128 lines
3.7 KiB
C++
128 lines
3.7 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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// [START import]
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#include <memory>
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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 "ortools/base/init_google.h"
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#include "ortools/base/logging.h"
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#include "ortools/linear_solver/linear_solver.h"
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// [END import]
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namespace operations_research {
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void AssignmentMip() {
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// Data
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// [START data_model]
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const std::vector<std::vector<double>> costs{
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{90, 80, 75, 70}, {35, 85, 55, 65}, {125, 95, 90, 95},
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{45, 110, 95, 115}, {50, 100, 90, 100},
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};
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const int num_workers = costs.size();
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const int num_tasks = costs[0].size();
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// [END data_model]
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// Solver
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// [START solver]
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// Create the mip solver with the SCIP backend.
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std::unique_ptr<MPSolver> solver(MPSolver::CreateSolver("SCIP"));
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if (!solver) {
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LOG(WARNING) << "SCIP solver unavailable.";
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return;
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}
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// [END solver]
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// Variables
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// [START variables]
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// x[i][j] is an array of 0-1 variables, which will be 1
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// if worker i is assigned to task j.
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std::vector<std::vector<const MPVariable*>> x(
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num_workers, std::vector<const MPVariable*>(num_tasks));
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for (int i = 0; i < num_workers; ++i) {
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for (int j = 0; j < num_tasks; ++j) {
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x[i][j] = solver->MakeIntVar(0, 1, "");
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}
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}
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// [END variables]
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// Constraints
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// [START constraints]
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// Each worker is assigned to at most one task.
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for (int i = 0; i < num_workers; ++i) {
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LinearExpr worker_sum;
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for (int j = 0; j < num_tasks; ++j) {
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worker_sum += x[i][j];
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}
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solver->MakeRowConstraint(worker_sum <= 1.0);
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}
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// Each task is assigned to exactly one worker.
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for (int j = 0; j < num_tasks; ++j) {
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LinearExpr task_sum;
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for (int i = 0; i < num_workers; ++i) {
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task_sum += x[i][j];
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}
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solver->MakeRowConstraint(task_sum == 1.0);
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}
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// [END constraints]
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// Objective.
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// [START objective]
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MPObjective* const objective = solver->MutableObjective();
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for (int i = 0; i < num_workers; ++i) {
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for (int j = 0; j < num_tasks; ++j) {
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objective->SetCoefficient(x[i][j], costs[i][j]);
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}
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}
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objective->SetMinimization();
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// [END objective]
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// Solve
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// [START solve]
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const MPSolver::ResultStatus result_status = solver->Solve();
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// [END solve]
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// Print solution.
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// [START print_solution]
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// Check that the problem has a feasible solution.
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if (result_status != MPSolver::OPTIMAL &&
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result_status != MPSolver::FEASIBLE) {
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LOG(FATAL) << "No solution found.";
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}
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LOG(INFO) << "Total cost = " << objective->Value() << "\n\n";
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for (int i = 0; i < num_workers; ++i) {
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for (int j = 0; j < num_tasks; ++j) {
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// Test if x[i][j] is 0 or 1 (with tolerance for floating point
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// arithmetic).
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if (x[i][j]->solution_value() > 0.5) {
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LOG(INFO) << "Worker " << i << " assigned to task " << j
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<< ". Cost = " << costs[i][j];
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}
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}
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}
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// [END print_solution]
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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::AssignmentMip();
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return EXIT_SUCCESS;
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}
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// [END program]
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