opt

from cvxpy import *
import numpy as np

#current level 
level = np.array([[5,5,10,10,10],[5,5,10,20,10],[0,5,5,10,5],[0,0,0,5,0]])

# desired level 
desired_level = np.ones([4,5])*6

# inflow - outflow matrix (inflow positive, outflow negative)
b = level - desired_level
b = np.reshape(b,(1,20));
b = b*np.ones((20,1))
b = b.T

#cost matrix according to Euclidian distance
costs = np.zeros([20,20]);

for i in range(4):
    for j in range(5):
        for i_ in range(4):
            for j_ in range(5):
                costs[5*i+j, 5*i_ + j_] = np.sqrt((i-i_)*(i-i_)+(j-j_)*(j-j_))

                     
f = Variable(20,20)

objective = Minimize(sum(costs * f))
constraints = [f >= 0,  b + sum(f) == sum(f.T) ]

prob = Problem(objective, constraints)
result = prob.solve()

print result