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assignment_min_flow.py
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#!/usr/bin/env python3
# Copyright 2010-2025 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]
"""Linear assignment example."""
# [START import]
from ortools.graph.python import min_cost_flow
# [END import]
def main():
"""Solving an Assignment Problem with MinCostFlow."""
# [START solver]
# Instantiate a SimpleMinCostFlow solver.
smcf = min_cost_flow.SimpleMinCostFlow()
# [END solver]
# [START data]
# Define the directed graph for the flow.
start_nodes = (
[0, 0, 0, 0] + [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4] + [5, 6, 7, 8]
)
end_nodes = (
[1, 2, 3, 4] + [5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8] + [9, 9, 9, 9]
)
capacities = (
[1, 1, 1, 1] + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + [1, 1, 1, 1]
)
costs = (
[0, 0, 0, 0]
+ [90, 76, 75, 70, 35, 85, 55, 65, 125, 95, 90, 105, 45, 110, 95, 115]
+ [0, 0, 0, 0]
)
source = 0
sink = 9
tasks = 4
supplies = [tasks, 0, 0, 0, 0, 0, 0, 0, 0, -tasks]
# [END data]
# [START constraints]
# Add each arc.
for start_node, end_node, capacity, cost in zip(
start_nodes, end_nodes, capacities, costs
):
smcf.add_arc_with_capacity_and_unit_cost(start_node, end_node, capacity, cost)
# Add node supplies.
for idx, supply in enumerate(supplies):
smcf.set_node_supply(idx, supply)
# [END constraints]
# [START solve]
# Find the minimum cost flow between node 0 and node 10.
status = smcf.solve()
# [END solve]
# [START print_solution]
if status == smcf.OPTIMAL:
print(f"Total cost = {smcf.optimal_cost()}")
for arc in range(smcf.num_arcs()):
# Can ignore arcs leading out of source or into sink.
if smcf.tail(arc) != source and smcf.head(arc) != sink:
# Arcs in the solution have a flow value of 1. Their start and end nodes
# give an assignment of worker to task.
if smcf.flow(arc) > 0:
print(
f"Worker {smcf.tail(arc)} assigned to task {smcf.head(arc)}. "
f"Cost = {smcf.unit_cost(arc)}"
)
else:
print("There was an issue with the min cost flow input.")
print(f"Status: {status}")
# [END print_solution]
if __name__ == "__main__":
main()
# [END program]