It has been a while since I have done this so I am a bit rusty, but equation is:
max t(C)*x
s.t. Ax <=b
And I have my A matrix of constraints which is (1448x1359) :
[[ 1. 1. 0. ..., 0. 0. 0.]
...,
[ 0. 0. 0. ..., 1. 1. 1.]]
Then I have my binding b (1448x1):
[ 1. 1. 7. ..., 2. 1. 2.]
And my objective function to be maximised which is a vector of ones (1359,1).
Now in other packages my maximised objective function is 841, however using linprog:
res = linprog(c=OBJ_N, A_ub=A, b_ub=b, options={"disp": True})
It optimised successfully to -0.0 so I wonder if I'm using the right command in python and have my constraints the right way around?
Edit: Ok that makes sense, it was trying to minimise. I have rewritten now (swapped c and b and transposed A to minimise).
# (max t(C)*x s.t. Ax <=b) = min t(b)*x s.t. ATy = c, y ≥ 0
# (i): minimise number of shops no bounds
ID = np.ones(len(w[0]))
print(ID)
print(ID.shape) #1359
At = A.transpose()
need_divest = (A.dot(ID)) - 1
print(need_divest)
print(need_divest.shape) #1448
res = linprog(c=need_divest, A_eq=At, b_eq=ID, options={"disp": True})
print(res)
However, I get "message: 'Optimzation failed. Unable to find a feasible starting point.'"
I guess you are probably minimizing instead of maximizing your objective function.
Try with this (inserting a - in front of your objective function coefficients) :
res = linprog(c=-OBJ_N, A_ub=A, b_ub=b, options={"disp": True})
Your result should then be -841.
This works simply because :
min(f(x))=-max(-f(x))