
A_eq=np.vstack((A_eq_rows, A_eq_cols))
b_eq=np.hstack((b_eq_rows, b_eq_cols))

start_time = time.time()   # start timing

res = linprog(c, None, None, A_eq, b_eq)

end_time = time.time()   # end timing
elapsed_LP = end_time - start_time

print("Minimum cost = ", res.fun)
print("Elapsed time = ", elapsed_LP)

I keep getting my Minimum Cost as None and am not entirely sure what I’ve done wrong with this. I have a decent fundamental understanding of how to resolve this problem but have limited experience in doing this through Python.

I know that it has n^2 variables and 2n-1 linearly independent constraints. Therefore, a BFS of the assignment problem has 2n-1 basic variables, and for each assignments, exactly n of the n2 variables are nonzero so every BFS is degenerate. Any help in this would be greatly appreciated.

NOTE: I am aware I can solve this through the function scipy.optimize.linear sum assignment() and have done this but wanted to compare my answer by running this problem as a linear program.