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assignment_mb

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

First, you must install ortools package in this colab.

python

%pip install ortools

MIP example that solves an assignment problem.

python

import io

import pandas as pd

from ortools.linear_solver.python import model_builder



def main():
    # Data
    data_str = """
  worker  task  cost
      w1    t1    90
      w1    t2    80
      w1    t3    75
      w1    t4    70
      w2    t1    35
      w2    t2    85
      w2    t3    55
      w2    t4    65
      w3    t1   125
      w3    t2    95
      w3    t3    90
      w3    t4    95
      w4    t1    45
      w4    t2   110
      w4    t3    95
      w4    t4   115
      w5    t1    50
      w5    t2   110
      w5    t3    90
      w5    t4   100
  """

    data = pd.read_table(io.StringIO(data_str), sep=r"\s+")

    # Create the model.
    model = model_builder.Model()

    # Variables
    # x[i, j] is an array of 0-1 variables, which will be 1
    # if worker i is assigned to task j.
    x = model.new_bool_var_series(name="x", index=data.index)

    # Constraints
    # Each worker is assigned to at most 1 task.
    for unused_name, tasks in data.groupby("worker"):
        model.add(x[tasks.index].sum() <= 1)

    # Each task is assigned to exactly one worker.
    for unused_name, workers in data.groupby("task"):
        model.add(x[workers.index].sum() == 1)

    # Objective
    model.minimize(data.cost.dot(x))

    # Create the solver with the CP-SAT backend, and solve the model.
    solver = model_builder.Solver("sat")
    if not solver.solver_is_supported():
        return
    status = solver.solve(model)

    # Print solution.
    if (
        status == model_builder.SolveStatus.OPTIMAL
        or status == model_builder.SolveStatus.FEASIBLE
    ):
        print(f"Total cost = {solver.objective_value}\n")
        selected = data.loc[solver.values(x).loc[lambda x: x == 1].index]
        for unused_index, row in selected.iterrows():
            print(f"{row.task} assigned to {row.worker} with a cost of {row.cost}")
    else:
        print("No solution found.")


main()