MIP

pip install mip==1.4.2

from mip.model import *

"""*   c[i] is the return of each stock 
*   a[t][i] is the investment of each stock for year t
*   b[t] is the total investment limit each year

with i = 0, 1, 2, 3, 4;
> t = 0, 1, 2
"""

c = [90, 120, 100, 80, 130]
b = [45, 60, 50]
a = [[10, 15, 12, 9, 13],
     [20, 15, 25, 15, 10],
     [15, 20, 20, 15, 10]]
T, I = range(len(b)),range(len(c))

a[0][1]

"""Create an empty Mixed Integer Linear Programmning problem. The optimization sense is set to Maximize and the selected sovler is set to Cbc (Coin-or branch and cut)"""

m = Model(sense = MAXIMIZE,solver_name=CBC)

"""Create variables with *add_var()* 
Crate a vector of variables with n binary decision variables (n = 5) indicating whether a stock is selected or not.
"""

names = ['A','B','C','D','E']

x = [[m.add_var(name = names[i], var_type=BINARY) for i in I] for t in T]

sum(x[t][i] for i in I for t in T)

"""> Objective is to maximize the total return




> Use *xsum()* for summation expressions
"""

m.objective = maximize(xsum(c[i] * x[t][i] for i in I for t in T))

"""Add constraint in money available each year"""

for t in range(3):
  m += xsum(a[t][i] * x[t][i] for i in I) <= b[t]

"""> Optimize() method executes the optimization of a formulation. 


> optimize method returns the status (OptimizationStatus) of the search.


> OPTIMAL if the search was concluded and the optimal solution was found.
"""

status = m.optimize()

if status == OptimizationStatus.OPTIMAL:
  print('optimal solution cost {} found'.format(m.objective_value))

results = {}
for i in range(3):
  results[i+1] = [m.vars[j].x for j in range(5*i,5*i+5)]

results

import pandas as pd

result = pd.DataFrame(data = results, index = ['A','B','C','D','E'])

result

"""Visualize the result"""

import matplotlib.pyplot as plt

result.plot(kind='bar', subplots = True, title = ['Year 1', 'Year 2', 'Year 3'])
plt.tight_layout()