240 lines
6.6 KiB
C++
240 lines
6.6 KiB
C++
// Copyright 2010-2025 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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#include <stdlib.h>
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#include <cstdint>
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#include <map>
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#include <numeric>
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#include <string>
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#include <tuple>
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#include <vector>
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#include "absl/base/log_severity.h"
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#include "absl/log/globals.h"
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#include "absl/strings/str_format.h"
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#include "ortools/base/init_google.h"
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#include "ortools/base/logging.h"
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#include "ortools/sat/cp_model.h"
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#include "ortools/sat/cp_model.pb.h"
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#include "ortools/sat/cp_model_solver.h"
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// [END import]
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namespace operations_research {
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namespace sat {
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void ScheduleRequestsSat() {
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// [START data]
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const int num_nurses = 5;
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const int num_days = 7;
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const int num_shifts = 3;
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std::vector<int> all_nurses(num_nurses);
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std::iota(all_nurses.begin(), all_nurses.end(), 0);
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std::vector<int> all_days(num_days);
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std::iota(all_days.begin(), all_days.end(), 0);
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std::vector<int> all_shifts(num_shifts);
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std::iota(all_shifts.begin(), all_shifts.end(), 0);
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std::vector<std::vector<std::vector<int64_t>>> shift_requests = {
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{
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{0, 0, 1},
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{0, 0, 0},
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{0, 0, 0},
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{0, 0, 0},
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{0, 0, 1},
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{0, 1, 0},
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{0, 0, 1},
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},
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{
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{0, 0, 0},
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{0, 0, 0},
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{0, 1, 0},
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{0, 1, 0},
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{1, 0, 0},
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{0, 0, 0},
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{0, 0, 1},
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},
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{
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{0, 1, 0},
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{0, 1, 0},
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{0, 0, 0},
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{1, 0, 0},
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{0, 0, 0},
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{0, 1, 0},
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{0, 0, 0},
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},
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{
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{0, 0, 1},
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{0, 0, 0},
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{1, 0, 0},
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{0, 1, 0},
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{0, 0, 0},
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{1, 0, 0},
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{0, 0, 0},
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},
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{
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{0, 0, 0},
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{0, 0, 1},
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{0, 1, 0},
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{0, 0, 0},
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{1, 0, 0},
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{0, 1, 0},
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{0, 0, 0},
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},
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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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CpModelBuilder cp_model;
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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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std::map<std::tuple<int, int, int>, BoolVar> shifts;
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for (int n : all_nurses) {
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for (int d : all_days) {
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for (int s : all_shifts) {
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auto key = std::make_tuple(n, d, s);
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shifts[key] = cp_model.NewBoolVar().WithName(
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absl::StrFormat("shift_n%dd%ds%d", n, d, s));
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}
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}
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}
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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 (int d : all_days) {
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for (int s : all_shifts) {
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std::vector<BoolVar> nurses;
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for (int n : all_nurses) {
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auto key = std::make_tuple(n, d, s);
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nurses.push_back(shifts[key]);
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}
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cp_model.AddExactlyOne(nurses);
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}
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}
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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 (int n : all_nurses) {
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for (int d : all_days) {
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std::vector<BoolVar> work;
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for (int s : all_shifts) {
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auto key = std::make_tuple(n, d, s);
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work.push_back(shifts[key]);
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}
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cp_model.AddAtMostOne(work);
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}
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}
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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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int min_shifts_per_nurse = (num_shifts * num_days) / num_nurses;
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int max_shifts_per_nurse;
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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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}
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for (int n : all_nurses) {
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LinearExpr num_worked_shifts;
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for (int d : all_days) {
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for (int s : all_shifts) {
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auto key = std::make_tuple(n, d, s);
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num_worked_shifts += shifts[key];
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}
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}
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cp_model.AddLessOrEqual(min_shifts_per_nurse, num_worked_shifts);
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cp_model.AddLessOrEqual(num_worked_shifts, max_shifts_per_nurse);
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}
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// [END assign_nurses_evenly]
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// [START objective]
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LinearExpr objective_expr;
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for (int n : all_nurses) {
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for (int d : all_days) {
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for (int s : all_shifts) {
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if (shift_requests[n][d][s] == 1) {
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auto key = std::make_tuple(n, d, s);
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objective_expr += shifts[key] * shift_requests[n][d][s];
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}
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}
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}
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}
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cp_model.Maximize(objective_expr);
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// [END objective]
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// [START solve]
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const CpSolverResponse response = Solve(cp_model.Build());
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// [END solve]
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// [START print_solution]
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if (response.status() == CpSolverStatus::OPTIMAL) {
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LOG(INFO) << "Solution:";
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for (int d : all_days) {
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LOG(INFO) << "Day " << std::to_string(d);
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for (int n : all_nurses) {
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for (int s : all_shifts) {
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auto key = std::make_tuple(n, d, s);
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if (SolutionIntegerValue(response, shifts[key]) == 1) {
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if (shift_requests[n][d][s] == 1) {
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LOG(INFO) << " Nurse " << std::to_string(n) << " works shift "
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<< std::to_string(s) << " (requested).";
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} else {
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LOG(INFO) << " Nurse " << std::to_string(n) << " works shift "
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<< std::to_string(s) << " (not requested).";
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}
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}
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}
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}
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LOG(INFO) << "";
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}
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LOG(INFO) << "Number of shift requests met = " << response.objective_value()
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<< " (out of " << num_nurses * min_shifts_per_nurse << ")";
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} else {
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LOG(INFO) << "No optimal solution found !";
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}
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// [END print_solution]
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// Statistics.
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// [START statistics]
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LOG(INFO) << "Statistics";
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LOG(INFO) << CpSolverResponseStats(response);
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// [END statistics]
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}
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} // namespace sat
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} // namespace operations_research
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int main(int argc, char* argv[]) {
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InitGoogle(argv[0], &argc, &argv, true);
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absl::SetStderrThreshold(absl::LogSeverityAtLeast::kInfo);
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operations_research::sat::ScheduleRequestsSat();
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return EXIT_SUCCESS;
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}
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// [END program]
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