top_medium_example_cvxpy.py

import numpy as np
import cvxpy as cx


# Begin with the variables that describe the problem
x_shippers = cx.Variable((4, 2), boolean=True, name='shippers')
x_transports = cx.Variable((4, 2), boolean=True, name='transports')

# Data that helps implement the model
containers = np.array([[200, 0], [300, 1], [400, 0], [500, 1]])
shippers_costs = np.array([100, 130])
shippers_spaces = np.array([2, 1])
transport_costs = np.array([50, 70])

# Mappings that works as helpers.
train_map = np.array([1, 0])
destine_shippers_map = np.array([[1, 0], [0, 1]])
dest_ships_arr = destine_shippers_map[containers[:, 1]]

constraints = []

constraint00 = cx.sum(x_shippers, axis=1) <= 1
constraint01 = cx.sum(x_shippers, axis=0) <= shippers_spaces
constraint02 = x_shippers <= dest_ships_arr # Chosen shippers must also attend the destination of the container

constraints.extend([constraint00, constraint01, constraint02])

constraint10 = cx.sum(x_transports, axis=1) == cx.sum(x_shippers, axis=1) # Only transport containers that are assigned to a ship
constraint11 = cx.sum(x_transports @ train_map.T) <= 2 # There's only 2 slots available for trains

constraints.extend([constraint10, constraint11])

# Cost is associated to shippers, transport and containers that will remain in the factory
cost = cx.sum(x_shippers @ shippers_costs.T) + cx.sum(x_transports @ transport_costs.T) + containers[:, 0].T @ (1 - cx.sum(x_shippers, axis=1))

# Run the whole model
objective = cx.Minimize(cost)
problem = cx.Problem(objective, constraints)
problem.solve()
print(x_shippers.value)
print(x_transports.value)