examples/notebook/graph/balance_min_flow.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Assignment with teams of workers.
from ortools.graph.python import min_cost_flow
def main():
"""Solving an Assignment with teams of worker."""
smcf = min_cost_flow.SimpleMinCostFlow()
# Define the directed graph for the flow.
team_a = [1, 3, 5]
team_b = [2, 4, 6]
start_nodes = (
# fmt: off
[0, 0]
+ [11, 11, 11]
+ [12, 12, 12]
+ [1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6]
+ [7, 8, 9, 10]
# fmt: on
)
end_nodes = (
# fmt: off
[11, 12]
+ team_a
+ team_b
+ [7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10]
+ [13, 13, 13, 13]
# fmt: on
)
capacities = (
# fmt: off
[2, 2]
+ [1, 1, 1]
+ [1, 1, 1]
+ [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
+ [1, 1, 1, 1]
# fmt: on
)
costs = (
# fmt: off
[0, 0]
+ [0, 0, 0]
+ [0, 0, 0]
+ [90, 76, 75, 70, 35, 85, 55, 65, 125, 95, 90, 105, 45, 110, 95, 115, 60, 105, 80, 75, 45, 65, 110, 95]
+ [0, 0, 0, 0]
# fmt: on
)
source = 0
sink = 13
tasks = 4
# Define an array of supplies at each node.
supplies = [tasks, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -tasks]
# Add each arc.
for i in range(0, len(start_nodes)):
smcf.add_arc_with_capacity_and_unit_cost(
start_nodes[i], end_nodes[i], capacities[i], costs[i]
)
# Add node supplies.
for i in range(0, len(supplies)):
smcf.set_node_supply(i, supplies[i])
# Find the minimum cost flow between node 0 and node 10.
status = smcf.solve()
if status == smcf.OPTIMAL:
print("Total cost = ", smcf.optimal_cost())
print()
for arc in range(smcf.num_arcs()):
# Can ignore arcs leading out of source or intermediate, or into sink.
if (
smcf.tail(arc) != source
and smcf.tail(arc) != 11
and smcf.tail(arc) != 12
and smcf.head(arc) != sink
):
# Arcs in the solution will have a flow value of 1.
# There start and end nodes give an assignment of worker to task.
if smcf.flow(arc) > 0:
print(
"Worker %d assigned to task %d. Cost = %d"
% (smcf.tail(arc), smcf.head(arc), smcf.unit_cost(arc))
)
else:
print("There was an issue with the min cost flow input.")
print(f"Status: {status}")
main()