91 lines
2.9 KiB
Python
Executable File
91 lines
2.9 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2024 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# [START program]
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"""Linear assignment example."""
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# [START import]
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from ortools.graph.python import min_cost_flow
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# [END import]
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def main():
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"""Solving an Assignment Problem with MinCostFlow."""
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# [START solver]
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# Instantiate a SimpleMinCostFlow solver.
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smcf = min_cost_flow.SimpleMinCostFlow()
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# [END solver]
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# [START data]
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# Define the directed graph for the flow.
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start_nodes = (
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[0, 0, 0, 0] + [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4] + [5, 6, 7, 8]
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)
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end_nodes = (
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[1, 2, 3, 4] + [5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8, 5, 6, 7, 8] + [9, 9, 9, 9]
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)
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capacities = (
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[1, 1, 1, 1] + [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] + [1, 1, 1, 1]
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)
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costs = (
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[0, 0, 0, 0]
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+ [90, 76, 75, 70, 35, 85, 55, 65, 125, 95, 90, 105, 45, 110, 95, 115]
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+ [0, 0, 0, 0]
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)
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source = 0
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sink = 9
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tasks = 4
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supplies = [tasks, 0, 0, 0, 0, 0, 0, 0, 0, -tasks]
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# [END data]
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# [START constraints]
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# Add each arc.
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for start_node, end_node, capacity, cost in zip(
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start_nodes, end_nodes, capacities, costs
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):
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smcf.add_arc_with_capacity_and_unit_cost(start_node, end_node, capacity, cost)
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# Add node supplies.
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for idx, supply in enumerate(supplies):
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smcf.set_node_supply(idx, supply)
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# [END constraints]
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# [START solve]
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# Find the minimum cost flow between node 0 and node 10.
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status = smcf.solve()
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# [END solve]
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# [START print_solution]
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if status == smcf.OPTIMAL:
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print(f"Total cost = {smcf.optimal_cost()}")
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for arc in range(smcf.num_arcs()):
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# Can ignore arcs leading out of source or into sink.
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if smcf.tail(arc) != source and smcf.head(arc) != sink:
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# Arcs in the solution have a flow value of 1. Their start and end nodes
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# give an assignment of worker to task.
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if smcf.flow(arc) > 0:
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print(
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f"Worker {smcf.tail(arc)} assigned to task {smcf.head(arc)}. "
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f"Cost = {smcf.unit_cost(arc)}"
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)
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else:
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print("There was an issue with the min cost flow input.")
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print(f"Status: {status}")
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# [END print_solution]
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if __name__ == "__main__":
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main()
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# [END program]
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