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simple_min_cost_flow_program

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/graph/simple_min_cost_flow_program.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/ortools/graph/samples/simple_min_cost_flow_program.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

From Bradley, Hax and Maganti, 'Applied Mathematical Programming', figure 8.1.

python

import numpy as np

from ortools.graph.python import min_cost_flow



def main():
    """MinCostFlow simple interface example."""
    # Instantiate a SimpleMinCostFlow solver.
    smcf = min_cost_flow.SimpleMinCostFlow()

    # 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]

    # 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)

    # Find the min cost flow.
    status = smcf.solve()

    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} -> "
            f"{smcf.head(arc)}  {flow:3}  / {smcf.capacity(arc):3}       {cost}"
        )


main()