Python returning two identical matrices

February 1, 2022

I am trying to write a small program for Markov Decision Process (inventory problem) using Python. I cannot figure out why the program outputs two identical matrices (for profit and decision matrices). The programming itself has some problems too because the last two columns are all zeros, which should not happen. Any help on the program itself would also be super helpful!

import math
import numpy as np

def salvageCost(b):
    return 5 * b

def orderingCost(b):
    if b == 0:
        return 0
    else:
        return 4 + 2 * b

def holdingCost(b):
    return 1.5 * b

def revenue(b):
    return 8 * b

M = 10
N = 4
u = np.zeros((M+1,N))
T = np.array([4,3,2,1])
S = np.array(range(M+1))
A = np.array(range(M+1))
u[:,0] = S*5
d = np.zeros((11,4))

probs = np.array([0.05, 0.1, 0.15, 0.2, 0.2, 0.15, 0.1, 0.05, 0, 0, 0])
demands = np.array(range(11))
candidate = [0]*11
d = u

for i in T[1:N]:
    for j in S:
        for a in range(M-j+1):
            candidate[a] = -holdingCost(j) - orderingCost(a) \
            + np.array([probs[k]for k in range(j+a)]).dot(8*np.array([demands[k]for k in range(j+a)])) \
            + np.array([probs[p] for p in range(min(j+a+1,M+1),M+1)]).dot(np.array(range(min(j+a+1,M+1),M+1)))*80\
            + probs.dot(u[:,i-1])
        u[j,i] = max(candidate)
        d[j,i] = candidate.index(max(candidate))
    


print(d)
print(u)

This is the output

[[ 0.  0.  0.  0.]
 [ 5.  0.  0.  0.]
 [10.  0.  0.  0.]
 [15.  0.  0.  0.]
 [20.  0.  0.  0.]
 [25.  0.  0.  0.]
 [30.  0.  0.  0.]
 [35.  0.  0.  0.]
 [40.  0.  0.  0.]
 [45.  0.  0.  0.]
 [50.  0.  0.  0.]]
[[ 0.  0.  0.  0.]
 [ 5.  0.  0.  0.]
 [10.  0.  0.  0.]
 [15.  0.  0.  0.]
 [20.  0.  0.  0.]
 [25.  0.  0.  0.]
 [30.  0.  0.  0.]
 [35.  0.  0.  0.]
 [40.  0.  0.  0.]
 [45.  0.  0.  0.]
 [50.  0.  0.  0.]]