146 lines
5.0 KiB
Python
146 lines
5.0 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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"""Example of a simple nurse scheduling problem."""
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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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# Data.
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# [START data]
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num_nurses = 4
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num_shifts = 3
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num_days = 3
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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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# [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 the schedule period.
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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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shifts_worked = []
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for d in all_days:
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for s in all_shifts:
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shifts_worked.append(shifts[(n, d, s)])
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model.add(min_shifts_per_nurse <= sum(shifts_worked))
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model.add(sum(shifts_worked) <= max_shifts_per_nurse)
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# [END assign_nurses_evenly]
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# Creates the solver and solve.
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# [START parameters]
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solver = cp_model.CpSolver()
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solver.parameters.linearization_level = 0
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# Enumerate all solutions.
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solver.parameters.enumerate_all_solutions = True
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# [END parameters]
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# [START solution_printer]
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class NursesPartialSolutionPrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self, shifts, num_nurses, num_days, num_shifts, limit):
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cp_model.CpSolverSolutionCallback.__init__(self)
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self._shifts = shifts
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self._num_nurses = num_nurses
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self._num_days = num_days
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self._num_shifts = num_shifts
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self._solution_count = 0
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self._solution_limit = limit
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def on_solution_callback(self):
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self._solution_count += 1
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print(f"Solution {self._solution_count}")
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for d in range(self._num_days):
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print(f"Day {d}")
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for n in range(self._num_nurses):
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is_working = False
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for s in range(self._num_shifts):
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if self.value(self._shifts[(n, d, s)]):
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is_working = True
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print(f" Nurse {n} works shift {s}")
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if not is_working:
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print(f" Nurse {n} does not work")
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if self._solution_count >= self._solution_limit:
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print(f"Stop search after {self._solution_limit} solutions")
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self.stop_search()
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def solutionCount(self):
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return self._solution_count
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# Display the first five solutions.
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solution_limit = 5
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solution_printer = NursesPartialSolutionPrinter(
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shifts, num_nurses, num_days, num_shifts, solution_limit
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)
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# [END solution_printer]
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# [START solve]
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solver.solve(model, solution_printer)
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# [END solve]
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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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print(f" - solutions found: {solution_printer.solutionCount()}")
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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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