141 lines
4.8 KiB
Python
141 lines
4.8 KiB
Python
#!/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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"""Nurse scheduling problem with shift requests."""
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# [START import]
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from ortools.sat.python import cp_model
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# [END import]
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def main() -> None:
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# This program tries to find an optimal assignment of nurses to shifts
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# (3 shifts per day, for 7 days), subject to some constraints (see below).
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# Each nurse can request to be assigned to specific shifts.
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# The optimal assignment maximizes the number of fulfilled shift requests.
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# [START data]
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num_nurses = 5
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num_shifts = 3
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num_days = 7
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all_nurses = range(num_nurses)
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all_shifts = range(num_shifts)
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all_days = range(num_days)
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shift_requests = [
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[[0, 0, 1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 1]],
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[[0, 0, 0], [0, 0, 0], [0, 1, 0], [0, 1, 0], [1, 0, 0], [0, 0, 0], [0, 0, 1]],
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[[0, 1, 0], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 1, 0], [0, 0, 0]],
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[[0, 0, 1], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0]],
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[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 0]],
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]
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# [END data]
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# Creates the model.
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# [START model]
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model = cp_model.CpModel()
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# [END model]
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# Creates shift variables.
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# shifts[(n, d, s)]: nurse 'n' works shift 's' on day 'd'.
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# [START variables]
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shifts = {}
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for n in all_nurses:
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for d in all_days:
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for s in all_shifts:
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shifts[(n, d, s)] = model.new_bool_var(f"shift_n{n}_d{d}_s{s}")
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# [END variables]
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# Each shift is assigned to exactly one nurse in .
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# [START exactly_one_nurse]
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for d in all_days:
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for s in all_shifts:
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model.add_exactly_one(shifts[(n, d, s)] for n in all_nurses)
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# [END exactly_one_nurse]
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# Each nurse works at most one shift per day.
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# [START at_most_one_shift]
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for n in all_nurses:
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for d in all_days:
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model.add_at_most_one(shifts[(n, d, s)] for s in all_shifts)
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# [END at_most_one_shift]
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# [START assign_nurses_evenly]
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# Try to distribute the shifts evenly, so that each nurse works
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# min_shifts_per_nurse shifts. If this is not possible, because the total
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# number of shifts is not divisible by the number of nurses, some nurses will
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# be assigned one more shift.
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min_shifts_per_nurse = (num_shifts * num_days) // num_nurses
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if num_shifts * num_days % num_nurses == 0:
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max_shifts_per_nurse = min_shifts_per_nurse
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else:
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max_shifts_per_nurse = min_shifts_per_nurse + 1
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for n in all_nurses:
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num_shifts_worked = 0
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for d in all_days:
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for s in all_shifts:
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num_shifts_worked += shifts[(n, d, s)]
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model.add(min_shifts_per_nurse <= num_shifts_worked)
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model.add(num_shifts_worked <= max_shifts_per_nurse)
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# [END assign_nurses_evenly]
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# [START objective]
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model.maximize(
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sum(
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shift_requests[n][d][s] * shifts[(n, d, s)]
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for n in all_nurses
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for d in all_days
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for s in all_shifts
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)
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)
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# [END objective]
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# Creates the solver and solve.
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# [START solve]
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solver = cp_model.CpSolver()
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status = solver.solve(model)
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# [END solve]
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# [START print_solution]
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if status == cp_model.OPTIMAL:
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print("Solution:")
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for d in all_days:
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print("Day", d)
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for n in all_nurses:
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for s in all_shifts:
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if solver.value(shifts[(n, d, s)]) == 1:
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if shift_requests[n][d][s] == 1:
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print("Nurse", n, "works shift", s, "(requested).")
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else:
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print("Nurse", n, "works shift", s, "(not requested).")
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print()
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print(
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f"Number of shift requests met = {solver.objective_value}",
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f"(out of {num_nurses * min_shifts_per_nurse})",
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)
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else:
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print("No optimal solution found !")
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# [END print_solution]
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# Statistics.
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# [START statistics]
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print("\nStatistics")
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print(f" - conflicts: {solver.num_conflicts}")
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print(f" - branches : {solver.num_branches}")
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print(f" - wall time: {solver.wall_time}s")
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# [END statistics]
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if __name__ == "__main__":
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main()
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# [END program]
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