215 lines
7.3 KiB
C++
215 lines
7.3 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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#include <array>
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#include <cstddef>
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#include <cstdlib>
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#include <iterator>
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#include <numeric> // std::iota
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#include <sstream>
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#include <vector>
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#include "absl/base/log_severity.h"
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#include "absl/flags/flag.h"
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#include "absl/log/flags.h"
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#include "absl/log/globals.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/constraint_solver/constraint_solver.h"
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namespace operations_research {
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void SolveNursesExample() {
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// Instantiate the solver.
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Solver solver("NursesExample");
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std::array<int, 4> nurses;
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std::iota(std::begin(nurses), std::end(nurses), 0);
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{
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std::ostringstream oss;
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for (auto i : nurses) oss << ' ' << i;
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LOG(INFO) << "Nurses:" << oss.str();
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}
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// Nurse assigned to shift 0 means not working that day.
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std::array<int, 4> shifts;
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std::iota(std::begin(shifts), std::end(shifts), 0);
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{
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std::ostringstream oss;
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for (auto i : shifts) oss << ' ' << i;
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LOG(INFO) << "Shifts:" << oss.str();
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}
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std::array<int, 7> days;
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std::iota(std::begin(days), std::end(days), 0);
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{
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std::ostringstream oss;
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for (auto i : days) oss << ' ' << i;
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LOG(INFO) << "Days:" << oss.str();
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}
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// Create shift variables.
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std::vector<std::vector<IntVar*>> shifts_matrix(nurses.size());
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std::vector<IntVar*> shifts_flat;
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for (const auto nurse : nurses) {
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for (const auto day : days) {
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std::ostringstream oss;
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oss << "shifts(nurse: " << nurse << ", day: " << day << ")";
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IntVar* var = solver.MakeIntVar(shifts.front(), shifts.back(), oss.str());
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shifts_matrix[nurse].push_back(var);
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shifts_flat.push_back(var);
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}
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}
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// Create nurse variables.
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std::vector<std::vector<IntVar*>> nurses_matrix(shifts.size());
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for (const auto shift : shifts) {
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for (const auto day : days) {
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std::ostringstream oss;
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oss << "nurses(shift: " << shift << ", day: " << day << ")";
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IntVar* var = solver.MakeIntVar(nurses.front(), nurses.back(), oss.str());
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nurses_matrix[shift].push_back(var);
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}
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}
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// Set relationships between shifts and nurses.
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for (const auto day : days) {
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std::vector<IntVar*> nurses_for_day(shifts.size());
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for (const auto shift : shifts) {
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nurses_for_day[shift] = nurses_matrix[shift][day];
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}
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for (const auto nurse : nurses) {
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IntVar* s = shifts_matrix[nurse][day];
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solver.AddConstraint(
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solver.MakeEquality(solver.MakeElement(nurses_for_day, s), nurse));
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}
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}
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// Make assignments different on each day i.e.
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for (const auto day : days) {
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// no shift can have two nurses
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std::vector<IntVar*> shifts_for_day(nurses.size());
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for (const auto nurse : nurses) {
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shifts_for_day[nurse] = shifts_matrix[nurse][day];
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}
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solver.AddConstraint(solver.MakeAllDifferent(shifts_for_day));
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// no nurses can have more than one shifts a day
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std::vector<IntVar*> nurses_for_day(shifts.size());
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for (const auto shift : shifts) {
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nurses_for_day[shift] = nurses_matrix[shift][day];
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}
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solver.AddConstraint(solver.MakeAllDifferent(nurses_for_day));
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}
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// Each nurse works 5 or 6 days in a week.
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for (const auto nurse : nurses) {
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std::vector<IntVar*> nurse_is_working;
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for (const auto day : days) {
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nurse_is_working.push_back(
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solver.MakeIsGreaterOrEqualCstVar(shifts_matrix[nurse][day], 1));
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}
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solver.AddConstraint(solver.MakeSumGreaterOrEqual(nurse_is_working, 5));
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solver.AddConstraint(solver.MakeSumLessOrEqual(nurse_is_working, 6));
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}
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// Create works_shift variables.
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// works_shift_matrix[n][s] is True if
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// nurse n works shift s at least once during the week.
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std::vector<std::vector<IntVar*>> works_shift_matrix(nurses.size());
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for (const auto nurse : nurses) {
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for (const auto shift : shifts) {
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std::ostringstream oss;
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oss << "work_shift(nurse: " << nurse << ", shift: " << shift << ")";
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works_shift_matrix[nurse].push_back(solver.MakeBoolVar(oss.str()));
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}
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}
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for (const auto nurse : nurses) {
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for (const auto shift : shifts) {
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std::vector<IntVar*> shift_s_for_nurse;
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for (const auto day : days) {
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shift_s_for_nurse.push_back(
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solver.MakeIsEqualCstVar(shifts_matrix[nurse][day], shift));
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}
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solver.AddConstraint(
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solver.MakeEquality(works_shift_matrix[nurse][shift],
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solver.MakeMax(shift_s_for_nurse)->Var()));
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}
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}
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// For each shift(other than 0), at most 2 nurses are assigned to that shift
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// during the week.
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for (std::size_t shift = 1; shift < shifts.size(); ++shift) {
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std::vector<IntVar*> nurses_for_shift;
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for (const auto nurse : nurses) {
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nurses_for_shift.push_back(works_shift_matrix[nurse][shift]);
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}
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solver.AddConstraint(solver.MakeSumLessOrEqual(nurses_for_shift, 2));
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}
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// If a nurse works shifts 2 or 3 on,
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// he must also work that shift the previous day or the following day.
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for (const auto shift : {2, 3}) {
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for (const auto day : days) {
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IntVar* v0 = solver.MakeIsEqualVar(nurses_matrix[shift][day],
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nurses_matrix[shift][(day + 1) % 7]);
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IntVar* v1 = solver.MakeIsEqualVar(nurses_matrix[shift][(day + 1) % 7],
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nurses_matrix[shift][(day + 2) % 7]);
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solver.AddConstraint(solver.MakeEquality(solver.MakeMax(v0, v1), 1));
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}
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}
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// ----- Search monitors and decision builder -----
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// Create the decision builder.
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DecisionBuilder* const main_phase = solver.MakePhase(
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shifts_flat, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);
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// Search log.
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SearchMonitor* const search_log = nullptr;
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SearchLimit* limit = nullptr;
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// Create the solution collector.
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SolutionCollector* const collector = solver.MakeAllSolutionCollector();
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collector->Add(shifts_flat);
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// Solve
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solver.Solve(main_phase, search_log, nullptr, limit, collector);
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LOG(INFO) << "Number of solutions: " << collector->solution_count();
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LOG(INFO) << "";
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// Display a few solutions picked at random.
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std::array<int, 4> a_few_solutions = {859, 2034, 5091, 7003};
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for (const auto solution : a_few_solutions) {
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LOG(INFO) << "Solution " << solution << ":";
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for (const auto day : days) {
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LOG(INFO) << "Day " << day << ":";
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for (const auto nurse : nurses) {
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LOG(INFO) << "Nurse " << nurse << " assigned to Task "
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<< collector->Value(solution,
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shifts_flat[nurse * days.size() + day]);
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}
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}
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}
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LOG(INFO) << "Advanced usage:";
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LOG(INFO) << "Time: " << solver.wall_time() << "ms";
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}
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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::SolveNursesExample();
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return EXIT_SUCCESS;
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}
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