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simple_min_cost_flow_program.py
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simple_min_cost_flow_program.py
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#!/usr/bin/env python3
# Copyright 2010-2024 Google LLC
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# [START program]
"""From Bradley, Hax and Maganti, 'Applied Mathematical Programming', figure 8.1."""
# [START import]
import numpy as np
from ortools.graph.python import min_cost_flow
# [END import]
def main():
"""MinCostFlow simple interface example."""
# [START solver]
# Instantiate a SimpleMinCostFlow solver.
smcf = min_cost_flow.SimpleMinCostFlow()
# [END solver]
# [START data]
# Define four parallel arrays: sources, destinations, capacities,
# and unit costs between each pair. For instance, the arc from node 0
# to node 1 has a capacity of 15.
start_nodes = np.array([0, 0, 1, 1, 1, 2, 2, 3, 4])
end_nodes = np.array([1, 2, 2, 3, 4, 3, 4, 4, 2])
capacities = np.array([15, 8, 20, 4, 10, 15, 4, 20, 5])
unit_costs = np.array([4, 4, 2, 2, 6, 1, 3, 2, 3])
# Define an array of supplies at each node.
supplies = [20, 0, 0, -5, -15]
# [END data]
# [START constraints]
# Add arcs, capacities and costs in bulk using numpy.
all_arcs = smcf.add_arcs_with_capacity_and_unit_cost(
start_nodes, end_nodes, capacities, unit_costs
)
# Add supply for each nodes.
smcf.set_nodes_supplies(np.arange(0, len(supplies)), supplies)
# [END constraints]
# [START solve]
# Find the min cost flow.
status = smcf.solve()
# [END solve]
# [START print_solution]
if status != smcf.OPTIMAL:
print("There was an issue with the min cost flow input.")
print(f"Status: {status}")
exit(1)
print(f"Minimum cost: {smcf.optimal_cost()}")
print("")
print(" Arc Flow / Capacity Cost")
solution_flows = smcf.flows(all_arcs)
costs = solution_flows * unit_costs
for arc, flow, cost in zip(all_arcs, solution_flows, costs):
print(
f"{smcf.tail(arc):1} -> {smcf.head(arc)} {flow:3} / {smcf.capacity(arc):3} {cost}"
)
# [END print_solution]
if __name__ == "__main__":
main()
# [END program]