import pulp
import numpy as np
import pandas as pd

prob = pulp.LpProblem("max_latency_gain", pulp.LpMaximize)

V = 100 # nb_videos
E = 10 # nb_endpoints
R = 100 # nb_requests
C = 10 # nb_cache_servers
X = 100 # cache Serveur Capacity

# Problem Data
R = np.zeros([V,C])
Ld = np.zeros(E)
L = np.zeros([C,E])
S = np.zeros(V)

def var_array(pattern):
    """Creates a two-dimension array of variables created by function pattern(i, j).
    The array is transformed into an np.array.
    """
    array = [
        [
            pattern(i, j)
            for j in range(V)
        ] for i in range(C)
    ]
    return np.array(array)

# Optimization Variable
m = var_array(lambda i, j: pulp.LpVariable("m_%d_%d" % (i, j), 0, 3))

# Objective function
prob += sum([ sum([ sum([ R[j][e]*(Ld[e] - L[i][e]*m[i][j]) for j in range(V)]) for i in range(C)]) for e in range(E)])

# Constraints
for i in range(C):
	prob += sum([ S[j]*m[i][j] for j in range(V)]) <= X # Cache Serveur Capacity